---
abstract: 'The reaction $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ has been investigated at a beam energy of 1.4 GeV using the WASA-at-COSY facility. The total cross section is found to be (324 $\pm$ $21_\text{systematic}$ $\pm$ $58_\text{normalization}$) $\mu$b. In order to study the production mechanism, differential kinematical distributions have been evaluated. The differential distributions indicate that both initial state protons are excited into intermediate $\Delta(1232)$ resonances, each decaying into a proton and a single pion, thereby producing the pion pair in the final state. No significant contribution of the Roper resonance $N^{*}(1440)$ via its decay into a proton and two pions is found.'
address:
- 'Division of Nuclear Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden'
- 'Physikalisches Institut, Friedrich–Alexander–Universität Erlangen–Nürnberg, Erwin–Rommel-Str. 1, 91058 Erlangen, Germany'
- 'Department of Nuclear Reactions, The Andrzej Soltan Institute for Nuclear Studies, ul. Hoza 69, 00-681, Warsaw, Poland'
- 'Physikalisches Institut, Eberhard–Karls–Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany'
- 'Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland'
- 'Institut für Kernphysik, Westfälische Wilhelms–Universität Münster, Wilhelm–Klemm–Str. 9, 48149 Münster, Germany'
- 'High Energy Physics Department, The Andrzej Soltan Institute for Nuclear Studies, ul. Hoza 69, 00-681, Warsaw, Poland'
- 'Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai–400076, Maharashtra, India'
- 'Helmholtz–Institut für Strahlen– und Kernphysik, Rheinische Friedrich–Wilhelms–Universität Bonn, Nu[ß]{}allee 14–16, 53115 Bonn, Germany'
- 'Institut für Kernphysik, Forschungszentrum Jülich, 52425 Jülich, Germany'
- 'Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425 Jülich, Germany'
- 'Institut für Experimentalphysik I, Ruhr–Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany'
- 'Zentralinstitut für Elektronik, Forschungszentrum Jülich, 52425 Jülich, Germany'
- 'Institute for Theoretical and Experimental Physics, State Scientific Center of the Russian Federation, Bolshaya Cheremushkinskaya 25, 117218 Moscow, Russia'
- 'II. Physikalisches Institut, Justus–Liebig–Universität Gie[ß]{}en, Heinrich–Buff–Ring 16, 35392 Giessen, Germany'
- 'High Energy Physics Division, Petersburg Nuclear Physics Institute, Orlova Rosha 2, 188300 Gatchina, Russia'
- 'August Che[ł]{}kowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland'
