---
abstract: 'Single top quark production through weak interactions is considered to be an important source of charged Higgs in the Minimal Super Symmetric Standard Model. In the s-channel single top production having largest cross-section may appear as a propagator in the form of heavy resonance state decaying to a pair of top and bottom quark. The process under investigation is $pp \rightarrow H^{\pm}\rightarrow tb \rightarrow b\bar{b}W^{\pm} \rightarrow b\bar{b}\tau^{\pm} \nu_{\tau}$, where top quark exclusively decays into a pair of bottom quark and W boson while W boson subsequently decays to $\tau$ jet and neutrino. So the final state is characterized by the presence of two b jets, hadronic $\tau$ decay and missing transverse energy. Within the presence of QCD multijet and electroweak background events at LHC, it has been demonstrated that the charged Higgs signal observability is possible within the available MSSM parameter space (tan$\beta$, $m_{H^{\pm}})$ respecting all experimental and theoretical constraints. In order to show the observability potential of charged Higgs, the exclusion curves at 95$\%$ confidence level and 5$\sigma$ contours are plotted at different integrated luminosities with $\sqrt{s}=$14 TeV.'
author:
- Ijaz Ahmed
- Nadia Kausar
- Mahpara Ghazanfar
title: 'Possibility of observing charged Higgs in the single top production via its $\tau$ lepton decay at LHC'
---

