HADES

HADES is a versatile magnetic spectrometer installed at GSI Darmstadt at SIS18 [1]. Thanks to its high acceptance, powerful particle ($p/K/\pi/e$) identification and very good mass resolution ($2-3\%$ for dielectrons in the light vector meson mass range) it allows to study both hadron and rare dilepton production in $N+N$, $p+A$, $A+A$ collisions at a few AGeV beam energy range. In collisions $p+p$ @ $1.25$ $GeV$, the intermediate $\Delta(1232)$ resonance is expected to play a dominant role in the pion production, but it is known to be not sufficient to describe fully the data. The resonance cross section was determined from exclusive $pp\pi^{0}$ and $np\pi^{+}$ channels [2] in the framework of a OPE model with accuracy of $20-30\%$. Investigation of these reaction channels by means of the PWA (Partial Wave Analysis) was also done [3] by the Bonn-Gatchina group at a smaller beam energy [4]. It revealed a dominant contribution of $\Delta(1232)p$ intermediate state but also sizeable non-resonant terms and interference effects. In this work we report on the PWA of the single-pion production in proton-proton collisions (as in [2]) measured with HADES. The $pp$ is a pure isospin $I=1$ state and, at this beam energy the following initial $pp$-states contribute: (J=0) $^{1}S_{0}$, $^{3}P_{0}$, (J=1) $^{3}P_{1}$, (J=2) $^{1}D_{2}$, $^{3}P_{2}$, $^{3}F_{2}$, (J=3) $^{3}F_{3}$ and (J=4) $^{1}G_{4}$, $^{3}H_{4}$. Unlike in proton-proton collisions at lower energies, higher partial waves are necessary for a proper data description. The final states are limited to $S-$, $P-$, $D-$, $F-$, $G-$ and $H-$ wave states with the two possible intermediate resonance states $P_{33}(1232)$ and $P_{11}(1440)$. The data samples (for both channels, $pp\pi^{0}$ and $pn\pi^{+}$) were analysed with the event-by-event background estimation (Q factors). The analysis was preformed together with other available data (see [5], 11 measurements for $pp\pi^{0}$ and only two for $pn\pi^{+}$ channel) covering mostly lower beam energies. The stability of solutions was investigated based on a few parametrisations of the transition amplitude $A_{tr}$ (with total energy dependence) and various descriptions of resonance states ($\Delta$ and $N^{*}$). The obtained solutions generally describe the HADES data very well in various projection observables (CM angular distributions, invariant masses, angular distributions in the helicity and the Gottfried-Jackson frames). The analysis shows the dominant $P_{33}(1232)$ contribution in $np\pi^{+}$ at the level of $95\%$ and in $pp\pi^{0}$ ($80\%$) which is an important message for the dilepton analysis, where the branching of $\Delta$ Dalitz decays can be identified (in the $pe^{+}e^{-}$ channel).

[1] G. Agakishiev et al., Eur. Phys. J. A41 (2009) 243 [2] G. Agakishiev et al., Eur. Phys. J. A48 (2012) 74 [3] A. V. Anisovich et al., Eur Phys. J. A34 (2007) 129 [4] K. N. Ermakov et al., Eur. Phys. J. A47 (2011) 159 [5] Data Base on page http://pwa.hiskp.uni-bonn.de/