- 'The Henryk Niewodnicza[ń]{}ski Institute of Nuclear Physics, Polish Academy of Sciences, 152 Radzikowskiego St, 31-342 Kraków, Poland'
- 'Veksler and Baldin Laboratory of High Energiy Physics, Joint Institute for Nuclear Physics, Joliot–Curie 6, 141980 Dubna, Russia'
- 'Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Physics, Joliot–Curie 6, 141980 Dubna, Russia'
- 'Institute of Modern Physics, Chinese Academy of Sciences, 509 Nanchang Rd., 730000 Lanzhou, China'
- 'Department of Cosmic Ray Physics, The Andrzej Soltan Institute for Nuclear Studies, ul. Uniwersytecka 5, 90-950 Lodz, Poland'
author:
- |
    The WASA-at-COSY Collaboration\
    P. Adlarson
- 'C. Adolph'
- 'W. Augustyniak'
- 'M. Bashkanov'
- 'T. Bednarski'
- 'F.S. Bergmann'
- 'M. Ber[ł]{}owski'
- 'H. Bhatt'
- 'K.–T. Brinkmann'
- 'M. Büscher'
- 'H. Calén'
- 'H. Clement'
- 'D. Coderre'
- 'E. Czerwi[ń]{}ski'
- 'E. Doroshkevich'
- 'R. Engels'
- 'W. Erven'
- 'W. Eyrich'
- 'P. Fedorets'
- 'K. Föhl'
- 'K. Fransson'
- 'F. Goldenbaum'
- 'P. Goslawski'
- 'K. Grigoryev'
- 'C.–O. Gullström'
- 'L. Heijkenskjöld'
- 'J. Heimlich'
- 'V. Hejny'
- 'F. Hinterberger'
- 'M. Hodana'
- 'B. Höistad'
- 'M. Jacewicz'
- 'M. Janusz'
- 'A. Jany'
- 'B.R. Jany'
- 'L. Jarczyk'
- 'T. Johansson'
- 'B. Kamys'
- 'G. Kemmerling'
- 'O. Khakimova'
- 'A. Khoukaz'
- 'S. Kistryn'
- 'J. Klaja'
- 'H. Kleines'
- 'B. K[ł]{}os'
- 'F. Kren'
- 'W. Krzemie[ń]{}'
- 'P. Kulessa'
- 'A. Kupść'
- 'K. Lalwani'
- 'B. Lorentz'
- 'H. Machner'
- 'A. Magiera'
- 'R. Maier'
- 'B. Maria[ń]{}ski'
- 'P. Marciniewski'
- 'M. Mikirtychiants'
- 'H.–P. Morsch'
- 'P. Moskal'
- 'B.K. Nandi'
- 'S. Nied[ź]{}wiecki'
- 'H. Ohm'
- 'A. Passfeld'
- 'C. Pauly'
- 'E. Perez del Rio'
- 'Y. Petukhov'
- 'N. Piskunov'
- 'P. Pluci[ń]{}ski'
- 'P. Podkopa[ł]{}'
- 'A. Povtoreyko'
- 'D. Prasuhn'
- 'A. Pricking'
- 'K. Pysz'
- 'T. Rausmann'
- 'C.F. Redmer'
- 'J. Ritman'
- 'Z. Rudy'
- 'S. Sawant'
- 'S. Schadmand'
- 'A. Schmidt'
- 'T. Sefzick'
- 'V. Serdyuk'
- 'N. Shah'
- 'M. Siemaszko'
- 'T. Skorodko'
- 'M. Skurzok'
- 'J. Smyrski'
- 'V. Sopov'
- 'R. Stassen'
- 'J. Stepaniak'
- 'G. Sterzenbach'
- 'H. Stockhorst'
- 'A. Szczurek'
- 'A. Täschner'
- 'T. Tolba'
- 'A. Trzci[ń]{}ski'
- 'R. Varma'
- 'P. Vlasov'
- 'G.J. Wagner'
- 'W. Wglorz'
- 'U. Wiedner'
- 'A. Winnemöller'
- 'M. Wolke'
- 'A. Wro[ń]{}ska'
- 'P. Wüstner'
- 'P. Wurm'
- 'X. Yuan'
- 'L. Yurev'
- 'J. Zabierowski'
- 'C. Zheng'
- 'M.J. Zieli[ń]{}ski'
- 'W. Zipper'
- 'J. Z[ł]{}oma[ń]{}czuk'
- 'P. [Ż]{}upra[ń]{}ski'
title: '$\pi^{0}\pi^{0}$ Production in Proton-Proton Collisions at $T_{p}$=1.4 GeV'
---