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

It has been seen that the discovery of the neutral scalar particle at Large Hadron Collider (LHC) with a measured mass of 125 GeV approximately by the CMS and ATLAS experiments [@Higgs_Discovery1; @Higgs_Discovery2; @Higgs_Discovery3] proved that the Standard Model (SM) predictions are well compatible with the measured values. However, there are very convincing evidences from experimental signatures and theoretical calculations that SM needs to overlooked by some other dynamical models in order to deal with the issues regarding neutrino masses, dark matter and the hierarchy problem. Several attempts were made to extend the SM scalar sector which was finalized in the form of Minimal Supersymmetric Standard Model (MSSM) [@mssm1; @mssm2; @mssm3], Two Higgs Doublet Model (THDM) [@2hdm1; @2hdm2; @2hdm3; @2hdm4] and several others e.g.,[@nmssm1; @nmssm2]. Several among these physics models with extended Higgs sector are testable at LHC. In this study the MSSM framework is used as a benchmark which leads to five physical scalar Higgs bosons: light Higgs boson, h and heavy Higgs boson with CP-even, H, a CP-odd Higgs boson, A and two charged Higgs bosons, $H^{\pm}$. The observability of these new Higgs particles would be a clear indication that the extended Higgs sector may be a source of Electroweak Symmetry Breaking.\
Apart from other Higgs particles, the charged Higgs has significantly interesting features and challenging at particle colliders, because it provides unique signature due to having charge which provides different kinds of signatures in terms of their interactions and decay properties from other neutral Higgs bosons. If $m_{H^{\pm}} < m_{t} - m_{b}$, the dominant mechanism for charged Higgs production is via top quark decay: $t \rightarrow bH^{\pm}$. Therefore the charged Higgs produce preferably via $t\bar{t}$ production. The focus of this study at Tevatron, LEP and LHC was mostly performed in the domain of low mass charged Higgs, where charged Higgs predominantly decays into a pair of $\tau$ lepton and neutrino at tan$\beta > 5$ [@feynhiggs1; @feynhiggs2; @feynhiggs3] or into pair of charm and strange jets $(H^{\pm}\rightarrow cs)$. If $m_{H^{\pm}} > m_{t} + m_{b}$ the top quark associated production $H^{\pm}tb$ is the dominant production, where charged Higgs prefer to decays in to a pair of top and bottom quark, i.e., $H^{\pm}\rightarrow tb$. This decay is allowed kinematically and interesting channel for heavy charged Higgs analysis. However, identification of the final state particles in the $t\bar{t}b\bar{b}$ process and the presence of the huge irreducible background becomes hard to remove. That is why the early analyses usually focus on the decays like $H^{\pm}\rightarrow \tau \nu$ and $H^{\pm}\rightarrow cs$ in order to exploit the advantage of suppressed backgrounds by using $\tau$-identification package.\
In the past few years, the charged Higgs study through single top production processes is also proposed at LHC in both light and heavy mass regions resulted quite promising agreements for charged Higgs discovery. Currently, there are just a few analyses where single top acts as a source of charged Higgs boson, e.g., the t-channel single top production in light charged Higgs study through top quark decay $(pp\rightarrow tq\rightarrow qbH^{\pm}\rightarrow qb\tau\nu)$, where $\tau$ lepton decays hadronically [@st1] or leptonicaly [@SingleTop_CH], the s-channel single top production in heavy charged Higgs analysis in the leptonic final state $(pp\rightarrow tb\rightarrow bbW^{\pm}\rightarrow bbl^{\pm}\nu_{l})$ [@st2] is studied. The analysis based on off-diagonal coupling contribution in the production cross-section of s-channel charged Higgs also studied that enhance the total cross-section a factor of 2.7 [@myplb]. Similarly in [@st3] the t-channel single top is considered as a source of charged Higgs exchange, through being observable at very high integrated luminosities and high tan$\beta$ values. Recently, the fully hadronic final state in the s-channel charged Higgs is studied to investigate the potential of the charged Higgs discovery in all jets final state [@ijazepjc]. This paper will follow the continuation of the same process but with $\tau$-jet final state while applying $\tau$-jet identification algorithm to find an alternate way for charged Higgs reconstruction. The objective of this article is the reconstruction of charged Higgs invariant mass in s$-$channel single top in chain $(pp\rightarrow tb\rightarrow bbW^{\pm}\rightarrow b\bar{b}\tau^{\pm}\nu_{\tau})$, where two b-jets and one $\tau$-jet along with missing transverse energy is found at LHC. This work is accomplished using Monte Carlo generators performing hadronization and fragmentation processes and concentrating on the charged Higgs mass in the available region of the parameter space not yet excluded, +i.e., $200 <m_{H^{\pm}}<400$ GeV. The exclusion bounds and discovery reach will be explored in the context of the CP-conserving 2HDM Type II which is also called MSSM. There are some background processes like W+jets and QCD multi jets that could make it a challenging analysis. However, by applying some kinematic cuts wisely, they can be well under controlled.\
The current experimental constraints on charged Higgs searches have been performed, at colliders like LEP [@lepexclusion1], Tevatron [@cdf3] and LHC using the ATLAS [@CHtaunu8TeVATLAS; @CHIndirect8TeVATLAS; @LightCH7TeVATLAS2; @LightCH7TeVATLAS1] and CMS [@cms2; @cms3] experiments. In the direct and indirect searches the experimental exclusion limits are set by these experiments and can be seen in [@ijazepjc].\
The following sections of the article contains signal and background processes generation which naturally shows interference and even selection procedure where different mass hypotheses are presented for charged Higgs invariant mass reconstruction. A 5 $\sigma$ discovery and exclusion at 95$\%$ Confidence Level (CL) is provided in the accessible regions of MSSM parameter space. The $m_h-max$ scenario with the given parameters: $M_{2}$ = 200 GeV, $M_{\tilde{g}}$ = 800 GeV, $\mu$ = 200 GeV and $M_{SUSY}$ = 1 TeV is used and estimation of all parameters is performed within theoretical framework of MSSM. The given $m_h-max$ scenario is optimized in such a way to define a benchmark point that maximize the upper bound on $m_{h}$ for a fixed $m_{t}$, the soft SUSY breaking parameter $M_{SUSY}$ at a given tan$\beta$. The advantage of using this benchmark point is to maximize the parameter space in $m_{h}$ direction conservative exclusion limits for tan$\beta$.\

