---
author:
- 'S. Adrián-Martínez'
- 'A. Albert'
- 'M. André'
- 'G. Anton'
- 'M. Ardid'
- 'J.-J. Aubert'
- 'B. Baret'
- 'J. Barrios-Martí'
- 'S. Basa'
- 'V. Bertin'
- 'S. Biagi'
- 'C. Bogazzi'
- 'R. Bormuth'
- 'M. Bou-Cabo'
- 'M.C. Bouwhuis'
- 'R. Bruijn'
- 'J. Brunner'
- 'J. Busto'
- 'A. Capone'
- 'L. Caramete'
- 'J. Carr'
- 'T. Chiarusi'
- 'M. Circella'
- 'R. Coniglione'
- 'H. Costantini'
- 'P. Coyle'
- 'A. Creusot'
- 'I. Dekeyser'
- 'A. Deschamps'
- 'G. De Bonis'
- 'C. Distefano'
- 'C. Donzaud'
- 'D. Dornic'
- 'D. Drouhin'
- 'A. Dumas'
- 'T. Eberl'
- 'D. Elsässer'
- 'A. Enzenhöfer'
- 'K. Fehn'
- 'I. Felis'
- 'P. Fermani'
- 'F. Folger'
- 'L.A. Fusco'
- 'S. Galatà'
- 'P. Gay'
- 'S. Gei[ß]{}elsöder'
- 'K. Geyer'
- 'V. Giordano'
- 'A. Gleixner'
- 'R. Gracia-Ruiz'
- 'K. Graf'
- 'H. van Haren'
- 'A.J. Heijboer'
- 'Y. Hello'
- 'J.J.  Hernández-Rey'
- 'A. Herrero'
- 'J. Hö[ß]{}l'
- 'J. Hofestädt'
- 'C. Hugon'
- 'C.W James'
- 'M. de Jong'
- 'M. Kadler'
- 'O. Kalekin'
- 'U. Katz'
- 'D. Kie[ß]{}ling'
- 'P. Kooijman'
- 'A. Kouchner'
- 'I. Kreykenbohm'
- 'V. Kulikovskiy'
- 'R. Lahmann'
- 'G. Lambard'
- 'D. Lattuada'
- 'D.  Lefèvre'
- 'E. Leonora'
- 'S. Loucatos'
- 'M. Marcelin'
- 'A. Margiotta'
- 'J.A. Martínez-Mora'
- 'S. Martini'
- 'A. Mathieu'
- 'T. Michael'
- 'P. Migliozzi'
- 'A. Moussa'
- 'C. Mueller'
- 'M. Neff'
- 'E. Nezri'
- 'G.E. Păvălaş'
- 'C. Pellegrino'
- 'C. Perrina'
- 'P. Piattelli'
- 'V. Popa'
- 'T. Pradier'
- 'C. Racca'
- 'G. Riccobene'
- 'R. Richter'
- 'K. Roensch'
- 'A. Rostovtsev'
- 'M. Saldaña'
- 'D. F. E. Samtleben'
- 'M. Sanguineti'
- 'P. Sapienza'
- 'J. Schmid'
- 'J. Schnabel'
- 'S. Schulte'
- 'F. Schüssler'
- 'T. Seitz'
- 'C. Sieger'
- 'M. Spurio'
- 'J.J.M. Steijger'
- 'Th. Stolarczyk'
- 'A. S[á]{}nchez-Losa'
- 'M. Taiuti'
- 'C. Tamburini'
- 'A. Trovato'
- 'M. Tselengidou'
- 'C. Tönnis'
- 'B. Vallage'
- 'C. Vallée'
- 'V. Van Elewyck'
- 'E. Visser'
- 'D. Vivolo'
- 'S. Wagner'
- 'J. Wilms'
- 'J.D. Zornoza'
- 'J. Zúñiga'
title: Search of Dark Matter Annihilation in the Galactic Centre using the ANTARES Neutrino Telescope
---

Introduction
============

Observations in cosmology and astrophysics indicate that about $84$% of the matter in the Universe, the so-called dark matter, is non-baryonic, non-relativistic, and does interact only through gravity. [@darkmatter; @dmschumann; @dmsalati; @pdg2012].

These observations involve the internal dynamics of galaxy clusters [@galclust], the rotation curves of galaxies [@galrot], weak lensing [@bulclust], also the Cosmic Microwave Background (CMB) from which the relic density of cold dark matter (CDM) in the Universe is at present deduced to be $\rm \Omega_{CDM}h^{2} = 0.1199 \pm 0.0022$ (Planck+WMAP) [@planck2015; @wmap7yr].

A common assumption is that dark matter is made of Weakly Interacting Massive Particles (WIMPs) that form halos in which the visible baryonic part of galaxies is embedded. There are a variety of candidates for WIMPs, among which those provided by theories based on supersymmetry (SUSY) attract a great deal of interest. In some classes of minimal supersymmetric (MSSM) and minimal universal extra-dimensional (mUED) extensions of the Standard Model (SM), the lightest particle (LP) is stable thanks to the conservation of a model-dependent parity that forbids its decay into SM particles. Consequently, these LPs can only annihilate in pairs, making them a possible WIMP candidate for dark matter [@lsp; @lkp]. In these models, secondary high-energy neutrinos are produced from the decay of the LPs’ self-annihilation products. In mUED models, neutrinos can even be produced directly in the self-annihilations, since there is no helicity suppression of fermion pair production.

The search for WIMPs can be performed either directly by recording the recoil energy of nuclei when WIMPs scatter off them in suitable detectors, or indirectly. The indirect approach, which is adopted here, exploits a radiation signature (gamma-ray, synchroton, positron, anti-proton or, as in this case, neutrino flux) produced by the self-annihilation of WIMPs accumulated in massive astrophysical objects such as the Galactic Centre (GC), the Sun or the Earth [@indirectdm].

For the case of the GC, dealt with in this paper, where the density of dark matter in the galactic halo is supposed to be the highest, WIMPs self-annihilate to SM particles whose decay or hadronisation (if not directly to neutrinos) give rise to the production of high energy neutrinos which can travel from the GC to the Earth and be detected by neutrino telescopes.

In this paper, the indirect search for dark matter by looking for high-energy neutrinos coming from the GC, using the 2007-2012 data recorded by the ANTARES neutrino telescope, is described. The layout of the paper is as follows. In Section \[antares\], the main features of the ANTARES neutrino telescope and the reconstruction algorithms used in this work are explained. In Section \[simulation\], the expected signal from WIMP self-annihilation from the GC, and the background expected from atmospheric muons and neutrinos are reported. In Section \[optimisation\], the method used to optimise the selection of the neutrino events is described. Finally, the results obtained are discussed in Section \[results\], where limits on the neutrino plus anti-neutrino flux $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$ are derived from the absence of a signal. The corresponding 90% C.L. upper limits on the velocity-averaged annihilation cross-section $\rm <\sigma_{A}v>$ are obtained for different benchmark channels of self-annihilation, and compared to the latest constraints from other experiments. In the following, neutrino will mean neutrino plus anti-neutrino, unless explicitly stated otherwise.

The ANTARES Neutrino Telescope {#antares}
==============================

ANTARES is the first undersea neutrino telescope and the largest of its kind in the Northern Hemisphere [@antares]. It is located at 2475 m below the Mediterranean Sea level, $40$ km offshore from Toulon (France) at $42^{\circ} 48$’ N and $6^{\circ} 10$’ E. The telescope consists of $12$ detection lines with 25 storeys each. A standard storey includes three optical modules (OMs) [@OM], each housing a 10-inch photomultiplier [@PMT] and a local control module that contains the electronics [@frontend; @DAQ]. The OMs are orientated 45$^{\circ}$ downwards in order to optimise their acceptance to upgoing light and to avoid the effect of sedimentation and biofouling [@biofouling]. The length of a line is 450 m and the horizontal distance between neighbouring lines is 60-75 m. In one of the lines, the upper storeys are dedicated to a test system for acoustic neutrino detection [@amadeus]. Similar acoustic devices are also installed in an additional line that contains instrumentation aimed to measure environmental parameters [@instrumentation]. The location of the active components of the lines is known to better than 10 cm by a combination of tiltmeters and compasses in each storey and a series of acoustic transceivers (emitters and receivers) in certain storeys along the line and surrounding the telescope [@alignment]. A common time reference is maintained in the full detector by means of a 25 MHz clock signal broadcast from shore. The time offsets of the individual optical modules are determined in dedicated calibration facilities onshore and regularly monitored in situ by means of optical beacons distributed at various points of the apparatus which emit short light pulses through the water [@OBs]. This allows a sub-nanosecond accuracy on the relative timing [@timing]. Additional information on the detector can be found in Ref. [@antares].

Data-taking started with the first 5 lines of the detector installed in 2007. The full detector was completed in May 2008 and has been operating continuously ever since, except for some short periods in which repair and maintenance operations have taken place. Other physics results using this data-taking period can be found elsewhere [@diffuse; @monopole; @nuosc; @ps; @grb; @atmnu; @dmsun; @fermibub; @pe].

High-energy muon neutrinos interacting in the matter before the detector produce relativistic muons that can travel hundreds of metres and cross the detector or pass nearby. These muons induce Cherenkov light when travelling through the water, which is detected by the OMs. From the time and position information of the photons provided by the OMs, the direction of the muons, which is well correlated with that of the neutrinos, is reconstructed.

![Effective area to muon neutrinos (black) and anti-neutrinos (red), $\rm A_{eff}^{\nu}$ (m$\rm ^2$), for $\rm QFit$ (dashed line) and $\rm \Lambda Fit$ (solid line), for the 12 line configuration of the detector. The $\rm QFit$ is limited here to its energy range of relevance, $\rm E_{\nu} \leq 2$ TeV.[]{data-label="aefffig"}](./Aeff_12Line_BBFitS_AAFitM_LogScale_ANUNU_New.eps){width="0.8\linewidth"}

Two reconstruction algorithms are used in this paper. The first one is based on the minimisation of a $\rm \chi^{2}$-like quality parameter of the reconstruction, $\rm Q$, which uses the difference between the expected and measured times of the detected photons, taking into account the effect of light absorption in the water [@bbfit]. The second algorithm consists of a multi-step procedure to fit the direction of the muon track by maximising a likelihood ratio, $\rm \Lambda$, which describes the quality of the reconstruction [@ps]. In addition to the $\rm \Lambda$ parameter, the uncertainty of the muon track angle, $\rm \beta$, is used for the track selection. These two algorithms are respectively called here $\rm QFit$ and $\rm \Lambda Fit$. $\rm QFit$ is used for muon events reconstructed in a single detection line (single-line events), and $\rm \Lambda Fit$ for muon events reconstructed on more than one detection line (multi-line events) in order to reach the best efficiency of reconstruction in the entire neutrino energy range. For $\rm QFit$ and $\rm \Lambda Fit$, a selection on the quality parameter $\rm Q < 0.8$ and the couple ($\rm \Lambda > -5.7$; $\rm \beta < 0.5^{\circ}$) have been used, respectively. These values of quality parameters are extracted from the optimisation step detailed in Section \[optimisation\]. $\rm QFit$ and $\rm \Lambda Fit$ present different efficiencies of reconstruction, characterised by the effective areas for muon neutrinos, $\rm A_{eff}^{\nu}$ ($\rm m^2$), which are shown in Figure \[aefffig\] as a function of the energy of the primary neutrinos $\rm E_{\nu}$ (GeV). An effective area, $\rm A_{eff}^{\nu}$, at a given energy is defined as the ratio between the neutrino event rate ($\rm s^{-1}$) in a detector and the neutrino flux ($\rm m^{-2} \cdot s^{-1}$) at that energy. As one can see, the $\rm QFit$ reconstruction strategy has a larger efficiency in the low energy regime with $\rm A_{eff}^{\nu}$ higher than the one obtained with $\rm \Lambda Fit$ for $\rm E_{\nu} < 100$ GeV.

