# Twist-3 contributions to $\gamma\gamma\rightarrow\pi^+\pi^-,K^+K^-$ processes in perturbative QCD approach

## TL;DR

This paper investigates twist-3 contributions to gamma-gamma to meson pair processes using perturbative QCD with k_T factorization, highlighting their significance at intermediate energies and agreement with some experimental data.

## Contribution

It introduces a detailed analysis of twist-3 corrections in gamma-gamma to meson processes within the perturbative QCD framework, emphasizing their dominant role at certain energies.

## Key findings

- Twist-3 corrections are significant in the intermediate energy region.
- Results for cross sections agree with BELLE and ALEPH measurements.
- Discrepancies remain in angular distribution predictions.

## Abstract

As one of the simplest hadronic processes, $\gamma\gamma\rightarrow M^{+}M^{-}$ ($M=\pi,K$) could be a good testing ground for our understanding of the perturbative and nonperturbative structure of QCD, and will be studied with high precision at BELLE-\RNum{2} in the near future. In this paper, we revisit these processes with twist-3 corrections in the perturbative QCD approach based on the $k_{T}$ factorization theorem, in which transverse degrees of freedom as well as resummation effects are taken into account. The influence of the distribution amplitudes on the cross sections are discussed in detail. Our work shows that not only the transverse momentum effects but also the twist-3 corrections play a significant role in the processes $\gamma\gamma\rightarrow M^{+}M^{-}$ in the intermediate energy region. Especially in the few GeV region, the twist-3 contributions become dominant in the cross sections. And it is noteworthy that both the twist-3 result of the $\pi^{+}\pi^{-}$ cross section and that of the $K^{+}K^{-}$ cross section agree well with the BELLE and ALEPH measurements. For the pion and kaon angular distributions, there still exist discrepancies between our results and the experimental measurements. Possible reasons for these discrepancies are discussed briefly.