Collider Analysis
-----------------

The signal process under study is $pp \rightarrow tb\rightarrow W^{\pm}bb\rightarrow \tau\nu bb$, where the top and bottom quarks are produced through the s-channel charged Higgs mediating as resonance in the single top production process. The $\tau$ lepton is analyzed through its hadronic decay. The main background with same final states arise from processes i.e., $W^{\pm}jj$, $W^{\pm}bb$, $W^{\pm}cc$, single top t-channel, $t\bar{t}$. We study the fully hadronic decay of $\tau$ lepton which are resulted from the W boson decay. The decay widths and cross-sections are extracted as calculated in [@ijazepjc]. The parton density function is provided by LHAPDF 5.9.1 [@lhapdf] with the version CTEQ 6.6. The background process $W^{\pm}jj$, $W^{\pm}bb$, $W^{\pm}cc$ combinely referred as “W + 2jets” are generated with Madgraph 2.3.3 [@madgraph] with a kinematic preselection applied as $E_{T}^{jets}>20$ GeV and $|\eta|<3.0$, while single top t-channel, $t\bar{t}$ samples are produced by PYTHIA 8.1.5.3 [@pythia]. All the signal process are produced with CompHEP 4.5.2 [@comphep]. The output of both these packages in Les Houches Event Format (LHEF) is used by PYTHIA8 for partonic showering, gluon radiation, fragmentation and hadronization. The reconstruction of all jets is performed with the jets clustering algorithm FASTJET 3.1.3 [@fastjet] using anti-kt algorithm [@antikt] and $E_{T}$ recombination scheme. The jet cone size is fixed at $\Delta R=0.4$, where $\Delta R=\sqrt {(\Delta \eta)^{2}+(\Delta \phi)^{2}}$ is jet cone radius, $\phi$ is azimuthal angle and $\eta =-ln$tan$\theta/2$ is pseudorapidity.

Event Selection strategy
------------------------

For the suppression of background events and selection of the signal events, a reasonable and effective understanding of event kinematics is required. The topological and kinematical differences between signal and background events help to apply the selection cuts. The above goals are achieved by plotting the kinematic distributions. The final state topology of the signal process under consideration contains two b-jets and One $\tau$-jet along with missing transverse energy $E_{T}$ as shown in Figure \[diagram\]. All the selection cuts are shown in Table \[selectioncuts\].

![The s-channel single top production via charged Higgs as a signal resonance process with $\tau$ hadronic decays.[]{data-label="diagram"}](diagram.pdf){width="60.00000%"}

The presence of two b-jets in the event is expected to suppress the large “W + 2jets” events. However $\bar{t}t$ will be seen to be main background at the end. The signal consist of a charged Higgs with mass $m_{H}= 200$ GeV and tan$\beta=$ 50 are shown through out the paper. The tan$\beta$ only contributes to the signal cross-section and also it is irrelevant for such distributions that is why the abbreviation used for the signal is “ST20050". This selected $\tan\beta$ and $m_{H^{\pm}}$ value has the highest cross-section. In Figure \[alljets\] jets multiplicity is shown with $E_{T}>20$ GeV and $|\eta|<3$. If the total number of jets are equal to three then the events are selected to perform further processes.

![The jet multiplicity is shown with both signal and background events for a center of mass energy of 14 TeV. .[]{data-label="alljets"}](alljets.pdf){width="60.00000%"}

The b-jet reconstruction with the jet-parton matching algorithm is performed where a jet is tagged to be a b-jet if the $\Delta R$ value between the jet and bottom or charm quarks with $p_{T}>20$ GeV and $|\eta|<3$ is less than 0.4. The efficiency of b-jet identification is assumed to be 40$\%$ while the c-jet mis-tagging rate is assumed to be 10$\%$.

