Axial Charmonium Production in Electron–Positron Annihilation at \(\mathbf {\sqrt{s}=10.6}\) GeV in the Framework of Bethe–Salpeter Equation

Abstract

We study the production of ground and excited axial charmonia in processes, \(e^- e^+ \rightarrow h_c(nP) + \eta _c(n'S)\), and \(e^- e^+ \rightarrow \chi _{c1}(nP) + h_c(n'P)\) for \(n,n'=1,2\), through leading order 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 at center of mass energy, \(\sqrt{s}=10.6\,{\textrm{GeV}}\). We employ the framework of \(4\times 4\) Bethe–Salpeter equation, and calculate their cross sections. These studies might be of interest for future experiments at B-factories, since \(h_c, \eta _c\), and \(\chi _{c1}, h_c\) production might provide opportunities for observing \(h_c\) with higher statistics in future.