Beside the effective area, $\rm QFit$ and $\rm \Lambda Fit$ yield different median angular resolutions, $\rm \tilde{\alpha} = med[\mid\arccos(\vec{d}_{rec}\cdot\vec{d}_{nu})\mid]$ ($^{\circ}$) between the reconstructed muons, $\rm \vec{d}_{rec}$, and the corresponding primary neutrinos, $\rm \vec{d}_{nu}$, as shown in Figure \[angresfig\]. For $\rm QFit$, since in single-line events only the zenith angle, $\rm \theta$, is reconstructed, $\rm \tilde{\alpha}$ is defined as the median of the difference between $\rm \theta_{rec}$ and $\rm \theta_{nu}$, $\rm \tilde{\alpha} = med[\mid\theta_{rec}-\theta_{nu}\mid]$. $\rm \Lambda Fit$ yields a median angular resolution $\rm 6^{\circ} > \tilde{\alpha} > 0.5^{\circ}$ for the primary neutrino energy range $\rm 100\,GeV < E_{\nu} < 10\,TeV$, whilst $\rm QFit$ reaches a $\rm 5.5^{\circ} > \tilde{\alpha} > 3.8^{\circ}$ for $\rm 15\,GeV < E_{\nu} < 1\,TeV$.

Both reconstruction algorithms are used in the search and the one with the best performance in a given energy range is selected to obtain the best possible limits in that range.

![Median angular resolution, $\rm \tilde{\alpha}$ ($^{\circ}$), on the muon neutrino direction, for the complete 12 line configuration of the detector. The performances for $\rm QFit$ (dashed line) and $\rm \Lambda Fit$ (solid line) are illustrated, as is the kinematic counterpart (dotted line), the median angle between the primary neutrino and the outgoing muon at the vertex of interaction. For $\rm QFit$, $\rm \tilde{\alpha}$ is defined as the median resolution on the zenith angles $\rm \theta_{rec,nu}$ (see text for details).[]{data-label="angresfig"}](./AngRes_12Line_2012_woBBFitM_wKinematic_New_New.eps){width="0.8\linewidth"}

Signal and background simulation {#simulation}
================================

The energy spectrum of muon neutrinos arriving at the Earth’s surface from WIMP self-annihilation occurring in the GC’s vicinity is computed using Ref. [@cirelli]. The muon neutrinos resulting from the self-annihilation channels in SM particles are propagated to the Earth for 17 different WIMP masses in the range from 25 GeV to 10 TeV. To compute the initial energy spectra at the GC, five benchmark self-annihilation channels of WIMP-like dark matter particles into SM particles are used:

$$\rm{WIMP\,WIMP \rightarrow b\bar{b},W^{+}W^{-},\tau^{+}\tau^{-},\mu^{+}\mu^{-},\nu_{\alpha}\bar{\nu}_{\alpha}} \, .
\label{benchch}$$

Also, neutrinos flavours, $\rm \alpha = e,\mu,\tau$, can be produced directly or as subsequent decay products of the SM particles listed above. The propagation of the neutrinos includes the three-flavour neutrino oscillations in vacuum along the line of sight from the GC to the surface of the Earth using the values from Table 8 in Ref. [@oscs]. The muon neutrino energy spectrum can be written as:

![Example of muon neutrino energy spectra at the surface of the Earth $\rm dN_{\nu_{\mu}}/dE_{\nu_{\mu}}\Big|_{\oplus}$ as a function of their energy $\rm E_{\nu_{\mu}}$ for a WIMP mass $\rm M_{WIMP} = 360$ GeV. The primary self-annihilation channels: $\rm WIMP\,WIMP$ $\rm \rightarrow$ $\rm b\bar{b}\,(green)$, $\rm W^{+}W^{-}\,(blue)$, $\rm \tau^{+}\tau^{-}\,(red)$, $\rm \mu^{+}\mu^{-}\,(black)$, $\rm \nu_{\mu}\bar{\nu}_{\mu}\,(orange)$ are shown.[]{data-label="benchchfig"}](./Cirelli_ESpectra_M360_Linear_Smooth_New.eps){width="0.8\linewidth"}

$$\rm{\frac{dN_{\nu_{\mu}}}{dE_{\nu_{\mu}}}\Big|_{\oplus} = \sum_{\alpha} P(\nu_{\alpha}\rightarrow\nu_{\mu}) \frac{dN_{\nu_{\alpha}}}{dE_{\nu_{\alpha}}}\Big|_{\ominus}} \, ,
\label{nuoscs}$$

where $\rm dN_{\nu_{\mu}}/dE_{\nu_{\mu}}\Big|_{\oplus}$ is the muon neutrino energy spectrum at the Earth, $\rm P(\nu_{\alpha}\rightarrow\nu_{\mu})$ is the probability to observe the oscillation $\rm \nu_{\alpha}\rightarrow\nu_{\mu}$, where $\rm \alpha = e,\mu,\tau$, and $\rm dN_{\nu_{\alpha}}/dE_{\nu_{\alpha}}\Big|_{\ominus}$ is the corresponding energy spectrum at the GC. Examples of muon neutrino energy spectra at the surface of the Earth, $\rm dN_{\nu_{\mu}}/dE_{\nu_{\mu}}\Big|_{\oplus}$, are shown in Figure \[benchchfig\] as a function of their energy $\rm E_{\nu_{\mu}}$ (GeV) (the spectra in muon anti-neutrinos are identical), for an indicative mass $\rm M_{WIMP} = 360$ GeV. In this figure, the three-flavour oscillations process in vacuum over the GC-Earth line of sight is used as expressed in Equation \[nuoscs\]. As with the dark matter search in the direction of the Sun [@dmsun], $\rm WIMP\,WIMP$$\rm \rightarrow$$\rm b\bar{b}$ is the softest channel of muon neutrino production. The hardest channel of muon neutrino production from the GC is the primary $\rm WIMP\,WIMP \rightarrow \nu_{\alpha}\bar{\nu}_{\alpha}$. It is calculated taking into account the contribution of electroweak corrections discussed in Ref. [@cirelli]. The three other channels, $\rm WIMP\,WIMP \rightarrow W^{+}W^{-},\,\tau^{+}\tau^{-},\,\mu^{+}\mu^{-}$, present a hard contribution to the full spectrum of muon neutrinos at Earth. It can be noted that the channels to $\rm \tau^{+}\tau^{-}$ and $\rm \mu^{+}\mu^{-}$ differ only for $\rm E_{\nu_{\mu}} < 100$ GeV in this example.

In order to be as model-independent as possible, a self-annihilation branching ratio $\rm BR=1$ is used for each of the channels in Expression \[benchch\]. Beyond-the-SM particle physics with $\rm BR<1$ can be accommodated by scaling the fluxes in Equation \[nuoscs\] linearly with the appropriate branching ratio.

[./MC\_QFit\_Q\_New.eps]{} (15,60) [$\displaystyle QFit$]{}

[./MC\_LambdaFit\_Lambda\_New.eps]{} (85,60) [$\displaystyle\Lambda Fit$]{}

[./MC\_QFit\_costh\_New.eps]{} (15,60) [$\displaystyle QFit$]{}

[./MC\_LambdaFit\_costh\_New.eps]{} (85,60) [$\displaystyle\Lambda Fit$]{}

The main backgrounds for this analysis are atmospheric muons and neutrinos, both produced in the interactions of cosmic rays with the Earth’s atmosphere. Downgoing atmospheric muons dominate the trigger rate, which ranges from $3$ to $10$ Hz depending on the trigger conditions. They are simulated using MUPAGE [@mupage]. Upgoing atmospheric neutrinos, which are recorded at a rate of $\sim$50 $\mu$Hz (about four per day), are simulated according to the parameterisation of the atmospheric $\rm \nu_{\mu}$ flux from Ref. [@bartol] in the energy range from 10 GeV to 10 PeV using GENHEN [@genhen]. Furthermore, the propagation of muon tracks is simulated with the KM3 package [@genhen]. The Cherenkov light produced in the vicinity of the detector is propagated taking into account light absorption and scattering in sea water [@transmission]. The characteristics of the PMTs are taken from Ref. [@OM] and the overall geometry corresponds to the different layouts of the ANTARES detector during each data-taking period.

The simulated effective area is used to evaluate the expected signal from WIMP self-annihilations. The expected background is estimated from the scrambled data in order to avoid systematic uncertainties from the simulation. The scrambling consists in a uniform randomisation of the UTC time of the events in the data-taking period. The zenith and azimuth angles of the reconstructed tracks are kept so as to preserve the angular response of the detector in the optimisation of the selection criteria. This procedure provides a means to follow a data blinding strategy while using all the relevant information on the detector performance.

The criteria to select events and to reduce the background from atmospheric muons and neutrinos, and to improve the sensitivity of ANTARES to a dark matter signal, are devised following a blind procedure on the srambled data before performing the analysis on the data.

Optimisation of the event selection criteria {#optimisation}
============================================

The data used in this search were recorded between the $\rm 27^{th}$ of January 2007 and the $\rm 31^{st}$ of October 2012, corresponding to a total livetime of about $\rm 1321$ days. This livetime is not corrected for the visibility of the GC. During this time, the detector consisted of $5$ lines for most of $\rm 2007$ and $12$ lines from $\rm 2008$ to $\rm 2012$, with short periods of $\rm 8, 9$ and 10 lines.

The $\rm QFit$ and $\rm \Lambda Fit$ methods, as introduced in Section \[antares\], are respectively used for single- and multi-line track fit reconstructions. Pre-selection cuts are applied to obtain an event sample, dominated by well-reconstructed atmospheric neutrinos. For $\rm QFit$, only upgoing events are used, i.e. $\rm \cos(\theta_{rec}) > 0$. For $\rm \Lambda Fit$, the error estimate of the reconstructed muon track direction, $\beta$, should be smaller than $\rm 0.5$, and a cut $\rm \cos(\theta_{rec}) > -0.1$ is applied. The distributions of the track fit quality parameters, $\rm Q$ and $\rm \Lambda$, for the resulting event samples are shown in Figure \[qcutfig\] for both reconstruction methods. By choosing additionally the cuts $\rm Q < 0.8$ and $\rm \Lambda > -5.7$, a purity of $\rm 69$% and $\rm 72$% in muon neutrinos is reached for $\rm QFit$ and $\rm \Lambda Fit$, respectively. The zenith angle distributions of the event samples after the cuts in $\rm Q$ and $\rm \Lambda$ are shown in Figure \[costhcutfig\]. Single-line events, as reconstructed by $\rm QFit$, are mostly found close to the vertical direction, as illustrated in Figure \[costhcutfig\] (top).

