PA-JOU-2014-002

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 ($\pi N$) TDAs with the future \={P}ANDA detector at the FAIR facility.
At high center of mass energy and high invariant mass of the lepton pair $q^2$,
the amplitude of the signal channel $\bar{p}p \to e^+e^- \pi^0$ admits a QCD factorized description
in terms of $\pi N$ 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 $\bar{p}p \to e^+e^- \pi^0$
with the \={P}ANDA detector.
Detailed simulations on signal reconstruction efficiency as well as on rejection of the most
severe background channel, {\it i.e.} $\bar{p}p \to \pi^+\pi^- \pi^0$
were performed for the center of mass energy squared $s = 5$ GeV$^2$ and $s = 10$ GeV$^2$ ,
in the kinematic regions $3.0 < q^2 < 4.3$ GeV$^2$ and $5 < q^2 < 9$ GeV$^2$,
respectively, with a neutral pion scattered in the forward or backward cone
$| \cos\theta_{\pi^0}| > 0.5 $ in the proton-antiproton center of mass frame.
Results of the simulation show that the particle identification capabilities
of the \={P}ANDA detector will allow to achieve a background rejection factor of $10^8$
while keeping the signal reconstruction efficiency at around $40\%$ and that a
clean lepton signal can be reconstructed with the expected statistics corresponding to $2$ fb$^{-1}$
of integrated luminosity. The future measurement of the signal channel cross section with \={P}ANDA
will provide a new test of perturbative QCD description of the novel class of
hard exclusive reactions and will open the possibility of experimentally accessing $\pi N$ TDAs.