![The multiplicity distribution of b-jets with both signal and background events are shown.[]{data-label="bjets"}](bjetMult.pdf){width="60.00000%"}

        3 jets                        $P_{T} > 20$ GeV, $|\eta| < 3$
  ------------------- ---------------------------------------------------------------
      2 b$-$jets         $P_{T}>20$ GeV, $|\eta|<3$, $\Delta R(jets, b-quark)<0.4$
    Leading tracks                      $\Delta R(jets,tracks)<0.4$
     Isolation cut     $0.05<\Delta R(Leading trks, trks)<0.4$, $P_{T}^{trks}>1$ GeV
       Ratio cut              $P_{T}^{max}/E_{T}^{jet}>0.3$, $P_{T}^{max}>4$
   Top mass windSow                    $150<m_{\tau \nu b}<190$ GeV
   $\Delta \eta$ cut                $\Delta \eta (\tau-jet,b-jet) < 1$
   $\Delta \phi$ cut                   $\Delta \phi (top,b-jet)>2.8$
    Missing $E_{T}$                        $E_{T}^{miss}>20$ GeV

  :  \[selectioncuts\]

The b-jet multiplicity is shown in Figure \[bjets\] from both signal and background events. In each event, two such b-jets are required which fulfill the above criteria. A slight dependence of b-jets distributions can be seen on charged Higgs mass in the signal events. The b-jet production is kinematically suppressed in the heavy charged Higgs production and its decays to top quark because of a smaller phase space availability. In the objects reconstruction procedure, the next phase is the selection of $\tau$-jets through its hadronic decays. In this analysis the algorithm used for $\tau$-jet identification is the standard algorithm developed for LHC experiments. The low charged particle multiplicity is the important signature of $\tau$-jets through hadronic decay, where the highest leading tracks (high $P_{T}$) in the cone around $\tau-$lepton is supposed to be harder than the corresponding tracks in the light jets. Therefore to remove such soft $P_{T}$ tracks from the other light jets, the requirement of the leading tracks with $P_{T}$ $>$ 4 GeV is applied which makes the signal more cleaner and visible. The isolation requirement applied on $\tau$-jets is based on the fact that the $\tau$-jet accommodates only few charged tracks around the central axis of the jet cone. Therefore no charged tracks with $P_{T}$ above a certain threshold ($P_{T}$ $>$ 1 GeV) are expected to be in the annulus defined with cone size $0.05 < \Delta R < 0.4$. This cone annulus is defined around the leading tracks as shown in Figure \[LeadingTPt\] in the $\tau$-jet cone. Since τ$\tau$-jets preferably decay to either one or three charged pions, so one can expect one or three charged tracks in the signal cone defined as $\Delta R < 0.05$ around the leading track. The distribution of the tracks present in the signal cone as well as tracks from background are shown in Figure \[nstracks\]. The number of signal tracks within the defined signal cone are either one or three. So there should be only one jet satisfying all the above requirements of the $\tau$-identification algorithm. On the other hand missing transverse energy is calculated as the negative sum over the particle momenta in horizontal and vertical directions. In Figure \[met\], the missing transverse energy $E_{T}$ distribution is shown in signal and background events. The $E_{miss}^{T}$ and tau-jet components are used for invariant mass reconstruction of W boson four-momentum. The z-component of the neutrino momentum is generally unknown at hadron colliders and thus is constructed by giving a right value for the W mass in the $\tau \nu$ combination, i.e.,$m_{\tau\nu} = $80 GeV. In case If such a solution is not found, $p^{\nu}_{z}$ is set to zero. In rare cases this situation occurs, resulting in a W candidate mass different from the nominal value. Therefore a mass window on the W candidate invariant mass is not necessary to be applied. Now the right b-jet from the top quark decay is found by calculating the top quark invariant mass using W boson four momentum through the $\tau\nu b$ combination and finding the b-jet which gives the closest top quark mass $m_{\tau \nu b}$ to the nominal value, i.e., $m_{top} = 173$ GeV. The $\Delta \eta(\tau$-jet, b-jet) cut which is plotted in Figure \[deltaeta\] helps to find such a true b-jet that is decaying from top quark. The $m_{\tau \nu b}$ distribution is shown in Figure \[topmass\] along with the surviving background processes.\

![Number of tracks in the signal cone of $\tau-$jet candidate in signal as well as background events[]{data-label="nstracks"}](NSTracks.pdf){width="60.00000%"}

![Leading tracks distribution in both signal and background events.[]{data-label="LeadingTPt"}](LeadingTPt.pdf){width="60.00000%"}