After the pre-selection, the angular separation, $\rm \Psi$, between the reconstructed track and the GC’s direction is used in an optimisation of the model rejection factor [@mrf] as a function of the WIMP mass, $\rm M_{WIMP}$. For each WIMP mass and annihilation channels listed in the Tables \[tab:qresultsone\]+\[tab:qresultstwo\]+\[tab:qresultsthree\]+\[tab:qresultsfour\], the selected value $\rm \Psi$ is the one that minimises the average 90% confidence level (C.L.) upper limit on the $\rm \nu_{\mu}+\bar{\nu}_{\mu}$ flux, $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$, defined as:

$$\rm{\overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu} = \frac{\bar{\mu}^{90\%}}{\sum\limits_{i} \bar{A}_{eff}^{i}(M_{WIMP}) \times T_{eff}^{i}}} \, ,
\label{mrfeq}$$

where the index $\rm i$ denotes the periods with different detector configurations, $\rm \bar{\mu}^{90\%}$ is the average upper limit of the background from scrambled data at $90$% C.L. (computed using a Poisson distribution in the Feldman-Cousins approach [@feldmancousins]), and $\rm {T_{eff}^{i}}$ is the effective livetime for each detector configuration. The effective area averaged over the neutrino energy, $\rm{\bar{A}_{eff}^{i}(M_{\rm WIMP})}$, is defined as:

$$\begin{aligned}
\rm{\bar{A}_{eff}^{i}(M_{\rm WIMP})} & = & 
\rm{\frac{\int_{E_{\nu_{\mu}}^{th}}^{M_{WIMP}} \left ( A_{eff}^{\nu_{\mu},i}+A_{eff}^{\bar{\nu}_{\mu},i} \right ) \, \frac{dN_{\nu_{\mu}}}{dE_{\nu_{\mu}}}\Big|_{\oplus} dE_{\nu_{\mu}}}
{2 \, \int_{0}^{M_{\rm WIMP}}\frac{dN_{\nu_{\mu}}}{dE_{\nu_{\mu}}} dE_{\nu_{\mu}}}} \, ,
\label{aeffeq}\end{aligned}$$

[./Accept\_All\_BBFitS\_AAFitM\_LogScale\_Other.eps]{} (70,15)[![Example of the acceptance $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$ ($\rm m^{2}\cdot yr$) to the signal of WIMP self-annihilation towards the GC as a function of WIMP masses $\rm 25\,GeV < M_{WIMP} < 10\,TeV$. The acceptances for the primary self-annihilation channels (from bottom to top) $\rm WIMP\,WIMP \rightarrow b\bar{b}(green),W^{+}W^{-} (blue),\tau^{+}\tau^{-} (red),\mu^{+}\mu^{-} (black),\nu_{\mu}\bar{\nu}_{\mu} (orange)$ are shown. $\rm QFit$ (dashed lines) and $\rm \Lambda Fit$ (solid lines) are compared.[]{data-label="aeffmwimpfig"}](./Channels_Legend.eps "fig:")]{} (15,55)[![Example of the acceptance $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$ ($\rm m^{2}\cdot yr$) to the signal of WIMP self-annihilation towards the GC as a function of WIMP masses $\rm 25\,GeV < M_{WIMP} < 10\,TeV$. The acceptances for the primary self-annihilation channels (from bottom to top) $\rm WIMP\,WIMP \rightarrow b\bar{b}(green),W^{+}W^{-} (blue),\tau^{+}\tau^{-} (red),\mu^{+}\mu^{-} (black),\nu_{\mu}\bar{\nu}_{\mu} (orange)$ are shown. $\rm QFit$ (dashed lines) and $\rm \Lambda Fit$ (solid lines) are compared.[]{data-label="aeffmwimpfig"}](./Fits_Legend.eps "fig:")]{}

where $\rm E_{\nu_{\mu}}^{th}\simeq15$ GeV is the energy threshold for neutrino detection in ANTARES, $\rm dN_{\nu_{\mu}}/dE_{\nu_{\mu}}\Big|_{\oplus}=dN_{\bar{\nu}_{\mu}}/dE_{\bar{\nu}_{\mu}}\Big|_{\oplus}$ is the energy spectrum of the neutrinos at the surface of the Earth as shown in Figure \[benchchfig\], and $\rm A_{eff}^{\nu_{\mu}/\bar{\nu}_{\mu}}$ is the effective area of ANTARES as a function of the neutrino or anti-neutrino energy for tracks coming from the direction of the GC (Figure \[aefffig\] for illustration). Due to their different cross-sections, the effective areas for neutrinos and anti-neutrinos are slightly different and therefore are considered separately, whereas the fluxes of muon neutrinos and anti-neutrinos from the GC are identical.

The optimisation procedure provides a set of optimum values of angular separation to the GC, $\rm \Psi$, for each mass of the WIMP and for each benchmark channel. The distributions of $\rm \Psi$ as a function of the WIMP mass, $\rm M_{WIMP}$, are given in Tables \[tab:qresultsone\]+\[tab:qresultstwo\] and \[tab:qresultsthree\]+\[tab:qresultsfour\]. Regardless of self-annihilation channels and reconstruction algorithms, an optimised angular separation $\rm \Psi$ to the GC is wider for low $\rm M_{WIMP}$ due to the degradation of the angular resolution $\rm \tilde{\alpha}$ at low neutrino energy (Figure \[angresfig\]). Moreover, the optimimum $\rm \Psi$ for a given $\rm M_{WIMP}$ depends on the softness of the self-annihilation channel, $\rm \Psi$ being wider the softer the channel.

An example of the acceptance $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$ is shown in Figure \[aeffmwimpfig\]. The visibility of the GC and the data-taking periods from 2007 to 2012 are included. The $\rm QFit$ (dashed lines) and $\rm \Lambda Fit$ (solid lines) are compared for each self-annihilation channel, inside their respective angular separations, $\rm \Psi = 10^{\circ}$ and $\rm \Psi = 2^{\circ}$, that are typical over all the WIMP masses (Tables \[tab:qresultsone\]+\[tab:qresultstwo\]+\[tab:qresultsthree\]+\[tab:qresultsfour\]). Notice that the softer a self-annihilation channel is, the lower the corresponding acceptance, due to the decrease of the effective area $\rm A_{eff}^{\nu}$ shown in Figure \[aefffig\] towards the low neutrino energies. Also, the channels $\rm WIMP\,WIMP \rightarrow \nu_{\alpha}\bar{\nu}_{\alpha}$ and $\rm WIMP\,WIMP \rightarrow b\bar{b}$ show respectively the largest and smallest acceptance to a WIMP self-annihilation signal. This will respectively induce the best and worse limits for a neutrino flux $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$, as shown in Equation \[mrfeq\]. The $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$ distribution of the $W^{+}W^{-}$ channel is kinematically allowed for $M_{\rm WIMP} > M_{W} = 80.4$ GeV [@pdg2012]. However, the low mass region, $\rm 25\,GeV < M_{\rm WIMP} < M_{W}$, is probed by other channels. Moreover, the energy range for which $\rm QFit$ is more efficient than $\rm \Lambda Fit$ will change slightly according to the softness of the self-annihilation channel. As can be seen in Figure \[benchchfig\], most of the contribution of the $b\bar{b}$ channel lies in the range $\rm E_{\nu_{\mu}} < 100$ GeV, for $\rm M_{WIMP} = 360$ GeV, where $\rm QFit$ yields a higher effective area compared to $\rm \Lambda Fit$. Therefore, $\rm QFit$ is preferred over the range of masses $\rm M_{WIMP} < 1.5$ TeV to compute the best $b\bar{b}$ limit. Furthermore, this evolves according to the self-annihilation channel spectrum and the WIMP mass, as described in the following Section \[results\].

[./Data\_VS\_Bkg\_Derived\_SymmErrors\_SmoothBkg.eps]{} (15,52) [$\displaystyle QFit$]{} (30,35) [$\displaystyle\Lambda Fit$]{}

[./Limit\_Phinu\_Versus\_Mwimp\_Color\_Other\_New.eps]{} (70,50)[![$90$% C.L. upper limits on the neutrino flux, $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$, as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the self-annihilation channels (from top to bottom) $\rm WIMP\,WIMP \rightarrow b\bar{b} (green),W^{+}W^{-} (blue),\tau^{+}\tau^{-} (red),\mu^{+}\mu^{-} (black),\nu_{\mu}\bar{\nu}_{\mu} (orange)$. The $\rm QFit$ and $\rm \Lambda Fit$ results are combined.[]{data-label="phinulimitfig"}](./Channels_Legend.eps "fig:")]{}

[./JFactor\_Psi.eps]{} (60,20)[![Distributions of the integrated J-Factor ($\rm GeV^{2} \cdot cm^{-5}$) as a function of the angular separation to the GC, $\rm \Psi$. The dark matter density profiles: a contracted NFW [@contrnfw] (dotted line), Einasto [@einasto] (dot-dashed line), NFW [@nfw] (solid line) and isothermal [@isoth] (dashed line), are compared.[]{data-label="jfactorpsi"}](./Halos_Legend.eps "fig:")]{}

[./sigmav\_Limit\_MwimpVersus\_LogScale\_New.eps]{} (70,50)[![The $90$% C.L. upper limits on the WIMP velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the self-annihilation channels $\rm WIMP\,WIMP \rightarrow b\bar{b} (green)$, $\rm W^{+}W^{-} (blue)$, $\rm \tau^{+}\tau^{-} (red)$, $\rm \mu^{+}\mu^{-} (black)$, $\rm \nu_{\mu}\bar{\nu}_{\mu} (orange)$. The $\rm QFit$ and $\rm \Lambda Fit$ results are combined.[]{data-label="sigmalimitfig"}](./Channels_Legend.eps "fig:")]{}

![The $90$% C.L. upper limit on the WIMP velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the self-annihilation channel $\rm WIMP\,WIMP \rightarrow \tau^{+}\tau^{-}$ for ANTARES 2007-2012 (red) with $\rm QFit$ and $\rm \Lambda Fit$ results combined. This is compared to the limits from IceCube 59 2009-2010 [@icecube59] for the Virgo cluster (black), Fermi-LAT 2008-2014 [@fermilat] for the combined analysis of 15 satellite galaxies (green) and MAGIC 2011-2013 [@magic] for Segue 1 (purple), and the IceCube-DeepCore 79 2010-2011 sensitivity [@icecube79] for the GC (blue) is also shown. Interpreting observed electron/positron excesses as dark matter self-annihilations, the orange (PAMELA) and green (PAMELA, Fermi-LAT and H.E.S.S.) ellipses have been obtained [@pamelainterp]. The dashed line indicates the natural scale for which a WIMP is a thermal relic of the early Universe [@naturalscale].[]{data-label="sigmalimitothersfig"}](./sigmav_Limit_MwimpVersus_LogScale_Others_New_New.eps){width="0.8\linewidth"}

[./sigmav\_Limit\_MwimpVersus\_LogScale\_Syst\_New.eps]{} (15,15)[![The $90$% C.L. upper limits on the WIMP velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the self-annihilation channel $\rm WIMP\,WIMP \rightarrow \tau^{+}\tau^{-}$. The dark matter density profiles used in the $\rm <\sigma_{A}v>$ computation are NFW [@nfw] (solid line), Einasto [@einasto] (dot-dashed line), isothermal [@isoth] (dashed line) and a contracted NFW [@contrnfw] (dotted line).[]{data-label="sigmalimitsystfig"}](./Halos_Legend_Red.eps "fig:")]{}

Results and discussion {#results}
======================

Given the pre-selection and optimisation processes described in Section \[antares\] and \[optimisation\], a total of 369 and 401 events for the unblinded 2007-2012 data are found within an angular separation $\rm \Psi$ of $\rm 20^{\circ}$ from $\rm QFit$ and $\rm \Lambda Fit$, respectively. This angle is large enough to contain all values of the optimal angular separation $\rm \Psi$ for all WIMP masses and for each channel. Figure \[databkgfig\] shows the integrated distribution of the reconstructed event numbers as a function of their relative angular separation to the GC, $\rm \Psi$. Data are in good agreement with the expected background for both reconstruction algorithms. As no statistically significant excess is observed in the direction of the GC, upper limits on a neutrino flux can be set.

The $90$% C.L. upper limits on the $\rm \nu_{\mu}+\bar{\nu}_{\mu}$ flux at Earth, $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$, are computed from the data according to Equation \[mrfeq\], where the average $90$% C.L. upper limit $\rm \bar{\mu}^{90\%}$ is replaced by the upper limit at $90$% C.L. on the number of observed events, $\rm \mu^{90\%}$. Systematic uncertainties are taken into account and included in the evaluation of the limits using the [Pole]{} software following the approach described in Ref. [@conrad]. The total systematic uncertainty on the detector efficiency is about 20% and comes mainly from the uncertainties on the average quantum efficiency and the angular acceptance of the PMTs, and the sea water absorption length. The detailed uncertainty study is described in Ref. [@timing]. This total systematic uncertainty translates into a degradation of the upper limits between 3% and 6%, depending on the WIMP mass. The corresponding limits are presented in Figure \[phinulimitfig\] for all the benchmark self-annihilation channels. In this figure, the results from $\rm QFit$ and $\rm \Lambda Fit$ are combined to reach the best upper limit over the whole $\rm M_{WIMP}$ range. Given its soft energy spectrum (Figure \[aeffmwimpfig\]), the channel $b\bar{b}$ yields the least stringent limit, while it is the opposite for $\nu_{\alpha}\bar{\nu}_{\alpha}$. The upper limits, $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$, improve from low to high WIMP masses, as expected from the general hardness of the neutrino spectra at the surface of the Earth, the absence of interaction during the neutrino propagation along the line of sight from the GC (no absorption or diffusion are present), and the tightness of the optimum angular separation around the GC, $\rm \Psi$, for high WIMP masses (Table \[tab:qresultsfour\]).

