Probing Pion Valence Quark Distribution with Beam-charge Asymmetry of Pion-induced $J\mathrm{/}\psi$ Production

We consider the beam-charge asymmetry of the $J\mathrm{/}\psi$ production cross sections in ${\pi }^{-}$- versus ${\pi }^{+}$-induced reactions on proton or nuclear targets. We show that the $J\mathrm{/}\psi$ production cross section difference between ${\pi }^{-}$ and ${\pi }^{+}$ beams impinging on a proton target has a positive sign with a magnitude proportional to the product of pion’s valence quark distribution, $V_{\pi }$, and proton’s up and down valence quark distribution difference, $u^V-d^V$. The existing $J\mathrm{/}\psi$ production data for ${\pi }^{-}+p$ and ${\pi }^{+}+p$ at 39.5 and 200 GeV/c are consistent with the expected positive beam-charge asymmetry. The magnitude of the asymmetry is compared with calculations performed within two theoretical frameworks, the Color Evaporation Model (CEM) and the Non-Relativistic QCD (NRQCD) formalism. We also examine the beam-charge dependence for pion-induced $J\mathrm{/}\psi$ production cross sections measured on the neutron-rich platinum target, and find good agreement between the data and theory for both the negative sign and the magnitude of the beam-charge asymmetry. The comparison between data and theoretical calculations for both proton and platinum targets suggests that the beam-charge asymmetry in pion-induced $J\mathrm{/}\psi$ production is a viable method of accessing the valence quark distribution of the pion.