$\gamma \gamma \to M^{+}{M}^{-}(M=\pi ,K)$ processes with twist-3 corrections in QCD

We study the $\gamma \gamma \to M^{+}{M}^{-}(M=\pi ,K)$ processes with the contributions from the two-particle twist-2 and twist-3 distribution amplitudes of pion and kaon mesons on BHL prescription in the standard hard-scattering approach. The results show that the contributions from twist-3 parts are actually not power suppressed comparing with the leading-twist contributions and the cross sections agree well with the experimental data in the two-photon center-of-mass energy $W>2.8$ GeV. We also predict the cross section ratio ${\sigma }_0({\pi }^{+}{\pi }^{-})\mathrm{/}{\sigma }_0(K^{+}{K}^{-})$, which is compatible with the experimental data from TPC and Belle.