The neutrino flux from the self-annihilation of dark matter particles at the GC can be expressed as:

$$\begin{aligned}
\rm{\Phi_{\nu_{\mu}+\bar{\nu}_\mu}} & = & \rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP} \times J(\Delta\Omega)} \, , \label{phinupsieqone} \\
\rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP}} & = & \rm{\frac{1}{4\pi}\frac{<\sigma_{A}v>}{2M_{WIMP}^{2}} N_{\nu_{\mu}+\bar{\nu}_\mu}} \, , \label{phinupsieqtwo} \\
\rm{J(\Delta\Omega)} & = & \rm{\int_{\Delta\Omega} \int \rho_{DM}^{2}dl\,d\Omega} \, , \label{phinupsieqthree}\end{aligned}$$

with $\rm{\Xi_{\nu_{\mu}+\bar{\nu}_\mu}^{PP}}$ as the particle physics term, which depends on the WIMP velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, and the number of neutrinos, $N_{\nu_{\mu}+\bar{\nu}_\mu}$, that reach the surface of the Earth. $N_{\nu_{\mu}+\bar{\nu}_\mu}$ is computed from the integration over the neutrino energy of the GC’s self-annihilation spectra. The astrophysical J-Factor is the integral over the line of sight, $l$, and the solid angle around the GC, $\Omega$, of the dark matter density, $\rm \rho_{DM}$, squared. The density $\rm \rho_{DM}$ depends on the chosen dark matter galactic halo profile. The Navarro-Frenk-White (NFW) profile [@nfw] is selected as a reference for which the density profile of dark matter is expressed as:

$$\rm{\rho(r) = \frac{\rho_{s}}{(r/r_{s})(1+r/r_{s})^{2}}} \, ,
\label{nfwprofile}$$

with $\rm r_{s} = 21.7$ kpc. The normalization of the profile density, $\rm \rho_{s}$, is computed by fixing the dark matter density at the Sun’s position $\rm \rho(r_{Sun} = 8.5\,kpc) = 0.4\,GeV \cdot cm^{-3}$ [@catena; @salucci]. The systematic uncertainty introduced by the choice of a specific halo profile is discussed at the end of this section.

The J-Factor can be computed using the package CLUMPY [@clumpy] with the contribution from clumps turned off. As demonstrated in Equation \[phinupsieqthree\], the J-Factor is a function of the solid angle $\rm \Delta\Omega = 2\pi(1-\cos(\Psi))$. Figure \[jfactorpsi\] shows the result of the computation of the integrated J-Factor for the NFW profile as a function of $\rm \Psi$. Upper limits for the WIMP velocity-averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$, can be set following Equation \[phinupsieqone\] for each benchmark self-annihilation channel, with known J-Factor for a given optimum angular separation $\rm \Psi$ for each $\rm M_{WIMP}$, and upper limits $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$ as given in Figure \[phinulimitfig\]. Figure \[sigmalimitfig\] shows the $90$% C.L. upper limits on $\rm <\sigma_{A}v>$ as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the whole set of self-annihilation channels from Expression \[benchch\].

The $\rm <\sigma_{A}v>$ upper limits obtained from the 2007-2012 ANTARES data are comparable with those obtained by other experiments. Figure \[sigmalimitothersfig\] shows the resulting $90$% C.L. upper limit on $\rm <\sigma_{A}v>$ as a function of the WIMP mass in the range $\rm 25\,GeV < M_{WIMP} < 10\,TeV$ for the self-annihilation channel $\rm WIMP\,WIMP \rightarrow \tau^{+}\tau^{-}$ from this analysis compared to the results from IceCube-DeepCore 79 [@icecube79], IceCube 59 [@icecube59], and to the most stringent gamma-ray limits from Fermi-LAT [@fermilat], and MAGIC [@magic]. ANTARES 2007-2012 data provides the best upper limit at $90$% C.L. on $\rm <\sigma_{A}v>$ for the channel $\tau^{+}\tau^{-}$ from a neutrino telescope. Furthermore, the interpretation [@pamelainterp] of the PAMELA excess as a dark matter self-annihilation signature, after being constrained by Fermi-LAT and H.E.S.S., is rejected at $90$% C.L..

All the results are summarised in Tables \[tab:qresultsone\]+\[tab:qresultstwo\] and \[tab:qresultsthree\]+\[tab:qresultsfour\], where for each WIMP mass and channel the values of the optimised angular separation, $\rm \Psi$, the 90% C.L. sensitivity, $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$, computed from the background without signal expectation, the 90% C.L. upper limits, $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$, the acceptance, $\rm \bar{A}_{eff}(M_{\rm WIMP}) \times T_{eff}$, and the 90% C.L. upper limits on $\rm <$$\rm \sigma_{A}v>$ are presented. In these tables, the results shown in Figures \[phinulimitfig\] and \[sigmalimitfig\] are highlighted in bold. To evaluate the influence of the dark matter halo profile used in the computation of the $\rm <\sigma_{A}v>$ upper limits, different profiles have been tried. The Einasto profile [@einasto], favoured by recent dark matter-only simulations, is given by:

$$\rm{\rho(r) = \rho_{s}\exp\{-(2/\alpha)[(r/r_{s})^{\alpha}-1]\}} \, 
\label{einastoprofile}$$

where $\rm r_{s} = 21.7$ kpc and $\rm \alpha = 0.17$. The isothermal profile [@isoth] is given by:

$$\rm{\rho(r) = \frac{\rho_{s}}{1+(r/r_{s})^{2}}} \, 
\label{isoprofile}$$

where $\rm r_{s} = 4$ kpc. Finally, an adiabatic contraction of the NFW profile due to infall of baryonic matter in the GC region [@contrnfw] is given by:

$$\rm{\rho(r) = \frac{\rho_{s}}{(r/r_{s})^{\gamma}(1+r/r_{s})^{3-\gamma}}} \, 
\label{contrnfwprofile}$$

where $\rm \gamma = 1.3$. For all of these profiles, $\rm \rho_{s}$ is computed as for the NFW profile. Figure \[jfactorpsi\] summarises the different J-Factors for these profiles. Figure \[sigmalimitsystfig\] shows the 90% C.L. upper limit on $\rm <\sigma_{A}v>$ for the self-annihilation channel $\rm WIMP\,WIMP \rightarrow \tau^{+}\tau^{-}$ for the different dark matter halo profiles. The limits on $\rm <\sigma_{A}v>$ for different profiles vary by one to three orders of magnitude depending on the WIMP mass. The optimum angular separation $\rm \Psi$ (Tables \[tab:qresultstwo\] and \[tab:qresultsfour\]) is usually smaller in the high WIMP mass regime, making the computation of the $\rm <\sigma_{A}v>$ more sensitive to the cuspiness of a profile for high WIMP masses (Equation \[phinupsieqthree\] and Figure \[jfactorpsi\]).

Summary and conclusion {#conclusion}
======================

Using the 2007-2012 data set recorded by the ANTARES neutrino telescope, an indirect search for dark matter towards the Galactic Centre has been performed. The observed number of neutrino events in the Galactic Centre’s direction is compatible with the expectation from atmospheric backgrounds (Figure \[databkgfig\]), for both reconstruction algorithms, optimised for low and high energy events. The 90% C.L. upper limits have been derived for the neutrino flux, $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$ (Figure \[phinulimitfig\]), and the velocity averaged self-annihilation cross-section, $\rm <\sigma_{A}v>$ (Figure \[sigmalimitfig\]), for all the self-annihilation channels $\rm WIMP\,WIMP \rightarrow b\bar{b}$, $\rm W^{+}W^{-}$, $\rm \tau^{+}\tau^{-}$, $\rm \mu^{+}\mu^{-}$, $\rm \nu_{\mu}\bar{\nu}_{\mu}$, in the range of WIMP masses $\rm 25\,GeV < M_{WIMP} < 10\,TeV$. The 90% C.L. upper limit on $\rm <\sigma_{A}v>$ for the channel $\rm WIMP\,WIMP \rightarrow \tau^{+}\tau^{-}$ is the most stringent coming from a neutrino telescope, and is complementary to the most constraining upper limits obtained by the Fermi-LAT and MAGIC observatories (Figure \[sigmalimitsystfig\]). Furthermore, the performance of the ANTARES neutrino telescope through this study allows the rejection at 90% C.L. of the interpretation [@pamelainterp] of the PAMELA electron/positron excess (constrained by Fermi-LAT and H.E.S.S.) as a signal from dark matter self-annihilation.

Acknowledgments {#acknowledgments .unnumbered}
===============

The authors acknowledge the financial support of the funding agencies: Centre National de la Recherche Scientifique (CNRS), Commissariat à l’énegie atomique et aux énergies alternatives (CEA), Agence National de la Recherche (ANR), Commission Européenne (FEDER fund and Marie Curie Program), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d’Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie (FOM), Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Ciencia e Innovación (MICINN), Prometeo of Generalitat Valenciana and MultiDark, Spain; Agence de l’Oriental and CNRST, Morocco. We also acknowledge the technical support of Ifremer, AIM and Foselev Marine for the sea operation and the CC-IN2P3 for the computing facilities.

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  --------------------------- ---------------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- ------------------------------- -- --
                                                                                                                                                                                                                                                                                                                                                           
