The Excited Charmonium Production in $e^{+}e^{-}$ Annihilation

TL;DR

This paper calculates the form factor and cross section for excited charmonium production in electron-positron annihilation using light-cone sum rules, emphasizing the importance of relativistic effects and matching experimental data.

Contribution

It introduces a method to incorporate the evolution of the distribution amplitude with energy scale, highlighting the significance of relativistic effects in charmonium production calculations.

Findings

Relativistic effects significantly increase the form factor and cross section.

Results align well with Belle experimental data.

The energy scale evolution of the distribution amplitude is crucial for accurate predictions.

Abstract

We calculate the form factor and cross section of the excited charmonium production process $e^{+}+e^{-}\rightarrow \psi \left ( 2S \right )+\eta _{c}$ by light-cone sum rules. In our method, the form factor depends on the distribution amplitude of $\eta _{c}$ meson. Experimentally, the energy scale of $e^{+}+e^{-}\rightarrow \psi \left ( 2S \right )+\eta _{c}$ process is much larger than the initial energy scale of $\eta _{c}$ meson in our BHL model. Therefore, we further consider the evolution of the distribution amplitude with the energy scale, and select the distribution amplitude as our input parameter when the final effective energy scale is $\mu=5.00\ GeV$. This treatment means that we have chosen the relativistic distribution amplitude. The results show that the relativistic effect contributes greatly to the form factor and cross section. Our results are consistent with Belle experimental data.