![The reconstructed invariant mass distribution of $b\tau\nu$ candidate as signal and dominant background.[]{data-label="topmass"}](topmass.pdf){width="60.00000%"}

A mass window of top quark invariant mass distribution is applied and another b-jet is combined with the top quark candidate to reconstruct the charged Higgs boson candidate invariant mass e.g., $m_{\tau \nu bb}$. A very interesting fact of signal events is that they tend to produce back to back top and bottom quark in opposite direction and this feature appears in the azimuthal plane of the detector. So it is natural to apply cut on the azimuthal angle between top and bottom to make the signal more dominant on top of the background as shown in Figure \[deltaphitb\]. Finally $E_{miss}^{T}$ selection cut is applied. Finally the charged Higgs candidate is reconstructed through $\tau\nu bb$ combination which is correlated as charged Higgs plotted in Figure \[CHmass\] and a cut on missing $E_{T} > 20$ GeV is applied to suppress further background events.\

![The pseudorapidity difference between the tau-jet and bottom quark is shown. []{data-label="deltaeta"}](deltaeta.pdf){width="60.00000%"}

![The difference in azimuthal angle between top and bottom quark is plotted. This cut helps to suppress those events which are not produce back-to-back.[]{data-label="deltaphitb"}](deltaphitb.pdf){width="60.00000%"}

![The missing transverse energy distribution is shown.[]{data-label="met"}](Met.pdf){width="60.00000%"}

![The reconstructed charged Higgs invariant mass distribution is obtained from $bb\tau\nu$ combination. Both signal and background events are normalized to unity to investigate the most probable process[]{data-label="CHmass"}](CHmass.pdf){width="60.00000%"}

![The reconstructed charged Higgs mass distributions at different input mass hypothesis.[]{data-label="chmassall"}](CHmassAll.pdf){width="60.00000%"}

Now all signal and background events are allowed to pass through all above constraints separately and corresponding relative efficiencies are obtained with respect to previous cut as given in Table \[signalcuts\] for signal events and Table \[backgroundcuts\] for background events. The Table \[signalcuts\] corresponds to four charged Higgs mass hypotheses $m_{H^{\pm}}$ = 200, 250, 300, 400 GeV at tan$\beta=$ 50. The charged Higgs with $m_{H^{\pm}}=180$ GeV has not been considered because of having mass close to top quark mass and it becomes hard to observe due to a very limited parameter space available for charged Higgs to decay into top and bottom quarks. Usually this feature results a soft kinematics of the final state particles. The $t\bar{t}$ events may also be treated as a source of charged Higgs bosons, when one of the top quark decays to charged Higgs, i.e., $t\bar{t}\rightarrow H^{\pm}W^{\pm}b\bar{b}\rightarrow \tau \nu jjb\bar{b}$. Such events are unlikely to be selected by the single top selection procedure and rejected badly. Consequently, the $t\bar{t}$ has no sizable contribution in addition of asking 3 jets in each event. The soft QCD multi jet sample is also entirely vanished. Taking $m_{H^{\pm}}$ = 200 GeV as an example the $\sigma \times BR(H^{\pm}\rightarrow tb$) is 5.63 $pb$ and a total efficiency of 0.0018 is obtained which leads to 1013 events at 100 $fb^{-1}$ being the largest statistics out of all signal hypotheses. In principle the invariant mass distribution of top and bottom quark should make the charged Higgs boson mass, however due to several effects e.g., jet energy resolution, false jet combination, mis-identification of jets and errors in their energy and flight directions create the shifts in the peaks of charged Higgs invariant mass around the input mass as can be observed in Figure \[chmassall\].\
Each obtained distribution is normalized with the real number of events at 100 $fb^{-1}$ including selection efficiencies as shown in Figure \[CHmassbins\]. Finally the number of signal and background events, efficiencies corresponding to different charged Higgs mass windows, signal to background ratio ($S/B$) and optimized signal significance ($S/\sqrt{B}$) are shown in Table \[significance\].