   \[-0.1in\] $\rm M_{WIMP}$               Channel                   $\rm \Psi$      $\rm \bar{\mu}^{90\%}$   $\rm \mu^{90\%}$   $\rm \bar{A}_{eff}(M_{\rm WIMP})$   $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$   $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$       $\rm J-Factor$        $\rm \overline{<\sigma_{A}v>}$        $\rm <\sigma_{A}v>$          
                                                                                                                                       $\rm \times T_{eff}$                                                                                                                                                                                                
          $\rm (GeV)$                                             ($\rm ^{\circ}$)                                                        ($\rm m^2.yr$)                         ($\rm km^{-2}.yr^{-1}$)                     ($\rm km^{-2}.yr^{-1}$)          ($\rm GeV^{2}.cm^{-5}$)       ($\rm cm^{3}.s^{-1}$)            ($\rm cm^{3}.s^{-1}$)         
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
        \[-0.1in\] $25$                   $b\bar{b}$                   $14.6$                 $34$                  $22$               $1.5\times 10^{-11}$                        $2.3\times 10^{18}$                     $\mathbf{1.5\times 10^{18}}$          $3\times 10^{22}$            $2\times 10^{-19}$         $\mathbf{1.3\times 10^{-19}}$     
              $$                       $\tau\bar{\tau}$                $14.6$                 $34$                  $22$                $2.1\times 10^{-8}$                        $1.6\times 10^{15}$                     $\mathbf{1.1\times 10^{15}}$          $3\times 10^{22}$           $8.2\times 10^{-22}$        $\mathbf{5.3\times 10^{-22}}$     
              $$                       $\mu^{+}\mu^{-}$                $14.6$                 $34$                  $22$                $5.5\times 10^{-8}$                        $6.2\times 10^{14}$                      $\mathbf{4\times 10^{14}}$           $3\times 10^{22}$           $7.9\times 10^{-22}$        $\mathbf{5.1\times 10^{-22}}$     
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $10.3$                 $30$                  $17$                $1.2\times 10^{-6}$                        $2.5\times 10^{13}$                     $\mathbf{1.4\times 10^{13}}$         $2.2\times 10^{22}$          $5.8\times 10^{-23}$        $\mathbf{3.3\times 10^{-23}}$     
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
        \[-0.1in\] $50$                   $b\bar{b}$                   $14.6$                 $34$                  $22$                $6\times 10^{-10}$                         $5.7\times 10^{16}$                    $\mathbf{13.7\times 10^{16}}$          $3\times 10^{22}$           $1.6\times 10^{-20}$         $\mathbf{1\times 10^{-20}}$      
              $$                       $\tau\bar{\tau}$                $12.5$                 $32$                  $18$                $3.8\times 10^{-7}$                        $8.5\times 10^{13}$                     $\mathbf{4.8\times 10^{13}}$         $2.6\times 10^{22}$          $1.9\times 10^{-22}$        $\mathbf{1.1\times 10^{-22}}$     
              $$                       $\mu^{+}\mu^{-}$                $12.1$                 $32$                  $21$                 $1\times 10^{-6}$                         $3.1\times 10^{13}$                     $\mathbf{2.1\times 10^{13}}$         $2.6\times 10^{22}$          $1.9\times 10^{-22}$        $\mathbf{1.2\times 10^{-22}}$     
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $8.95$                 $28$                  $17$                $1.4\times 10^{-5}$                         $2\times 10^{12}$                      $\mathbf{1.2\times 10^{12}}$          $2\times 10^{22}$           $2.1\times 10^{-23}$        $\mathbf{1.3\times 10^{-23}}$     
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
        \[-0.1in\] $90$                   $b\bar{b}$                   $12.5$                 $32$                  $18$                 $5\times 10^{-9}$                         $6.4\times 10^{15}$                     $\mathbf{3.6\times 10^{15}}$         $2.6\times 10^{22}$          $5.4\times 10^{-21}$         $\mathbf{3\times 10^{-21}}$      
              $$                         $W^{+}W^{-}$                   $12$                  $32$                  $20$                $8.6\times 10^{-8}$                        $3.7\times 10^{14}$                     $\mathbf{2.3\times 10^{14}}$         $2.5\times 10^{22}$          $3.7\times 10^{-22}$        $\mathbf{2.4\times 10^{-22}}$     
              $$                       $\tau\bar{\tau}$                 $12$                  $32$                  $20$                $1.9\times 10^{-6}$                        $1.7\times 10^{13}$                      $\mathbf{1\times 10^{13}}$          $2.5\times 10^{22}$          $1.3\times 10^{-22}$         $\mathbf{8\times 10^{-23}}$      
              $$                       $\mu^{+}\mu^{-}$                 $12$                  $32$                  $20$                $5.3\times 10^{-6}$                         $6\times 10^{12}$                      $\mathbf{3.8\times 10^{12}}$         $2.5\times 10^{22}$          $1.2\times 10^{-22}$        $\mathbf{7.3\times 10^{-23}}$     
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.95$                 $29$                  $18$                $4.3\times 10^{-5}$                        $6.8\times 10^{11}$                     $\mathbf{4.2\times 10^{11}}$         $2.2\times 10^{22}$          $2.1\times 10^{-23}$        $\mathbf{1.3\times 10^{-23}}$     
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $100$                   $b\bar{b}$                   $12.5$                 $32$                  $18$                 $7\times 10^{-9}$                         $4.6\times 10^{15}$                     $\mathbf{2.6\times 10^{15}}$         $2.6\times 10^{22}$          $4.6\times 10^{-21}$        $\mathbf{2.6\times 10^{-21}}$     
              $$                         $W^{+}W^{-}$                   $12$                  $32$                  $20$                $1.2\times 10^{-7}$                        $2.7\times 10^{14}$                     $\mathbf{1.7\times 10^{14}}$         $2.5\times 10^{22}$          $3.4\times 10^{-22}$        $\mathbf{2.1\times 10^{-22}}$     
              $$                       $\tau\bar{\tau}$                 $12$                  $32$                  $20$                $2.5\times 10^{-6}$                        $1.3\times 10^{13}$                     $\mathbf{8.1\times 10^{12}}$         $2.5\times 10^{22}$          $1.2\times 10^{-22}$        $\mathbf{7.7\times 10^{-23}}$     
              $$                       $\mu^{+}\mu^{-}$                 $12$                  $32$                  $20$                $6.8\times 10^{-6}$                        $4.7\times 10^{12}$                     $\mathbf{2.9\times 10^{12}}$         $2.5\times 10^{22}$          $1.1\times 10^{-22}$        $\mathbf{7.1\times 10^{-23}}$     
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $6.95$                 $25$                  $29$                $4.7\times 10^{-5}$                        $5.3\times 10^{11}$                         $6.1\times 10^{11}$              $1.6\times 10^{22}$          $2.7\times 10^{-23}$            $3.2\times 10^{-23}$          
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $150$                   $b\bar{b}$                    $12$                  $32$                  $20$                $2.1\times 10^{-8}$                        $1.5\times 10^{15}$                     $\mathbf{9.6\times 10^{14}}$         $2.5\times 10^{22}$          $3.1\times 10^{-21}$        $\mathbf{1.9\times 10^{-21}}$     
              $$                         $W^{+}W^{-}$                  $8.15$                 $27$                  $21$                $2.8\times 10^{-7}$                        $9.5\times 10^{13}$                         $7.4\times 10^{13}$              $1.8\times 10^{22}$          $3.7\times 10^{-22}$            $2.9\times 10^{-22}$          
              $$                       $\tau\bar{\tau}$                $8.15$                 $27$                  $21$                $5.1\times 10^{-6}$                        $5.3\times 10^{12}$                     $\mathbf{4.1\times 10^{12}}$         $1.8\times 10^{22}$          $1.5\times 10^{-22}$        $\mathbf{1.2\times 10^{-22}}$     
              $$                       $\mu^{+}\mu^{-}$                $8.15$                 $27$                  $21$                $1.4\times 10^{-5}$                         $2\times 10^{12}$                      $\mathbf{1.5\times 10^{12}}$         $1.8\times 10^{22}$          $1.5\times 10^{-22}$        $\mathbf{1.1\times 10^{-22}}$     
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.75$                 $29$                  $18$                $1.1\times 10^{-4}$                        $2.7\times 10^{11}$                         $1.7\times 10^{11}$              $2.1\times 10^{22}$          $2.2\times 10^{-23}$            $1.4\times 10^{-23}$          
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $180$                   $b\bar{b}$                    $12$                  $32$                  $20$                $3.2\times 10^{-8}$                         $1\times 10^{15}$                      $\mathbf{6.3\times 10^{14}}$         $2.5\times 10^{22}$          $2.7\times 10^{-21}$        $\mathbf{1.7\times 10^{-21}}$     
              $$                         $W^{+}W^{-}$                  $9.75$                 $29$                  $18$                $4.6\times 10^{-7}$                        $6.3\times 10^{13}$                         $3.9\times 10^{13}$              $2.1\times 10^{22}$           $3\times 10^{-22}$             $1.8\times 10^{-22}$          
              $$                       $\tau\bar{\tau}$                $9.75$                 $29$                  $18$                $8.1\times 10^{-6}$                        $3.6\times 10^{12}$                         $2.2\times 10^{12}$              $2.1\times 10^{22}$          $1.3\times 10^{-22}$            $7.9\times 10^{-23}$          
              $$                       $\mu^{+}\mu^{-}$                $9.75$                 $29$                  $18$                $2.1\times 10^{-5}$                        $1.4\times 10^{12}$                         $8.5\times 10^{11}$              $2.1\times 10^{22}$          $1.2\times 10^{-22}$            $7.5\times 10^{-23}$          
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.15$                 $28$                  $19$                $1.4\times 10^{-4}$                        $2.1\times 10^{11}$                         $1.4\times 10^{11}$               $2\times 10^{22}$           $2.4\times 10^{-23}$            $1.6\times 10^{-23}$          
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $200$                   $b\bar{b}$                    $12$                  $32$                  $20$                $4.1\times 10^{-8}$                        $7.8\times 10^{14}$                     $\mathbf{4.9\times 10^{14}}$         $2.5\times 10^{22}$          $2.5\times 10^{-21}$        $\mathbf{1.6\times 10^{-21}}$     
              $$                         $W^{+}W^{-}$                  $9.75$                 $29$                  $18$                $5.9\times 10^{-7}$                        $4.9\times 10^{13}$                          $3\times 10^{13}$               $2.1\times 10^{22}$          $2.8\times 10^{-22}$            $1.7\times 10^{-22}$          
              $$                       $\tau\bar{\tau}$                $9.75$                 $29$                  $18$                 $1\times 10^{-5}$                         $2.9\times 10^{12}$                         $1.8\times 10^{12}$              $2.1\times 10^{22}$          $1.3\times 10^{-22}$            $7.9\times 10^{-23}$          
              $$                       $\mu^{+}\mu^{-}$                $9.75$                 $29$                  $18$                $2.6\times 10^{-5}$                        $1.1\times 10^{12}$                          $7\times 10^{11}$               $2.1\times 10^{22}$          $1.2\times 10^{-22}$            $7.5\times 10^{-23}$          
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.15$                 $28$                  $19$                $1.7\times 10^{-4}$                        $1.6\times 10^{11}$                         $1.1\times 10^{11}$               $2\times 10^{22}$           $2.2\times 10^{-23}$            $1.5\times 10^{-23}$          
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $260$                   $b\bar{b}$                    $12$                  $32$                  $20$                $7.2\times 10^{-8}$                        $4.4\times 10^{14}$                     $\mathbf{2.8\times 10^{14}}$         $2.5\times 10^{22}$          $2.2\times 10^{-21}$        $\mathbf{1.4\times 10^{-21}}$     
              $$                         $W^{+}W^{-}$                  $7.85$                 $27$                  $21$                 $9\times 10^{-7}$                          $3\times 10^{13}$                          $2.3\times 10^{13}$              $1.8\times 10^{22}$          $3.4\times 10^{-22}$            $2.7\times 10^{-22}$          
              $$                       $\tau\bar{\tau}$                $8.05$                 $27$                  $20$                $1.5\times 10^{-5}$                        $1.8\times 10^{12}$                         $1.3\times 10^{12}$              $1.8\times 10^{22}$          $1.5\times 10^{-22}$            $1.1\times 10^{-22}$          
              $$                       $\mu^{+}\mu^{-}$                $8.05$                 $27$                  $20$                $3.7\times 10^{-5}$                        $7.2\times 10^{11}$                         $5.4\times 10^{11}$              $1.8\times 10^{22}$          $1.5\times 10^{-22}$            $1.1\times 10^{-22}$          
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $7.85$                 $27$                  $21$                 $2\times 10^{-4}$                         $1.3\times 10^{11}$                          $1\times 10^{11}$               $1.8\times 10^{22}$          $3.1\times 10^{-23}$            $2.4\times 10^{-23}$          
                                                                                                                                                                                                                                                                                                                                                           
          \[-0.1in\]                                                                                                                                                                                                                                                                                                                                       
       \[-0.1in\] $360$                   $b\bar{b}$                   $10.5$                 $30$                  $18$                $1.3\times 10^{-7}$                        $2.3\times 10^{14}$                         $1.4\times 10^{14}$              $2.3\times 10^{22}$          $2.2\times 10^{-21}$            $1.3\times 10^{-21}$          
              $$                         $W^{+}W^{-}$                  $9.25$                 $29$                  $17$                $1.6\times 10^{-6}$                        $1.7\times 10^{13}$                          $1\times 10^{13}$                $2\times 10^{22}$           $3.1\times 10^{-22}$            $1.9\times 10^{-22}$          
              $$                       $\tau\bar{\tau}$                $8.05$                 $27$                  $20$                $2.6\times 10^{-5}$                         $1\times 10^{12}$                          $7.6\times 10^{11}$              $1.8\times 10^{22}$          $1.6\times 10^{-22}$            $1.2\times 10^{-22}$          
              $$                       $\mu^{+}\mu^{-}$                $8.05$                 $27$                  $20$                $6.2\times 10^{-5}$                        $4.4\times 10^{11}$                         $3.2\times 10^{11}$              $1.8\times 10^{22}$          $1.6\times 10^{-22}$            $1.2\times 10^{-22}$          
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.35$                 $29$                  $16$                $3.1\times 10^{-4}$                        $9.2\times 10^{10}$                         $5.1\times 10^{10}$              $2.1\times 10^{22}$          $3.1\times 10^{-23}$            $1.7\times 10^{-23}$          
  --------------------------- ---------------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- ------------------------------- -- --

