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

TL;DR

This paper presents a relativistic approach to calculating double charmonium production in electron-positron annihilation, improving accuracy by accounting for relativistic effects and wave function properties, resulting in predictions that align well with experimental data.

Contribution

It introduces an exact relativistic treatment of meson wave functions and a second-order expansion of propagators, enhancing the precision of cross section calculations for double charmonium production.

Findings

Relativistic effects significantly increase predicted cross sections.

The new calculations agree well with experimental measurements.

The approach improves upon nonrelativistic models.

Abstract

New evaluation of the relativistic effects in the double production of $S$-wave charmonium states is performed on the basis of perturbative QCD and the relativistic quark model. The main improvement consists in the exact account of properties of the relativistic meson wave functions. 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. Compared to the nonrelativistic calculation we obtain a significant increase of the cross sections for the $S$-wave double charmonium production. This brings new theoretical results in good agreement with the available experimental data.