![[]{data-label="CHmassbins"}](CHmassbins.pdf){width="60.00000%"}

  -------------------------------- ------------------------- ------------------------- ------------------------- -------------------------
           Selection Cut                    Signal                    Signal                    Signal                    Signal
                                    $M_{H^{\pm}}$ = 200 GeV   $M_{H^{\pm}}$ = 250 GeV   $M_{H^{\pm}}$ = 300 GeV   $M_{H^{\pm}}$ = 400 GeV
       $\sigma$ x BR\[$pb$\]                 5.63                      4.68                      2.73                      0.98
               3 jets                       32$\%$                    25$\%$                   21.7$\%$                  18.5$\%$
              2 b-jets                      42$\%$                    56$\%$                   59.5$\%$                  61.5$\%$
           Leading tracks                  99.6$\%$                  99.8$\%$                  99.9$\%$                  99.9$\%$
           Isolation cut                    $37\%$                   36.7$\%$                  36.6$\%$                  36.6$\%$
             Ratio cut                      25$\%$                   25.7$\%$                   26$\%$                   26.7$\%$
        no. of signal tracks               97.8$\%$                   98$\%$                    98$\%$                   97.8$\%$
             1 tau jet                     $99.5\%$                  99.8$\%$                  99.7$\%$                  99.8$\%$
          Top mass window                  56.7$\%$                  44.4$\%$                   31$\%$                    21$\%$
   $\Delta \eta (\tau-jet,b-jet)$          75.7$\%$                  75.6$\%$                   67$\%$                   58.2$\%$
     $\Delta \phi (top,b-jet)$              $75\%$                    74$\%$                   80.6$\%$                  89.8$\%$
         $E^{missing}_{T}$                 $46.8\%$                   39$\%$                   41.7$\%$                   50$\%$
          Total Efficiency                 0.18$\%$                  0.13$\%$                  0.08$\%$                    0.06
          Expected events                    1013                       608                       218                       59
          at 100 $fb^{-1}$                                                                                       
  -------------------------------- ------------------------- ------------------------- ------------------------- -------------------------

  : Selection efficiencies are shown for all signal events. \[signalcuts\]

The charged Higgs mass window cut is applied in a specific region where a maximum signal significance is achieved which approaches to its best value of 32$\%$. This requirement significantly reduces background events e.g., the QCD jets are constrained due to jets-quark matching, eventhough from generation of million of events, few events could not survive. Now at the end we need to demonstrate the results validity in the MSSM parameter space by presenting all previous experimental constraints, 5$\sigma$ discovery contours and exclusion curves at 95$\%$ confidence level. These results are obtained by scanning the chosen charged Higgs mass points and tan$\beta$ values. On the basis of efficiencies obtained in Table \[signalcuts\] and Table \[backgroundcuts\], the phase space exclusion limits are obtained at the 95$\%$ confidence level using a TLimit class implemented in ROOT [@root] package. These results are shown in Figures \[95cl\] and \[5sigma\] incorporating previously excluded phase space areas by LEP, Tevatron and LHC data at 8 TeV.\

![The exclusion curves with three colour bands shown, corresponds to 95$\%$ confidence level contour between $m_H^{\pm}$ and tan$\beta$.[]{data-label="95cl"}](95CL.pdf){width="60.00000%"}