Introduction {#Int}
============

Investigations of the two-pion decay of mesons and baryons have been extensively carried out in pion-induced $\pi$$N$$\rightarrow$$\pi\pi$$N$ [@PhysRevC.69.045202] and photon-induced $\gamma$$N$$\rightarrow$$\pi\pi$$N$ [@Thoma:2007bm] reactions. Double pion production in nucleon-nucleon ($NN$) collisions is of particular interest in view of studying the simultaneous excitation of the two baryons and their subsequent decays. Here, the simplest case is considered: the excitation of the two nucleons into the $\Delta$(1232) resonance.\
Several theoretical models for double pion production have been suggested in the energy range from the production threshold up to several GeV [@Tejedor1994667; @Oset1985584]. A full reaction model describing the double pion production in $NN$ collisions has been developed by Alvarez-Ruso [@AlvarezRuso1998519]. More advanced calculations by Cao, Zou and Xu that include relativistic corrections based on the calculations of Ref. [@AlvarezRuso1998519] have been recently published [@PhysRevC.81.065201]. These models include and study both the resonant and the non-resonant terms of $\pi\pi$-production. The models predict that at energies near threshold the $\pi\pi$ production is dominated by the excitation of one of the nucleons into the Roper resonance $N$$^{*}$(1440)$P$$_{11}$ via $\sigma$-exchange, followed by its s-wave decay $N$$^{*}$$\rightarrow$$N$($\pi$$\pi$)$^{\text{s-wave}}_{I=0}$ (where $I$ indicates the isospin of the $\pi\pi$ system). As the beam energy increases, the p-wave decay $N$$^{*}$$\rightarrow$$\Delta$(1232)$\pi$$\rightarrow$N($\pi$$\pi$) gives an increasing contribution to the cross section. At higher energies the double $\Delta$(1232) excitation (dominantly via ($\pi$-$\rho$)-exchange) is expected to be the dominant reaction mechanism for $\pi\pi$ production.\
Such reactions have been studied experimentally at intermediate and higher energy regions [@Shimizu1982571; @PhysRev.138.B670]. Recently, exclusive high-statistics measurements have become available from near threshold ($T_{p}$=650 MeV) up to $T_{p}$=1.3 GeV from the PROMICE/WASA [@Johanson200275; @PhysRevLett.88.192301; @PhysRevC.67.052202], CELSIUS/WASA [@springerlink:10.1140/epja/i2008-10569-6; @PhysRevLett.102.052301; @Skorodko200930; @Skorodko2011115], COSY-TOF [@springerlink:10.1140/epja/i2008-10637-y] and ANKE [@PhysRevLett.102.192301] experiments. The analysis of the data obtained from these experiments, with the exception of ANKE (where only $pp$ final states in the diproton $^{1}$$S$$_{0}$ quasi-particle state have been considered), indicate that in case of $pp$ collisions (isovector channel) only two $t$-channel reaction mechanisms dominate: the excitation of the Roper resonance $N$$^{*}$(1440) (via $\sigma$-exchange) at energies close to threshold [@PhysRevLett.88.192301; @PhysRevLett.102.052301], and the excitation of the $\Delta\Delta$ system (via ($\pi$-$\rho$)-exchange) at energies $T_{p}$$\geq$1.3 GeV [@Skorodko2011115]. Model predictions are found to be in good agreement with the experimental results at energies close to threshold. At energies $T$$_{p}$$\geq$1 GeV, the Roper resonance contribution is over-predicted in the theoretical calculations. However, the predicted $\Delta\Delta$ excitation is in accordance with the data, if relativistic corrections are taken into account. A detailed description of the relativistic corrections applied to the model calculations of Ref. [@AlvarezRuso1998519] can be found in Refs. [@Skorodko200930; @Skorodko2011115]. On the other hand, the ANKE results reveal dominance of the $\Delta\Delta$ excitation already at $T_{p}$=0.8 GeV.\
In contrast to the exclusive measurements at low and intermediate energies, there is little experimental information on double pion production in $NN$ collisions at higher energies (i.e. $T_{p}$$>$1.3 GeV). Only the total cross sections are provided at $T_{p}$=1.36 GeV [@Koch2004] and $T_{p}$=1.48 GeV [@PhysRev.138.B670].\
Here, we report on the total as well as differential cross section measurements of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction at $T$$_{p}$ = 1.4 GeV using the WASA at COSY facility [@WASApro2004]. The beam energy corresponds to a center-of-mass energy of $\sqrt{s}$=2.48 GeV, $i.e.$ twice the $\Delta$ mass, thereby allowing a stringent test of the $t$-channel $\Delta\Delta$ mechanism as expected from the diverse model calculations.

Experimental Setup {#Exp}
==================

The experimental data were collected using the Wide Angle Shower Apparatus (WASA). WASA is an internal target experiment at the COoler SYnchrotron (COSY) of the Forschungszentrum Jülich, Germany. The detection system provides nearly full solid angle coverage for both charged and neutral particles. It allows multi-body final state hadronic interactions to be studied with high efficiency. The WASA facility consists of a central and a forward detector part and a cryogenic microsphere (pellet) target.\
The pellet target generator is located above the central detector. It provides frozen pure hydrogen or deuteron pellets of about 25 $\mu$m diameter (as the targets), thereby minimizing background reactions from other materials.\
The central detector is built around the interaction point and covers polar scattering angles between 20$^{\circ}$–169$^{\circ}$. The innermost detector, the mini drift chamber, is housed within the magnetic field of a superconducting solenoid and is used in determining the momenta of charged particles. The next layer, the plastic scintillator barrel provides fast signal for first level trigger and charged particle identification. As the outermost layer, 1012 CsI(Na) crystals of the calorimeter enable the measurement of the energy deposited by charged particles as well as the reconstruction of electromagnetic showers.\
The forward detection system covers the polar angular range of 3$^{\circ}$–18$^{\circ}$. The multi-plane straw tube detector is implemented for the precise reconstruction of charged particle track coordinates. An arrangement of segmented plastic scintillator layers, the forward range hodoscope, is used to reconstruct kinetic energies of scattered particles by the $\Delta$$E-E$ technique. A three-layered thin hodoscope provides fast charged particle discrimination. The forward detector can provide a tag on meson production via the missing mass of the reconstructed recoil particles. The trigger for the present experiment demanded at least one charged particle candidate to reach the first layer of the forward range hodoscope. For more details about the WASA-at-COSY facility see Ref. [@WASApro2004].