  --------------------------- ---------------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -----------------------
                                                                                                                                                                                                                                                                                                                        
   \[-0.1in\] $\rm M_{WIMP}$               Channel                   $\rm \Psi$      $\rm \bar{\mu}^{90\%}$   $\rm \mu^{90\%}$   $\rm \bar{A}_{eff}(M_{\rm WIMP})$   $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$   $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$       $\rm J-Factor$        $\rm \overline{<\sigma_{A}v>}$    $\rm <\sigma_{A}v>$
                                                                                                                                       $\rm \times T_{eff}$                                                                                                                                                             
          $\rm (GeV)$                                             ($\rm ^{\circ}$)                                                        ($\rm m^2.yr$)                         ($\rm km^{-2}.yr^{-1}$)                     ($\rm km^{-2}.yr^{-1}$)          ($\rm GeV^{2}.cm^{-5}$)       ($\rm cm^{3}.s^{-1}$)        ($\rm cm^{3}.s^{-1}$)
                                                                                                                                                                                                                                                                                                                        
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
       \[-0.1in\] $500$                   $b\bar{b}$                   $8.15$                 $27$                  $21$                $2.2\times 10^{-7}$                        $1.2\times 10^{14}$                         $9.6\times 10^{13}$              $1.8\times 10^{22}$          $2.5\times 10^{-21}$         $2\times 10^{-21}$
              $$                         $W^{+}W^{-}$                  $9.25$                 $29$                  $17$                $2.6\times 10^{-6}$                        $1.1\times 10^{13}$                         $6.4\times 10^{12}$               $2\times 10^{22}$           $3.5\times 10^{-22}$        $2.1\times 10^{-22}$
              $$                       $\tau\bar{\tau}$                $9.25$                 $29$                  $17$                $4.7\times 10^{-5}$                         $6\times 10^{11}$                          $3.6\times 10^{11}$               $2\times 10^{22}$           $1.6\times 10^{-22}$        $9.7\times 10^{-23}$
              $$                       $\mu^{+}\mu^{-}$                $9.25$                 $29$                  $17$                 $1\times 10^{-4}$                         $2.7\times 10^{11}$                         $1.6\times 10^{11}$               $2\times 10^{22}$           $1.6\times 10^{-22}$        $9.6\times 10^{-23}$
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.95$                 $29$                  $18$                $4.4\times 10^{-4}$                        $6.7\times 10^{10}$                         $4.1\times 10^{10}$              $2.2\times 10^{22}$          $3.5\times 10^{-23}$        $2.1\times 10^{-23}$
                                                                                                                                                                                                                                                                                                                        
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
       \[-0.1in\] $750$                   $b\bar{b}$                   $8.15$                 $27$                  $21$                $4.4\times 10^{-7}$                        $6.1\times 10^{13}$                         $4.7\times 10^{13}$              $1.8\times 10^{22}$          $2.5\times 10^{-21}$        $1.9\times 10^{-21}$
              $$                         $W^{+}W^{-}$                  $9.05$                 $28$                  $18$                $5.4\times 10^{-6}$                        $5.2\times 10^{12}$                         $3.3\times 10^{12}$               $2\times 10^{22}$           $3.6\times 10^{-22}$        $2.3\times 10^{-22}$
              $$                       $\tau\bar{\tau}$                $9.05$                 $28$                  $18$                $9.4\times 10^{-5}$                         $3\times 10^{11}$                          $1.9\times 10^{11}$               $2\times 10^{22}$           $1.8\times 10^{-22}$        $1.1\times 10^{-22}$
              $$                       $\mu^{+}\mu^{-}$                $9.05$                 $28$                  $18$                $1.9\times 10^{-4}$                        $1.5\times 10^{11}$                         $9.3\times 10^{10}$               $2\times 10^{22}$           $1.8\times 10^{-22}$        $1.1\times 10^{-22}$
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $9.05$                 $28$                  $18$                $8.5\times 10^{-4}$                        $3.3\times 10^{10}$                         $2.1\times 10^{10}$               $2\times 10^{22}$           $3.4\times 10^{-23}$        $2.2\times 10^{-23}$
                                                                                                                                                                                                                                                                                                                        
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
       \[-0.1in\] $1000$                  $b\bar{b}$                   $8.05$                 $27$                  $20$                $7.1\times 10^{-7}$                        $3.8\times 10^{13}$                         $2.8\times 10^{13}$              $1.8\times 10^{22}$          $2.5\times 10^{-21}$        $1.8\times 10^{-21}$
              $$                         $W^{+}W^{-}$                  $8.05$                 $27$                  $20$                $7.8\times 10^{-6}$                        $3.4\times 10^{12}$                         $2.6\times 10^{12}$              $1.8\times 10^{22}$          $4.4\times 10^{-22}$        $3.3\times 10^{-22}$
              $$                       $\tau\bar{\tau}$                $9.05$                 $28$                  $18$                $1.5\times 10^{-4}$                        $1.9\times 10^{11}$                         $1.2\times 10^{11}$               $2\times 10^{22}$           $1.9\times 10^{-22}$        $1.2\times 10^{-22}$
              $$                       $\mu^{+}\mu^{-}$                $9.05$                 $28$                  $18$                 $3\times 10^{-4}$                         $9.3\times 10^{10}$                         $5.9\times 10^{10}$               $2\times 10^{22}$           $1.9\times 10^{-22}$        $1.2\times 10^{-22}$
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $8.15$                 $27$                  $21$                $1.1\times 10^{-3}$                        $2.6\times 10^{10}$                          $2\times 10^{10}$               $1.8\times 10^{22}$          $4.5\times 10^{-23}$        $3.5\times 10^{-23}$
                                                                                                                                                                                                                                                                                                                        
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
       \[-0.1in\] $1500$                  $b\bar{b}$                   $8.05$                 $27$                  $20$                $1.4\times 10^{-6}$                         $2\times 10^{13}$                          $1.5\times 10^{13}$              $1.8\times 10^{22}$          $2.5\times 10^{-21}$        $1.9\times 10^{-21}$
              $$                         $W^{+}W^{-}$                  $8.15$                 $27$                  $21$                $1.4\times 10^{-5}$                        $1.9\times 10^{12}$                         $1.5\times 10^{12}$              $1.8\times 10^{22}$          $4.9\times 10^{-22}$        $3.8\times 10^{-22}$
              $$                       $\tau\bar{\tau}$                $8.05$                 $27$                  $20$                $2.8\times 10^{-4}$                        $9.8\times 10^{10}$                         $7.3\times 10^{10}$              $1.8\times 10^{22}$          $2.4\times 10^{-22}$        $1.8\times 10^{-22}$
              $$                       $\mu^{+}\mu^{-}$                $8.05$                 $27$                  $20$                $5.2\times 10^{-4}$                        $5.2\times 10^{10}$                         $3.9\times 10^{10}$              $1.8\times 10^{22}$          $2.4\times 10^{-22}$        $1.8\times 10^{-22}$
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $10.1$                 $30$                  $18$                $1.9\times 10^{-3}$                        $1.5\times 10^{10}$                         $9.3\times 10^{09}$              $2.2\times 10^{22}$          $4.1\times 10^{-23}$        $2.5\times 10^{-23}$
                                                                                                                                                                                                                                                                                                                        
          \[-0.1in\]                                                                                                                                                                                                                                                                                                    
       \[-0.1in\] $2000$                  $b\bar{b}$                   $8.05$                 $27$                  $20$                $2.1\times 10^{-6}$                        $1.3\times 10^{13}$                         $9.3\times 10^{12}$              $1.8\times 10^{22}$          $2.6\times 10^{-21}$         $2\times 10^{-21}$
              $$                         $W^{+}W^{-}$                  $8.75$                 $28$                  $18$                 $2\times 10^{-5}$                         $1.4\times 10^{12}$                         $9.2\times 10^{11}$              $1.9\times 10^{22}$          $5.6\times 10^{-22}$        $3.6\times 10^{-22}$
              $$                       $\tau\bar{\tau}$                $8.15$                 $27$                  $21$                $4.1\times 10^{-4}$                        $6.6\times 10^{10}$                         $5.1\times 10^{10}$              $1.8\times 10^{22}$          $2.7\times 10^{-22}$        $2.1\times 10^{-22}$
              $$                       $\mu^{+}\mu^{-}$                $8.15$                 $27$                  $21$                $7.4\times 10^{-4}$                        $3.6\times 10^{10}$                         $2.8\times 10^{10}$              $1.8\times 10^{22}$          $2.7\times 10^{-22}$        $2.1\times 10^{-22}$
              $$               $\nu_{\alpha}\bar{\nu}_{\alpha}$        $8.75$                 $28$                  $18$                $1.9\times 10^{-3}$                        $1.5\times 10^{10}$                         $9.5\times 10^{09}$              $1.9\times 10^{22}$           $7\times 10^{-23}$         $4.5\times 10^{-23}$
  --------------------------- ---------------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -----------------------

  --------------------------- ---------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -------------------------------
                                                                                                                                                                                                                                                                                                                  
