Double charmonium productions in electron-positron annihilation using Bethe-Salpeter approach

We calculate the double charmonium production cross section within the framework of $4\times 4$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}= 10.6$GeV, that proceeds through the exchange of a single virtual photon. In this calculation, we make use of the full Dirac structure of 4D BS wave functions of these charmonia, with the incorporation of all the Dirac covariants (both leading and sub-leading). The calculated cross-sections for the double charmonium productions for final states, ($J/\Psi, \eta_c$); ($\Psi',\eta_c$) ; ($J/\Psi, \eta_c'$); and ($\Psi',\eta_c'$) are close to experimental data, and in broad agreement with results of other theoretical models.