Data Analysis {#DSel}
=============

Recoil protons from the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction with $T_{p}$=1.4 GeV are detected in the forward detector, while the two neutral pions are reconstructed in the central detector. The main criterion to select the event sample demands 1 or 2 charged tracks in the forward detector and exactly 4 neutral tracks in the central detector. With this selection, the geometrical acceptance of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction is found to be $45$$\%$. Two event samples are selected: the first includes events with only one proton detected in the forward detector while the other proton is scattered outside the forward detector. The second contains events when two protons were detected in the forward detector. The combination of both data samples gives a finite acceptance over all of the avaliable phase space, as shown in Fig. 1. Here, as an example, two two-dimensional acceptance distributions of $p\pi$$^{0}$ pairs (left plot) and of $p\pi^{0}\pi^{0}$- versus $p\pi$$^{0}$-invariant masses (right plot) are presented. The Monte Carlo plots are based on equally populated phase space and show that nearly the full phase space is covered.

![Product of the geometrical acceptance times the detector efficiency plotted as two-dimensional function of the $p\pi$$^{0}$-invariant mass pairs (left) and the invariant mass of the $p\pi^{0}\pi^{0}$ versus $p\pi$$^{0}$ (right).](fig1.eps "fig:"){width=".23\textwidth"} ![Product of the geometrical acceptance times the detector efficiency plotted as two-dimensional function of the $p\pi$$^{0}$-invariant mass pairs (left) and the invariant mass of the $p\pi^{0}\pi^{0}$ versus $p\pi$$^{0}$ (right).](fig2.eps "fig:"){width=".23\textwidth"}

![Left: $\Delta E-E$ technique used for the identification of protons in the forward detector. Here, the deposited energy in the first layer of the forward range hodoscope is plotted versus the total deposited energy in all layers of the forward range hodoscope. The red lines represent the region used to select protons. Right: Two-dimensional distribution for both 2$\gamma$-pair invariant masses. All unique combinations of 4 photons forming 2$\pi$$^{0}$ are considered.](fig3.eps "fig:"){width=".23\textwidth"} ![Left: $\Delta E-E$ technique used for the identification of protons in the forward detector. Here, the deposited energy in the first layer of the forward range hodoscope is plotted versus the total deposited energy in all layers of the forward range hodoscope. The red lines represent the region used to select protons. Right: Two-dimensional distribution for both 2$\gamma$-pair invariant masses. All unique combinations of 4 photons forming 2$\pi$$^{0}$ are considered.](fig4.eps "fig:"){width=".23\textwidth"}

