Relativistic corrections to the pair double heavy diquark production ine+e−annihilation

Abstract

On the basis of perturbative QCD and a relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of double heavy diquarks. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving diquark $S$-wave bound states are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $s$ up to the second order. Relativistic corrections to the quark-quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that examined effects change essentially nonrelativistic results of the cross sections. The estimate of the yield of pairs of double heavy baryons $(ccq)$ at the $B$ factory is presented.