$J/\Psi$ and $\chi_{cJ}(J=0,1)$ production in electron-positron annihilation at $\sqrt{s}=10.6$ GeV in the framework of Bethe-Salpeter equation

TL;DR

This paper calculates the production cross sections of certain charmonium pairs in electron-positron collisions at 10.6 GeV using the Bethe-Salpeter equation, showing results close to experimental data.

Contribution

It introduces a Bethe-Salpeter equation approach to compute charmonium production cross sections at leading order, providing a more consistent treatment of quark motion inside hadrons.

Findings

Calculated cross sections align with experimental data.

Use of Bethe-Salpeter equation improves theoretical predictions.

Analysis includes ground and excited charmonium states.

Abstract

In present work we study the production of ground and excited charmonium pairs in $e^- e^+ \rightarrow \Psi(nS)+ \chi_{cJ}(nP)$ for $J=0,1$ and $n=1,2$, through leading order (LO) tree-level diagrams $\sim O(\alpha_{em} \alpha_s)$, which proceed through exchange of a virtual photon and an internal gluon line connecting two quark lines (in the triangle quark loop part of the diagram), in the framework of $4\times 4$ Bethe-Salpeter equation, at center of mass energy, $\sqrt{s}=10.6 GeV.$ We have tried to show that the cross sections for this process calculated with use of the four leading order $\sim O(\alpha_{em} \alpha_s)$ diagrams using BSE approach come close to experimental data, which might be mainly due to the consistent treatment of motion of quarks inside the hadrons in the BSE framework.