Backward charmonium production in $\pi N$ collisions

The QCD collinear factorization framework allows one to describe exclusive backward production of a $J/\psi$ meson in pion-nucleon collisions in terms of pion-to-nucleon transition distribution amplitudes. We calculate the scattering amplitude at the leading order in the strong coupling constant and estimate the cross section of this reaction in the backward kinematical region for a medium energy pion beam available at the J-Parc experimental facility.

Figure 1

Collinear factorization of the ${\pi }^{-}(p_{\pi })+N^p(p_1)\to N^n(p_2)+J/\psi (p_{\psi })$ reaction in the $u$-channel regime. DA stands for the distribution amplitude of the incoming nucleon; $\pi \to N$ TDA stands for the transition distribution amplitude from a pion to a nucleon.

Figure 2

Differential cross section $\frac{d\sigma }{d{\mathrm{\Delta }}^2}$ for ${\pi }^{-}p\to J/\psi n$ as a function of the pion beam momentum $P_{\pi }$ ($W^2\approx 2m_N{P}_{\pi }$) for ${\mathrm{\Delta }}_T^2=0$. Our estimate is based on the nucleon exchange contribution to the $\pi \to N$ TDAs and is independent of the specific form of the leading twist nucleon DA [see Eq. (25) and the corresponding discussion].

Figure 3

Differential cross section $\frac{d\sigma }{d{\mathrm{\Delta }}^2}$ for ${\pi }^{-}p\to J/\psi n$ as a function of $|u-u_{\max }|$ for $P_{\pi }=10$, 15, 20 GeV for $|u|\le 1{\mathrm{GeV}}^2$.

Figure 4

Angular distribution for the $d\sigma /d{\mathrm{\Delta }}^2$ cross section for the near-backward charmonium production (${\theta }_{\pi }^{*}\simeq 0$) for $-1{\mathrm{GeV}}^2\le {\mathrm{\Delta }}^2\le u_{\max }$. Dashed lines show the effect of the cutoff $|{\mathrm{\Delta }}^2|\le 1{\mathrm{GeV}}^2$ for the values of the pion CMS scattering angle ${\theta }_{\pi }^{*}$.

Figure 5

Small arrows show the direction of the longitudinal momentum flow in the ERBL-like regime for the following: (a) The longitudinal momentum flow for $N\to \pi$ TDAs defined in (a1). The longitudinal momentum transfer is $(p_{\pi }-p_N)·n\equiv \tilde{\mathrm{\Delta }}·n$. (b): The longitudinal momentum flow for $\pi \to N$ TDAs defined in (17). The longitudinal momentum transfer is $(p_N-p_{\pi })·n\equiv \mathrm{\Delta }·n$. Arrows on the nucleon and quark (antiquark) lines show the direction of flow of the baryonic charge.