Relativistic effects in the double S- and P-wave charmonium production in e^+e^- annihilation

TL;DR

This paper calculates relativistic and bound state corrections in the production of S-wave and P-wave charmonium pairs in electron-positron annihilation, showing significant effects on cross sections at 10.6 GeV.

Contribution

It provides a relativistic treatment of charmonium production processes, including wave function transformations and propagator expansions, improving upon nonrelativistic models.

Findings

Relativistic effects significantly alter cross section predictions.

Exact relativistic treatment ensures convergence of correction terms.

Results differ notably from nonrelativistic calculations at 10.6 GeV.

Abstract

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. 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 S- and P-wave mesons 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 $\sqrt{s}$ up to the second order. The exact relativistic treatment of the wave functions makes all such second order terms convergent, thus allowing the reliable calculation of their contributions to the production cross section. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the reaction $e^++e^-\to J/\Psi(\eta_c)+\chi_{cJ}(h_c)$ at the center-of-mass energy $\sqrt{s}=10.6$ GeV.