The identification of protons in the forward detector is based on the $\Delta E-E$ method, as shown in Fig. 2 (left plot). The depicted selection criterion selects not only protons that are stopped in the forward range hodoscope but also those that punch through. The selection helps to reject the contribution resulting from hadronic interactions in detector material.\
Neutral pions have been reconstructed from the photon pairs detected in the central detector. The reconstruction procedure is based on the minimum $\chi$$^{2}$ method which is applied to select the two-photon combinations with invariant masses closest to the $\pi$$^{0}$ mass. Figure 2 (right plot), shows the distribution of invariant masses ($M_{\gamma\gamma}$) for all three unique combinations of the 4 photons forming two $\gamma\gamma$ pairs. The figure shows that the $M_{\gamma\gamma}$ distribution peaks at the $\pi$$^{0}$ mass, as expected. The small background at low and high $\gamma\gamma$ masses is due to wrong $\gamma$-pair combinations and due to the finite resolution of the detector.\
Furthermore, a kinematic fit with six constraints, four for total energy-momentum conservation and two for each of the two $\gamma \gamma$ pair masses being equate to the $\pi$$^{0}$ mass, is applied in order to suppress the contribution from background channels and to recover the information of the unmeasured proton, scattered into the central detector or into inactive material. For consistency, the kinematic fit routine is always applied with one unmeasured proton in the final state. Hence, in the case where two protons are registered in the forward detector only one proton is selected and the other one is ignored. The proton with the lower energy is found to have better resolution. Therefore, it is chosen as the measured value in the kinematic fit routine while the higher energy one is treated as the unmeasured variable [@Tolba2010].\
The absolute normalization of the data has been achieved by normalizing to the measured $pp$$\rightarrow$$pp$$\eta$ cross section [@Chiavassa1994270]. Two decay modes of the $\eta$ meson, $\eta$$\rightarrow$$3\pi$$^{0}$ and $\eta$$\rightarrow$$2\gamma$, were chosen because they have similar final state particles as the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction. These channels have an additional advantage that they are the dominant neutral decay modes of the $\eta$ meson [@PDG2010].\
The data are corrected for the detector efficiency and acceptance by a Monte Carlo simulation using a toy model tuned to match the data. The tuned toy model is constructed by generating a four-body final state phase space distribution of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction, employing the GEANT phase space generator, based on the FOWL program [@James77]. Then, the generated event weight is modified to describe the 2$\pi$$^{0}$ production mechanism according to the production of two $\Delta$(1232)P$_{33}$ resonances in the intermediate state, each decaying into $p\pi$$^{0}$. The partial wave amplitude that describes the decay of $\Delta$(1232) into $p\pi$-system is derived in Ref. [@Risser197368]. This amplitude together with correction terms for the measured proton and pion angular distributions in the center-of-mass system, as well as for the $M$$_{\pi^{0}\pi^{0}}$ and $M$$_{p\pi^{0}}$ distributions are multiplied by the generated weights of each event. The Monte Carlo simulations are then compared with the data, and this step is repeated until the data and the simulations are in good agreement. The tuned toy model is explained in detail in Ref. [@Tolba2010].

Results {#Res}
=======

The total cross section of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction at $T$$_{p}$ = 1.4 GeV is determined to be $\sigma_\text{tot}$=(324 $\pm$ $21_\text{systematic}$ $\pm$ $58_\text{normalization}$) $\mu$b. The total cross section error is evaluated in terms of statistical and systematical uncertainties. The statistical error is found to be $<$1$\%$ and thus negligible compared to the systimatical contribution. The systematical error is constructed from two terms, systematic effects and normalization. The systematic contribution is estimated by observing the variation of the results with different analysis constraints where the varied parameters are assumed to be independent of each other. The systematic term is calculated from the following main contributions: 1) applying different selection regions to the flat part of the confidence level (probability) distribution of the kinematic fit, the contribution from this term is found to be 5$\%$, 2) the contribution from the correction for the detector acceptance generated by different Monte Carlo models is found to be 4$\%$, and 3) constraining the reconstruction particles to satisfy the geometrical boundaries of the central and the forward detectors, the contribution from this term is found to be 1$\%$. The total error from the systematic term is the square root of the quadratic sum of the individual terms and found to be 6.5$\%$. The normalization term is constructed from two main components: 1) contribution from the $pp$$\rightarrow$$pp$$\eta$ analysis, found to be 14$\%$, and 2) the uncertainty of the cross section value in Ref. [@Chiavassa1994270] which is found to be 11$\%$. The total error contribution from the normalization term is estimated to be 18$\%$.\
Figure 3 compares the cross section from this work (solid circle) with the previous experimental data [@Shimizu1982571; @Johanson200275; @Skorodko200930; @Koch2004; @PhysRev.138.B670] and to the theoretical expectations calculated in Ref. [@AlvarezRuso1998519]. The new data point is compatible with the earlier results [@Shimizu1982571; @PhysRev.138.B670; @Johanson200275; @Skorodko200930; @Koch2004] and corroborates the strongly rising trend of the cross section starting at $\sim$ 1170 MeV. As has been verified in Ref. [@Skorodko200930], the trend of rising total cross sections from threshold up to $T_{p}$$\sim$1 GeV is due to the dominance of the Roper resonance. Above 1 GeV, it levels off and proceeds with only a slight increase up to $T_{p}$$\sim$1170 MeV. The rise in the cross section values at higher energies $T_{p}$$>$1170 MeV is expected to be associated with the dominance of the $\Delta\Delta$ excitation. A similar interpretation with a better description of the excitation function is obtained with the modifications applied in Ref. [@Skorodko2011115]

