Experimental access to Transition Distribution Amplitudes with the P̄ANDA experiment at FAIR

Abstract

Baryon-to-meson Transition Distribution Amplitudes (TDAs) encoding valuable new information on hadron structure appear as building blocks in the collinear factorized description for several types of hard exclusive reactions. In this paper, we address the possibility of accessing nucleon-to-pion (πN) TDAs from \(\bar pp \to e^ + e^ - \pi ^0 \) reaction with the future P̄ANDA detector at the FAIR facility. At high center-of-mass energy and high invariant mass squared of the lepton pair q ², the amplitude of the signal channel \(\bar pp \to e^ + e^ - \pi ^0 \) admits a QCD factorized description in terms of πN TDAs and nucleon Distribution Amplitudes (DAs) in the forward and backward kinematic regimes. Assuming the validity of this factorized description, we perform feasibility studies for measuring \(\bar pp \to e^ + e^ - \pi ^0 \) with the P̄ANDA detector. Detailed simulations on signal reconstruction efficiency as well as on rejection of the most severe background channel, i.e. \(\bar pp \to \pi ^ + \pi ^ - \pi ^0 \) were performed for the center-of-mass energy squared s = 5 GeV² and s = 10 GeV², in the kinematic regions 3.0 < q ² < 4.3 GeV² and 5 < q ² GeV², respectively, with a neutral pion scattered in the forward or backward cone \(\left| {\cos \theta _{\pi ^0 } } \right| > 0.5\) in the proton-antiproton center-of-mass frame. Results of the simulation show that the particle identification capabilities of the P̄ANDA detector will allow to achieve a background rejection factor of 5 · 10⁷ (1 · 10⁷) at low (high) q ² for s = 5 GeV², and of 1 · 10⁸ (6 · 10⁶) at low (high) q ² for s = 10 GeV², while keeping the signal reconstruction efficiency at around 40%. At both energies, a clean lepton signal can be reconstructed with the expected statistics corresponding to 2 fb⁻¹ of integrated luminosity. The cross sections obtained from the simulations are used to show that a test of QCD collinear factorization can be done at the lowest order by measuring scaling laws and angular distributions. The future measurement of the signal channel cross section with P̄ANDA will provide a new test of the perturbative QCD description of a novel class of hard exclusive reactions and will open the possibility of experimentally accessing π TDAs.