Relativistic description of the double P-wave charmonium production in e^+e^- annihilation

TL;DR

This paper calculates relativistic and bound state corrections in the production of P-wave charmonium pairs in electron-positron annihilation, showing significant deviations from nonrelativistic predictions at 10.6 GeV.

Contribution

It introduces a comprehensive relativistic framework for P-wave charmonium production, including wave function transformations and propagator expansions, improving upon previous nonrelativistic models.

Findings

Relativistic effects significantly alter cross section predictions.

Bound state corrections impact the production amplitude.

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 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 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. 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 h_c+\chi_{cJ} at the center-of-mass energy sqrt{s}=10.6 GeV.