![Total cross section for the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction as a function of $T_{p}$. The result of this work (solid circle), at $T$$_{p}$ = 1.4 GeV, is compared to the data from PROMICE/WASA (open triangles) [@Johanson200275], CELSIUS/WASA (filled triangles) [@Skorodko200930], at 1.36 GeV (square) [@Koch2004], bubble chamber results (inverted triangles) [@Shimizu1982571] and (star) [@PhysRev.138.B670] and the theoretical calculations of Ref. [@AlvarezRuso1998519]. Here, the long dashed doted line represents the production via double $\Delta$(1232), the dashed line represents the production via Roper resonance decay $N$$^{*}$(1440)$\rightarrow$$\Delta\pi$$^{0}$, the dashed doted line represents the production via direct decay $N$$^{*}$(1440)$\rightarrow$$p\pi$$^{0}$$\pi$$^{0}$ and the solid black line represents the expected total cross section.](fig5.eps){width=".40\textwidth"}

In order to study the mechanism of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction, seven independent kinematic variables are necessary to cover the available phase space of the reaction. Therefore, different kinematical variables describing the system have been investigated after the data have been corrected for the detector efficiency and acceptance using the tuned toy model. The corrected data are compared to an uniformly populated phase space distribution and the models according to Refs. [@AlvarezRuso1998519] and [@Skorodko2011115]. All theoretical models are normalized to the same total cross section as the data. The differential distributions presented here have been chosen because they are sensitive to contributions from intermediate $\Delta$(1232) and/or the $N$$^{*}$(1440) resonances.

![Comparison of data (black dots) to the theoretical expectations calculated from Ref. [@AlvarezRuso1998519] (red-dashed line) and Ref. [@Skorodko2011115] (blue-line), and with uniformly populated phase space (shaded area). Left: differential distribution of the $\pi$$^{0}$$\pi$$^{0}$-invariant mass, $M$$_{\pi^{0}\pi^{0}}$. Right: differential distribution of two pion opening angle in the center-of-mass system, $cos$$\delta$$^\text{CM}_{\pi^{0}\pi^{0}}$.](fig6.eps "fig:"){width=".23\textwidth"} ![Comparison of data (black dots) to the theoretical expectations calculated from Ref. [@AlvarezRuso1998519] (red-dashed line) and Ref. [@Skorodko2011115] (blue-line), and with uniformly populated phase space (shaded area). Left: differential distribution of the $\pi$$^{0}$$\pi$$^{0}$-invariant mass, $M$$_{\pi^{0}\pi^{0}}$. Right: differential distribution of two pion opening angle in the center-of-mass system, $cos$$\delta$$^\text{CM}_{\pi^{0}\pi^{0}}$.](fig7.eps "fig:"){width=".23\textwidth"}

Figure 4 shows that the $\pi$$^{0}$$\pi$$^{0}$-invariant mass ($M$$_{\pi^{0}\pi^{0}}$) distribution (left plot) is similar to the uniformly populated phase space distribution, while it shows a strong deviation from the calculations of Ref. [@AlvarezRuso1998519], where the model calculations predict two large enhancements at lower and higher $M$$_{\pi^{0}\pi^{0}}$ values. The enhancement at higher $M$$_{\pi^{0}\pi^{0}}$ values is due to the dominance of the $\rho$ exchange in the model calculations. In contrast, the data are well described by the assumption of $t$-channel meson exchange leading to $\Delta\Delta$ excitation of Ref. [@Skorodko2011115] (blue line), where the $\rho$-exchange contribution is strongly reduced compared to the original calculations [@AlvarezRuso1998519]. The systematic enhancement at low $M$$_{\pi^{0}\pi^{0}}$ values indicates the tendency of the two pions to be emitted parallel with respect to each other in the center-of-mass frame. This behavior is seen as well in the two pion opening angle distribution $cos$$\delta$$^\text{CM}_{\pi^{0}\pi^{0}}$ (right plot of Fig. 4), where the data is enhanced at $cos$$\delta$$^\text{CM}_{\pi^{0}\pi^{0}}$ = 1, relative to the phase space spectrum. Here, the data are well described by the modified calculations of Ref. [@Skorodko2011115], while a large deviation is observed from the calculations of Ref. [@AlvarezRuso1998519]. The strong peaking of the latter calculations at an opening angle of 180$^{\circ}$ is due to the enhancement at higher values of $M$$_{\pi^{0}\pi^{0}}$ in left frame of Fig. 4.