   \[-0.1in\] $\rm M_{WIMP}$            Channel                $\rm \Psi$      $\rm \bar{\mu}^{90\%}$   $\rm \mu^{90\%}$   $\rm \bar{A}_{eff}(M_{\rm WIMP})$   $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$   $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$       $\rm J-Factor$        $\rm \overline{<\sigma_{A}v>}$        $\rm <\sigma_{A}v>$
                                                                                                                                 $\rm \times T_{eff}$                                                                                                                                                             
          $\rm (GeV)$                                       ($\rm ^{\circ}$)                                                        ($\rm m^2.yr$)                         ($\rm km^{-2}.yr^{-1}$)                     ($\rm km^{-2}.yr^{-1}$)          ($\rm GeV^{2}.cm^{-5}$)       ($\rm cm^{3}.s^{-1}$)            ($\rm cm^{3}.s^{-1}$)
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
        \[-0.1in\] $25$                $b\bar{b}$                $7.05$                 $13$                  $14$               $3.1\times 10^{-13}$                        $4.1\times 10^{19}$                         $4.4\times 10^{19}$              $1.6\times 10^{22}$          $6.8\times 10^{-18}$            $7.3\times 10^{-18}$
              $$                    $\tau\bar{\tau}$             $7.05$                 $13$                  $14$               $5.7\times 10^{-10}$                        $2.2\times 10^{16}$                         $2.4\times 10^{16}$              $1.6\times 10^{22}$          $2.1\times 10^{-20}$            $2.2\times 10^{-20}$
              $$                    $\mu^{+}\mu^{-}$             $7.05$                 $13$                  $14$                $1.6\times 10^{-9}$                        $7.9\times 10^{15}$                         $8.4\times 10^{15}$              $1.6\times 10^{22}$          $1.9\times 10^{-20}$             $2\times 10^{-20}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $7.05$                 $13$                  $14$                $1.8\times 10^{-8}$                         $7\times 10^{14}$                          $7.5\times 10^{14}$              $1.6\times 10^{22}$          $2.2\times 10^{-21}$            $2.4\times 10^{-21}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
        \[-0.1in\] $50$                $b\bar{b}$                $14.6$                 $28$                  $36$                $4\times 10^{-11}$                         $6.9\times 10^{17}$                          $9\times 10^{17}$                $3\times 10^{22}$           $1.9\times 10^{-19}$            $2.5\times 10^{-19}$
              $$                    $\tau\bar{\tau}$             $3.15$                 $6$                  $7.8$                $8.4\times 10^{-9}$                        $7.2\times 10^{14}$                         $9.3\times 10^{14}$              $7.5\times 10^{21}$          $5.7\times 10^{-21}$            $7.5\times 10^{-21}$
              $$                    $\mu^{+}\mu^{-}$             $3.15$                 $6$                  $7.8$                $2.2\times 10^{-8}$                        $2.7\times 10^{14}$                         $3.5\times 10^{14}$              $7.5\times 10^{21}$          $5.5\times 10^{-21}$            $7.1\times 10^{-21}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $2.45$                 $5$                  $9.5$                $5.2\times 10^{-7}$                        $9.7\times 10^{12}$                         $1.8\times 10^{13}$              $5.9\times 10^{21}$          $3.3\times 10^{-22}$            $6.3\times 10^{-22}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
        \[-0.1in\] $90$                $b\bar{b}$                $2.55$                $5.2$                  $9$                $2.3\times 10^{-10}$                        $2.2\times 10^{16}$                         $3.9\times 10^{16}$              $6.2\times 10^{21}$           $8\times 10^{-20}$             $1.4\times 10^{-19}$
              $$                      $W^{+}W^{-}$               $2.55$                $5.2$                  $9$                 $1.2\times 10^{-8}$                        $4.5\times 10^{14}$                         $7.8\times 10^{14}$              $6.2\times 10^{21}$          $1.9\times 10^{-21}$            $3.3\times 10^{-21}$
              $$                    $\tau\bar{\tau}$             $2.75$                $5.3$                 $9.9$                 $3\times 10^{-7}$                         $1.8\times 10^{13}$                         $3.3\times 10^{13}$              $6.7\times 10^{21}$          $5.3\times 10^{-22}$            $9.8\times 10^{-22}$
              $$                    $\mu^{+}\mu^{-}$             $2.75$                $5.3$                 $9.9$                $8.2\times 10^{-7}$                        $6.5\times 10^{12}$                         $1.2\times 10^{13}$              $6.7\times 10^{21}$          $4.9\times 10^{-22}$             $9\times 10^{-22}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.85$                $4.2$                 $3.5$                $1.2\times 10^{-5}$                        $3.4\times 10^{11}$                         $2.9\times 10^{11}$              $4.5\times 10^{21}$           $5\times 10^{-23}$             $4.2\times 10^{-23}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $100$                $b\bar{b}$                $2.55$                $5.2$                  $9$                 $4\times 10^{-10}$                         $1.3\times 10^{16}$                         $2.3\times 10^{16}$              $6.2\times 10^{21}$          $5.6\times 10^{-20}$            $9.7\times 10^{-20}$
              $$                      $W^{+}W^{-}$               $2.75$                $5.3$                 $9.9$                $2.4\times 10^{-8}$                        $2.2\times 10^{14}$                         $4.2\times 10^{14}$              $6.7\times 10^{21}$          $1.1\times 10^{-21}$             $2\times 10^{-21}$
              $$                    $\tau\bar{\tau}$             $2.75$                $5.3$                 $9.9$                $5.2\times 10^{-7}$                         $1\times 10^{13}$                          $1.9\times 10^{13}$              $6.7\times 10^{21}$          $3.7\times 10^{-22}$            $6.9\times 10^{-22}$
              $$                    $\mu^{+}\mu^{-}$             $2.75$                $5.3$                 $9.9$                $1.4\times 10^{-6}$                        $3.8\times 10^{12}$                          $7\times 10^{12}$               $6.7\times 10^{21}$          $3.5\times 10^{-22}$            $6.5\times 10^{-22}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.85$                $4.2$                 $3.5$                $2.3\times 10^{-5}$                        $1.8\times 10^{11}$                     $\mathbf{1.5\times 10^{11}}$         $4.5\times 10^{21}$          $3.3\times 10^{-23}$        $\mathbf{2.7\times 10^{-23}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $150$                $b\bar{b}$                $2.75$                $5.3$                 $9.9$                $3.3\times 10^{-9}$                        $1.6\times 10^{15}$                          $3\times 10^{15}$               $6.7\times 10^{21}$          $1.3\times 10^{-20}$            $2.3\times 10^{-20}$
              $$                      $W^{+}W^{-}$               $3.05$                $5.6$                  $9$                 $2.3\times 10^{-7}$                        $2.4\times 10^{13}$                     $\mathbf{3.9\times 10^{13}}$         $7.3\times 10^{21}$          $2.4\times 10^{-22}$        $\mathbf{3.8\times 10^{-22}}$
              $$                    $\tau\bar{\tau}$             $2.75$                $5.3$                 $9.9$                $3.1\times 10^{-6}$                        $1.7\times 10^{12}$                         $3.2\times 10^{12}$              $6.7\times 10^{21}$          $1.4\times 10^{-22}$            $2.6\times 10^{-22}$
              $$                    $\mu^{+}\mu^{-}$             $2.75$                $5.3$                 $9.9$                $8.6\times 10^{-6}$                        $6.2\times 10^{11}$                         $1.2\times 10^{12}$              $6.7\times 10^{21}$          $1.2\times 10^{-22}$            $2.3\times 10^{-22}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.55$                $3.8$                 $2.7$                $7.4\times 10^{-5}$                        $5.2\times 10^{10}$                     $\mathbf{3.6\times 10^{10}}$         $3.8\times 10^{21}$          $2.4\times 10^{-23}$        $\mathbf{1.7\times 10^{-23}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $180$                $b\bar{b}$                $2.75$                $5.3$                 $9.9$                $6.1\times 10^{-9}$                        $8.8\times 10^{14}$                         $1.6\times 10^{15}$              $6.7\times 10^{21}$          $9.2\times 10^{-21}$            $1.7\times 10^{-20}$
              $$                      $W^{+}W^{-}$               $3.05$                $5.6$                  $9$                 $4.4\times 10^{-7}$                        $1.3\times 10^{13}$                      $\mathbf{2\times 10^{13}}$          $7.3\times 10^{21}$          $1.8\times 10^{-22}$        $\mathbf{2.8\times 10^{-22}}$
              $$                    $\tau\bar{\tau}$             $3.05$                $5.6$                  $9$                 $5.7\times 10^{-6}$                         $1\times 10^{12}$                      $\mathbf{1.6\times 10^{12}}$         $7.3\times 10^{21}$           $1\times 10^{-22}$         $\mathbf{1.7\times 10^{-22}}$
              $$                    $\mu^{+}\mu^{-}$             $3.05$                $5.6$                  $9$                 $1.5\times 10^{-5}$                        $3.7\times 10^{11}$                     $\mathbf{5.9\times 10^{11}}$         $7.3\times 10^{21}$          $9.5\times 10^{-23}$        $\mathbf{1.5\times 10^{-22}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $2.85$                $5.4$                 $9.7$                $1.8\times 10^{-4}$                         $3\times 10^{10}$                      $\mathbf{5.5\times 10^{10}}$         $6.9\times 10^{21}$           $1\times 10^{-23}$         $\mathbf{1.9\times 10^{-23}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $200$                $b\bar{b}$                $2.75$                $5.3$                 $9.9$                $9.3\times 10^{-9}$                        $5.7\times 10^{14}$                         $1.1\times 10^{15}$              $6.7\times 10^{21}$          $7.2\times 10^{-21}$            $1.3\times 10^{-20}$
              $$                      $W^{+}W^{-}$               $3.05$                $5.6$                  $9$                 $7.1\times 10^{-7}$                         $8\times 10^{12}$                      $\mathbf{1.3\times 10^{13}}$         $7.3\times 10^{21}$          $1.3\times 10^{-22}$        $\mathbf{2.1\times 10^{-22}}$
              $$                    $\tau\bar{\tau}$             $3.05$                $5.6$                  $9$                 $8.7\times 10^{-6}$                        $6.5\times 10^{11}$                      $\mathbf{1\times 10^{12}}$          $7.3\times 10^{21}$          $8.3\times 10^{-23}$        $\mathbf{1.3\times 10^{-22}}$
              $$                    $\mu^{+}\mu^{-}$             $3.05$                $5.6$                  $9$                 $2.3\times 10^{-5}$                        $2.4\times 10^{11}$                     $\mathbf{3.9\times 10^{11}}$         $7.3\times 10^{21}$          $7.6\times 10^{-23}$        $\mathbf{1.2\times 10^{-22}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $3.05$                $5.6$                  $9$                 $2.8\times 10^{-4}$                         $2\times 10^{10}$                      $\mathbf{3.3\times 10^{10}}$         $7.3\times 10^{21}$          $7.7\times 10^{-24}$        $\mathbf{1.2\times 10^{-23}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $260$                $b\bar{b}$                $2.75$                $5.3$                 $9.9$                $2.9\times 10^{-8}$                        $1.8\times 10^{14}$                         $3.4\times 10^{14}$              $6.7\times 10^{21}$          $3.5\times 10^{-21}$            $6.5\times 10^{-21}$
              $$                      $W^{+}W^{-}$               $2.25$                $4.7$                  $9$                 $1.6\times 10^{-6}$                         $3\times 10^{12}$                      $\mathbf{5.7\times 10^{12}}$         $5.4\times 10^{21}$          $1.1\times 10^{-22}$        $\mathbf{2.1\times 10^{-22}}$
              $$                    $\tau\bar{\tau}$             $2.85$                $5.4$                 $9.7$                $2.2\times 10^{-5}$                        $2.4\times 10^{11}$                     $\mathbf{4.3\times 10^{11}}$         $6.9\times 10^{21}$          $5.5\times 10^{-23}$        $\mathbf{9.9\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $2.85$                $5.4$                 $9.7$                $5.9\times 10^{-5}$                        $9.1\times 10^{10}$                     $\mathbf{1.6\times 10^{11}}$         $6.9\times 10^{21}$          $4.9\times 10^{-23}$        $\mathbf{8.9\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.85$                $4.2$                 $3.5$                 $4\times 10^{-4}$                          $1\times 10^{10}$                      $\mathbf{8.7\times 10^{9}}$          $4.5\times 10^{21}$          $9.6\times 10^{-24}$        $\mathbf{8.1\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $360$                $b\bar{b}$                $2.85$                $5.4$                 $9.7$                $1.1\times 10^{-7}$                        $5.1\times 10^{13}$                     $\mathbf{9.2\times 10^{13}}$         $6.9\times 10^{21}$          $1.6\times 10^{-21}$        $\mathbf{2.9\times 10^{-21}}$
              $$                      $W^{+}W^{-}$               $1.85$                $4.2$                 $3.5$                $3.8\times 10^{-6}$                        $1.1\times 10^{12}$                     $\mathbf{9.2\times 10^{11}}$         $4.5\times 10^{21}$          $8.9\times 10^{-23}$        $\mathbf{7.5\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.85$                $4.2$                 $3.5$                 $5\times 10^{-5}$                         $8.3\times 10^{10}$                      $\mathbf{7\times 10^{10}}$          $4.5\times 10^{21}$          $5.4\times 10^{-23}$        $\mathbf{4.5\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.85$                $4.2$                 $3.5$                $1.3\times 10^{-4}$                        $3.2\times 10^{10}$                     $\mathbf{2.7\times 10^{10}}$         $4.5\times 10^{21}$          $4.9\times 10^{-23}$        $\mathbf{4.1\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.85$                $4.2$                 $3.5$                $8.8\times 10^{-4}$                        $4.7\times 10^{9}$                       $\mathbf{4\times 10^{9}}$           $4.5\times 10^{21}$          $7.2\times 10^{-24}$         $\mathbf{6\times 10^{-24}}$
  --------------------------- ---------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -------------------------------

