# Double Charmonium Productions in Electron-Positron Annihilation Using Bethe-Salpeter Approach

Negash, Hluf  (Department of Physics, Samara University, P.O. Box 132, Samara, Ethiopia) ; Bhatnagar, Shashank  (Department of Physics, University Institute of Sciences, Chandigarh University, Mohali 140413, India) ; Bhatnagar, Shashank  (Department of Physics, University Institute of Sciences, Chandigarh University, Mohali 140413, India)

03 March 2019

Abstract: We calculate the double charmonium production cross-section within the framework of $\mathrm{4}×\mathrm{4}$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}=\mathrm{10.6}$ 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 subleading). The calculated cross-sections for the double charmonium productions for final states, ( $J/\mathrm{\Psi },{\eta }_{c}$ ), ( ${\mathrm{\Psi }}^{\mathrm{\prime }},{\eta }_{c}$ ), ( $J/\mathrm{\Psi },{\eta }_{c}^{\mathrm{\prime }}$ ), and ( ${\mathrm{\Psi }}^{\mathrm{\prime }},{\eta }_{c}^{\mathrm{\prime }}$ ), are close to experimental data and in broad agreement with results of other theoretical models.

Published in: Advances in High Energy Physics 2019 (2019) 4029356