![The upper frame shows two dimensional differential cross section distributions of $p\pi$$^{0}$- and $p\pi$$^{0}$$\pi$$^{0}$-invariant masses divided by the available phase space volume. This presentation enhances the sensitivity to resonance contributions in the production mechanism. The lower frame shows one-dimensional projections of the differential cross section onto the $M$$_{p\pi^{0}}$ axis (left) and $M$$_{p\pi^{0}\pi^{0}}$ axis (right). See Fig. 4 for a description of the lines.](fig8.eps "fig:"){width=".23\textwidth"} ![The upper frame shows two dimensional differential cross section distributions of $p\pi$$^{0}$- and $p\pi$$^{0}$$\pi$$^{0}$-invariant masses divided by the available phase space volume. This presentation enhances the sensitivity to resonance contributions in the production mechanism. The lower frame shows one-dimensional projections of the differential cross section onto the $M$$_{p\pi^{0}}$ axis (left) and $M$$_{p\pi^{0}\pi^{0}}$ axis (right). See Fig. 4 for a description of the lines.](fig9.eps "fig:"){width=".23\textwidth"}

![The upper frame shows two dimensional differential cross section distributions of $p\pi$$^{0}$- and $p\pi$$^{0}$$\pi$$^{0}$-invariant masses divided by the available phase space volume. This presentation enhances the sensitivity to resonance contributions in the production mechanism. The lower frame shows one-dimensional projections of the differential cross section onto the $M$$_{p\pi^{0}}$ axis (left) and $M$$_{p\pi^{0}\pi^{0}}$ axis (right). See Fig. 4 for a description of the lines.](fig10.eps "fig:"){width=".23\textwidth"} ![The upper frame shows two dimensional differential cross section distributions of $p\pi$$^{0}$- and $p\pi$$^{0}$$\pi$$^{0}$-invariant masses divided by the available phase space volume. This presentation enhances the sensitivity to resonance contributions in the production mechanism. The lower frame shows one-dimensional projections of the differential cross section onto the $M$$_{p\pi^{0}}$ axis (left) and $M$$_{p\pi^{0}\pi^{0}}$ axis (right). See Fig. 4 for a description of the lines.](fig11.eps "fig:"){width=".23\textwidth"}

The upper and lower left plots of Fig. 5 show indications for the $\Delta\Delta$ excitation in the correlation of the $M$$_{p\pi^{0}}$ pairs (upper) and in the one-dimensional projection onto the $M$$_{p\pi^{0}}$-axis (lower). Here, evidence for the $\Delta$(1232) resonance can be seen as a strong enhancement at $M$$_{p\pi^{0}}$ $\sim$ $M$$_{\Delta}$ = 1.232 GeV/c$^{2}$. The uniform phase space distribution of the lower plot shows the strongest deviation with respect to the data due to the $\Delta$ excitation in the data points. In contrast, no significant evidence for the presence of the Roper resonance $N^{*}$(1440) is observed in the right-hand plots of Fig. 5. Here, one would expect an enhancement around $M$$_{p\pi^{0}\pi^{0}}$ = 1.44 GeV/c$^{2}$.\
The upper left plot of Fig. 6 shows the $pp$-invariant mass spectrum, $M$$_{pp}$, which peaks slightly to the right with respect to the uniformly populated phase space distribution. The $M$$_{pp}$ spectrum is complementary to that for $M$$_{\pi^{0}\pi^{0}}$ from Fig. 4 that is located to the left relative to the phase space spectrum. The upper right plot shows the angular distribution of the protons in the center-of-mass frame, $cos$$\theta$$^\text{CM}_{p}$. It exhibits an anisotropic behavior, in agreement with the theoretical calculations. The strong forward-backward peaking of the $cos$$\theta$$^\text{CM}_{p}$ spectrum is associated with $\pi$-$\rho$ exchange mediating the $pp$ interaction. The angular distribution of the $p\pi$$^{0}$-system in the center-of-mass frame, cos$\theta$$^\text{CM}_{p\pi^{0}}$, (lower right) shows a forward-backward symmetry. That is similar in shape to the $cos$$\theta$$^\text{CM}_{p}$ distribution as expected from the large p/$\pi$$^{0}$ mass ratio. In the $pp\pi$$^{0}$-invariant mass distribution, $M$$_{pp\pi^{0}}$, (lower left plot) the data peak near the sum of the proton and $\Delta$ masses as expected for $\Delta\Delta$ production at threshold. Here, the modified model [@Skorodko2011115] and the data points are in good agreement, while the calculations of Ref. [@AlvarezRuso1998519] are slightly shifted to lower $M$$_{pp\pi^{0}}$ values and deviate from the data points. The data deviate strongly from the distribution generated according to phase space of the process. This is due to the $\Delta$ excitation, consistent with the observations in the other invariant mass distributions.

