Relativistic corrections to double charmonium production in high energy proton-proton interaction

Abstract

On the basis of perturbative QCD and the relativistic quark model, we calculate relativistic corrections to the process of pair $J/\ensuremath{\psi}$ production in proton-proton collisions at LHC energy $\sqrt{S}=7\text{ }\text{ }\mathrm{TeV}$. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving $J/\ensuremath{\psi}$ mesons are taken into account. For the gluon and quark propagators entering the amplitude, we use a truncated expansion in relative quark momenta up to the second order. Relativistic corrections to the quark bound state wave functions are considered by means of the Breit-like potential. It turns out that the examined effects decrease initial nonrelativistic cross section more than two times. The final result lies below the experimental value measured by LHCb.