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

In present work we study the production of ground and excited charmonium pairs in $e^- e^+ \rightarrow Ψ(nS)+ χ_{cJ}(nP)$ for $J=0,1$ and $n=1,2$, through leading order (LO) tree-level diagrams $\sim O(α_{em} α_s)$, 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 $\sim O(α_{em} α_s)$ 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.