![Same as Fig. 4 but for differential cross sections of $M$$_{pp}$ (upper left), $cos$$\theta$$^\text{CM}_{p}$ (upper right), $cos$$\theta$$^\text{CM}_{p\pi^{0}}$ (lower right) and $M$$_{pp\pi^{0}}$ (lower left).](fig12.eps "fig:"){width=".23\textwidth"} ![Same as Fig. 4 but for differential cross sections of $M$$_{pp}$ (upper left), $cos$$\theta$$^\text{CM}_{p}$ (upper right), $cos$$\theta$$^\text{CM}_{p\pi^{0}}$ (lower right) and $M$$_{pp\pi^{0}}$ (lower left).](fig13.eps "fig:"){width=".23\textwidth"}

![Same as Fig. 4 but for differential cross sections of $M$$_{pp}$ (upper left), $cos$$\theta$$^\text{CM}_{p}$ (upper right), $cos$$\theta$$^\text{CM}_{p\pi^{0}}$ (lower right) and $M$$_{pp\pi^{0}}$ (lower left).](fig14.eps "fig:"){width=".23\textwidth"} ![Same as Fig. 4 but for differential cross sections of $M$$_{pp}$ (upper left), $cos$$\theta$$^\text{CM}_{p}$ (upper right), $cos$$\theta$$^\text{CM}_{p\pi^{0}}$ (lower right) and $M$$_{pp\pi^{0}}$ (lower left).](fig15.eps "fig:"){width=".23\textwidth"}

Conclusion and outlook {#con}
======================

Data for the total cross section of the $pp$$\rightarrow$$pp$$\pi$$^{0}$$\pi$$^{0}$ reaction at $T$$_{p}$ = 1.4 GeV have been obtained. Differential distributions are compared to theoretical predictions. Calculations of Ref. [@AlvarezRuso1998519] show a stronger deviation from the experimental data as compared to the refined calculations of Ref. [@Skorodko2011115]. The latter show small deviations for some differential distributions, e.g. $cos$$\theta$$^\text{CM}_{p\pi^{0}}$ (lower right plot of Figure 6), leaving room for further optimization of the model. From studying the reaction dynamics the $\pi$$^{0}$$\pi$$^{0}$ production at $T$$_{p}$ = 1.4 GeV is found to be dominated by the $t$-channel double $\Delta$(1232) excitation as intermediate state, without a significant contribution from the Roper resonance $N^{*}$(1440).\
The investigation of the production of charged pions ($\pi$$^{+}$$\pi$$^{-}$) is the next step in the study of the double pion production in $NN$ collisions with WASA-at-COSY. This channel is of special interest in order to study the contribution from the vector meson $\rho$$^{0}$(770) which is expected to play an important role in the $\pi$$^{+}$$\pi$$^{-}$ production. Moreover, the extension to higher proton energies will shed light on the role of heavier resonances.

Acknowledgments {#Ack}
===============

This work was in part supported by: the Forschungszentrum Jülich including the COSY-FFE program, the European Community under the FP7-Infrastructure-2008-1, the German-BMBF, the German-Indian DAAD-DST exchange program, VIQCD and the German Research Foundation (DFG), the Wallenberg Foundation, the Swedish Research Council, the Göran Gustafsson Foundation, the Polish Ministry of Science and Higher Education and the Polish National Science Center and Foundation for Polish Science - MPD program.\
We also want to thank the technical and administration staff at the Forschungszentrum Jülich and at the participating institutes.\
This work is part of the PhD thesis of Tamer Tolba.

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