  --------------------------- ---------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -------------------------------
                                                                                                                                                                                                                                                                                                                  
   \[-0.1in\] $\rm M_{WIMP}$            Channel                $\rm \Psi$      $\rm \bar{\mu}^{90\%}$   $\rm \mu^{90\%}$   $\rm \bar{A}_{eff}(M_{\rm WIMP})$   $\rm \overline{\Phi}_{\nu_{\mu}+\bar{\nu}_\mu}$   $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$       $\rm J-Factor$        $\rm \overline{<\sigma_{A}v>}$        $\rm <\sigma_{A}v>$
                                                                                                                                 $\rm \times T_{eff}$                                                                                                                                                             
          $\rm (GeV)$                                       ($\rm ^{\circ}$)                                                        ($\rm m^2.yr$)                         ($\rm km^{-2}.yr^{-1}$)                     ($\rm km^{-2}.yr^{-1}$)          ($\rm GeV^{2}.cm^{-5}$)       ($\rm cm^{3}.s^{-1}$)            ($\rm cm^{3}.s^{-1}$)
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $500$                $b\bar{b}$                $2.85$                $5.4$                 $9.7$                $2.3\times 10^{-7}$                        $2.4\times 10^{13}$                     $\mathbf{4.3\times 10^{13}}$         $6.9\times 10^{21}$          $1.3\times 10^{-21}$        $\mathbf{2.4\times 10^{-21}}$
              $$                      $W^{+}W^{-}$               $1.85$                $4.2$                 $3.5$                $7.1\times 10^{-6}$                        $5.9\times 10^{11}$                      $\mathbf{5\times 10^{11}}$          $4.5\times 10^{21}$          $8.7\times 10^{-23}$        $\mathbf{7.4\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.85$                $4.2$                 $3.5$                $9.7\times 10^{-5}$                        $4.3\times 10^{10}$                     $\mathbf{3.6\times 10^{10}}$         $4.5\times 10^{21}$          $5.2\times 10^{-23}$        $\mathbf{4.4\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.85$                $4.2$                 $3.5$                $2.4\times 10^{-4}$                        $1.8\times 10^{10}$                     $\mathbf{1.5\times 10^{10}}$         $4.5\times 10^{21}$          $4.7\times 10^{-23}$         $\mathbf{4\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.05$                $2.9$                  $2$                  $1\times 10^{-3}$                         $2.8\times 10^{9}$                       $\mathbf{2\times 10^{9}}$           $2.5\times 10^{21}$          $1.2\times 10^{-23}$        $\mathbf{8.6\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $750$                $b\bar{b}$                $1.85$                $4.2$                 $3.5$                $6.3\times 10^{-7}$                        $6.6\times 10^{12}$                     $\mathbf{5.6\times 10^{12}}$         $4.5\times 10^{21}$          $1.1\times 10^{-21}$        $\mathbf{9.1\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $1.05$                $2.9$                  $2$                 $1.3\times 10^{-5}$                        $2.3\times 10^{11}$                     $\mathbf{1.6\times 10^{11}}$         $2.5\times 10^{21}$          $1.2\times 10^{-22}$        $\mathbf{8.6\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.85$                $4.2$                 $3.5$                 $3\times 10^{-4}$                         $1.4\times 10^{10}$                     $\mathbf{1.2\times 10^{10}}$         $4.5\times 10^{21}$          $3.7\times 10^{-23}$        $\mathbf{3.1\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.85$                $4.2$                 $3.5$                $6.8\times 10^{-4}$                        $6.1\times 10^{9}$                      $\mathbf{5.1\times 10^{9}}$          $4.5\times 10^{21}$          $3.4\times 10^{-23}$        $\mathbf{2.8\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.05$                $2.9$                  $2$                  $2\times 10^{-3}$                         $1.4\times 10^{9}$                      $\mathbf{9.9\times 10^{8}}$          $2.5\times 10^{21}$          $1.2\times 10^{-23}$        $\mathbf{8.1\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $1000$               $b\bar{b}$                $1.85$                $4.2$                 $3.5$                $1.5\times 10^{-6}$                        $2.8\times 10^{12}$                     $\mathbf{2.4\times 10^{12}}$         $4.5\times 10^{21}$          $7.5\times 10^{-22}$        $\mathbf{6.3\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $1.05$                $2.9$                  $2$                 $2.7\times 10^{-5}$                        $1.1\times 10^{11}$                     $\mathbf{7.4\times 10^{10}}$         $2.5\times 10^{21}$          $9.7\times 10^{-23}$        $\mathbf{6.7\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.05$                $2.9$                  $2$                 $4.4\times 10^{-4}$                        $6.5\times 10^{9}$                      $\mathbf{4.5\times 10^{9}}$          $2.5\times 10^{21}$          $5.3\times 10^{-23}$        $\mathbf{3.7\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.05$                $2.9$                  $2$                 $9.7\times 10^{-4}$                         $3\times 10^{9}$                       $\mathbf{2.1\times 10^{9}}$          $2.5\times 10^{21}$          $4.8\times 10^{-23}$        $\mathbf{3.4\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.05$                $2.9$                  $2$                 $4.4\times 10^{-3}$                        $6.6\times 10^{8}$                      $\mathbf{4.6\times 10^{8}}$          $2.5\times 10^{21}$          $8.3\times 10^{-24}$        $\mathbf{5.8\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $1500$               $b\bar{b}$                $1.85$                $4.2$                 $3.5$                $3.4\times 10^{-6}$                        $1.2\times 10^{12}$                      $\mathbf{1\times 10^{12}}$          $4.5\times 10^{21}$          $6.4\times 10^{-22}$        $\mathbf{5.4\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $1.05$                $2.9$                  $2$                 $5.2\times 10^{-5}$                        $5.6\times 10^{10}$                     $\mathbf{3.9\times 10^{10}}$         $2.5\times 10^{21}$           $1\times 10^{-22}$         $7\mathbf{.1\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.05$                $2.9$                  $2$                 $9.6\times 10^{-4}$                         $3\times 10^{9}$                       $\mathbf{2.1\times 10^{9}}$          $2.5\times 10^{21}$          $5.2\times 10^{-23}$        $\mathbf{3.6\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.05$                $2.9$                  $2$                  $2\times 10^{-3}$                         $1.5\times 10^{9}$                       $\mathbf{1\times 10^{9}}$           $2.5\times 10^{21}$          $4.8\times 10^{-23}$        $\mathbf{3.3\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $1.05$                $2.9$                  $2$                 $6.5\times 10^{-3}$                        $4.4\times 10^{8}$                      $\mathbf{3.1\times 10^{8}}$          $2.5\times 10^{21}$           $1\times 10^{-23}$         $\mathbf{7.2\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $2000$               $b\bar{b}$                $1.85$                $4.2$                 $3.5$                 $7\times 10^{-6}$                          $6\times 10^{11}$                       $\mathbf{5\times 10^{11}}$          $4.5\times 10^{21}$           $5\times 10^{-22}$         $\mathbf{4.2\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $0.95$                $2.7$                 $2.2$                $9.2\times 10^{-5}$                        $2.9\times 10^{10}$                     $\mathbf{2.4\times 10^{10}}$         $2.3\times 10^{21}$          $9.8\times 10^{-23}$         $\mathbf{8\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $1.05$                $2.9$                  $2$                 $1.9\times 10^{-3}$                        $1.5\times 10^{9}$                       $\mathbf{1\times 10^{9}}$           $2.5\times 10^{21}$          $4.4\times 10^{-23}$         $\mathbf{3\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $1.05$                $2.9$                  $2$                 $3.8\times 10^{-3}$                        $7.5\times 10^{8}$                      $\mathbf{5.2\times 10^{8}}$          $2.5\times 10^{21}$          $4.1\times 10^{-23}$        $\mathbf{2.8\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $0.95$                $2.7$                 $2.2$                $1.1\times 10^{-3}$                        $2.4\times 10^{8}$                      $\mathbf{1.9\times 10^{8}}$          $2.3\times 10^{21}$          $9.5\times 10^{-24}$        $\mathbf{7.7\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $3000$               $b\bar{b}$                $1.05$                $2.9$                  $2$                 $1.5\times 10^{-5}$                         $2\times 10^{11}$                      $\mathbf{1.4\times 10^{11}}$         $2.5\times 10^{21}$          $5.8\times 10^{-22}$         $\mathbf{4\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $0.95$                $2.7$                 $2.2$                $2.4\times 10^{-4}$                        $1.1\times 10^{10}$                     $\mathbf{9.1\times 10^{9}}$          $2.3\times 10^{21}$          $7.5\times 10^{-23}$        $\mathbf{6.1\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $0.95$                $2.7$                 $2.2$                $5.2\times 10^{-3}$                        $5.2\times 10^{8}$                      $\mathbf{4.2\times 10^{8}}$          $2.3\times 10^{21}$          $3.6\times 10^{-23}$        $\mathbf{2.9\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $0.95$                $2.7$                 $2.2$                $9.6\times 10^{-3}$                        $2.8\times 10^{8}$                      $\mathbf{2.3\times 10^{8}}$          $2.3\times 10^{21}$          $3.4\times 10^{-23}$        $\mathbf{2.8\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $0.95$                $2.7$                 $2.2$                $2.8\times 10^{-3}$                        $9.5\times 10^{7}$                      $\mathbf{7.7\times 10^{7}}$          $2.3\times 10^{21}$          $7.3\times 10^{-24}$        $\mathbf{5.9\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
       \[-0.1in\] $5000$               $b\bar{b}$                $1.05$                $2.9$                  $2$                 $5.7\times 10^{-5}$                         $5\times 10^{10}$                      $\mathbf{3.5\times 10^{10}}$         $2.5\times 10^{21}$          $3.5\times 10^{-22}$        $\mathbf{2.4\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $0.95$                $2.7$                 $2.2$                $7.4\times 10^{-4}$                        $3.7\times 10^{9}$                       $\mathbf{3\times 10^{9}}$           $2.3\times 10^{21}$          $5.8\times 10^{-23}$        $\mathbf{4.7\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $0.95$                $2.7$                 $2.2$                $1.9\times 10^{-2}$                        $1.4\times 10^{8}$                      $\mathbf{1.1\times 10^{8}}$          $2.3\times 10^{21}$          $2.5\times 10^{-23}$         $\mathbf{2\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $0.95$                $2.7$                 $2.2$                $3.4\times 10^{-2}$                        $8.1\times 10^{7}$                      $\mathbf{6.5\times 10^{7}}$          $2.3\times 10^{21}$          $2.4\times 10^{-23}$        $\mathbf{1.9\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $0.95$                $2.7$                 $2.2$                $7.1\times 10^{-2}$                        $3.8\times 10^{7}$                      $\mathbf{3.1\times 10^{7}}$          $2.3\times 10^{21}$          $6.6\times 10^{-24}$        $\mathbf{5.3\times 10^{-24}}$
                                                                                                                                                                                                                                                                                                                  
          \[-0.1in\]                                                                                                                                                                                                                                                                                              
      \[-0.1in\] $10000$               $b\bar{b}$                $0.95$                $2.7$                 $2.2$                $3.3\times 10^{-4}$                        $8.2\times 10^{9}$                      $\mathbf{6.6\times 10^{9}}$          $2.3\times 10^{21}$           $2\times 10^{-22}$         $\mathbf{1.6\times 10^{-22}}$
              $$                      $W^{+}W^{-}$               $0.95$                $2.7$                 $2.2$                $3.2\times 10^{-3}$                        $8.4\times 10^{8}$                      $\mathbf{6.8\times 10^{8}}$          $2.3\times 10^{21}$          $4.3\times 10^{-23}$        $\mathbf{3.5\times 10^{-23}}$
              $$                    $\tau\bar{\tau}$             $0.95$                $2.7$                 $2.2$                 $1\times 10^{-1}$                         $2.6\times 10^{7}$                      $\mathbf{2.1\times 10^{7}}$          $2.3\times 10^{21}$          $1.7\times 10^{-23}$        $\mathbf{1.4\times 10^{-23}}$
              $$                    $\mu^{+}\mu^{-}$             $0.95$                $2.7$                 $2.2$                $1.6\times 10^{-1}$                        $1.7\times 10^{7}$                      $\mathbf{1.4\times 10^{7}}$          $2.3\times 10^{21}$          $1.7\times 10^{-23}$        $\mathbf{1.4\times 10^{-23}}$
              $$               $\nu_{\mu}\bar{\nu}_{\mu}$        $0.95$                $2.7$                 $2.2$                $2.6\times 10^{-1}$                         $1\times 10^{7}$                       $\mathbf{8.5\times 10^{6}}$          $2.3\times 10^{21}$          $5.6\times 10^{-24}$        $\mathbf{4.5\times 10^{-24}}$
  --------------------------- ---------------------------- ------------------ ------------------------ ------------------ ----------------------------------- ------------------------------------------------- -------------------------------------- ------------------------- -------------------------------- -------------------------------
