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

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-II 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.