  ---------------------------- ------------ --------------- --------------- -------------------- ------------- -------------
         Selection Cut          $t\bar{t}$   SM single top   SM single top         Wjets          Wb$\bar{b}$   Wc$\bar{c}$
                                               s-channel       t-channel                                       
     $\sigma$ x BR\[$pb$\]        285.4           5.8             133        1.69$\times10^{4}$       395           49
             3 jets              2.96$\%$       25$\%$          33$\%$             26$\%$           20 $\%$       29 $\%$
            2 b-jets              98$\%$        41$\%$          6.5$\%$           0.31$\%$           7$\%$        13$\%$
         Leading tracks           51$\%$       99.8$\%$        99.6$\%$           99.6$\%$          99$\%$       99.6$\%$
         Isolation cut            48$\%$        28$\%$          28$\%$             26$\%$           36$\%$        36$\%$
           Ratio cut              95$\%$        18$\%$          22$\%$             18$\%$           18$\%$        18 $\%$
    Number of signal tracks       52$\%$        97$\%$          97$\%$             91$\%$           97$\%$        95 $\%$
           1 tau jet              58$\%$       99.7$\%$        99.7$\%$           99.7$\%$          99$\%$        99 $\%$
        Top mass window           75$\%$        42$\%$          48$\%$             32$\%$           38$\%$        38$\%$
   $\Delta \eta (\tau,b-jet)$     59$\%$        75$\%$          69$\%$             53$\%$           60$\%$        60 $\%$
   $\Delta \phi (top,b-jet)$      90$\%$        74$\%$          33$\%$             49$\%$           68$\%$        68 $\%$
       $E^{missing}_{T}$          49$\%$        46$\%$          43$\%$             60$\%$           46$\%$        46 $\%$
        Total Efficiency         0.05$\%$      0.05$\%$        0.006$\%$        0.00018 $\%$      0.007 $\%$     0.017$\%$
        Expected events             80           2900            79800             304200           276500         83300
        at 100 $fb^{-1}$                                                                                       
  ---------------------------- ------------ --------------- --------------- -------------------- ------------- -------------

  : Selection efficiencies are shown for all background events. \[backgroundcuts\]

![The phase space plot between $m_H^{\pm}$ (GeV) and tan$\beta$ is shown in order to demonstrate the 5$\sigma$ discovery contours at different integrated luminosities along with previous experimental exclusion curves.[]{data-label="5sigma"}](5sigma.pdf){width="60.00000%"}

  --------------------------------- ------------- ------------- ------------ -------- ----------- --------------
               Sample                                 Total        no. of      S/B     Optimized  
                                     Lower limit   Upper limit   Efficiency   Events               S/$\sqrt{B}$
   Signal, $m_{H^{\pm}}$ = 200 GeV       114           150         0.0014      411       0.32           11
          Total Background               114           150                     1266               
   Signal, $m_{H^{\pm}}$ = 250 GeV       126           198         0.001       250       0.197          7
          Total Background               126           198                     1276               
   Signal, $m_{H^{\pm}}$ = 300 GeV       162           294         0.0005       72       0.132          3
          Total Background               162           294                     540                
   Signal, $m_{H^{\pm}}$ = 400 GeV       216           294           NS         15       0.09           1
          Total Background               216           294                     165                
  --------------------------------- ------------- ------------- ------------ -------- ----------- --------------

  : Signal to background ratio and signal significance values obtained for four different samples, where “NS” represents negligibly small. \[significance\]

Conclusion
==========

The charged Higgs observability potential is investigated in the single top s-channel process and proved a source of charged Higgs boson in $\tau$ fully hadronic decay at $\sqrt{s}=$14 TeV at LHC. The Optimized kinematical selection cuts result to enhance the signal to background ratio as well as signal significance specifically at phase space ($m_H^{\pm}$ = 200 GeV, tan$\beta$ = 50). On the basis of presented results of exclusion curves at 95$\%$ confidence level and 5$\sigma$ contours, it may be concluded that the charged Higgs signal can be well observed or excluded in a wide range of phase space particular (tan$\beta > 35$ at 500 $fb^{-1}$, tan$\beta > 25$ at 1000 $fb^{-1}$, tan$\beta > 15$ at 3000 $fb^{-1}$). An important source of ambiguities and uncertainties are the systematic errors and theoretical uncertainties which have not been taken into account in this study. Undoubtedly, in the realistic approach at hadron colliders experiments, one needs to incorporate all the sources of uncertainties which must be taken into account e.g., pile-up, electronic noise, trigger inefficiencies, acceptance and vertex reconstruction related errors etc. Such analysis where the final state is jets($b's$ and $\tau's$) so the expected dominant source of uncertainty is the jet energy resolution which may be less than 1$-$2 $\%$ in the central region of the detector for jets having transverse momentum in the range of 55-500 GeV [@jetscale].

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