A Estimate Of Twist-3 Correction For Two Photons Into Pi/K Pair Production With Transverse-momentum Dependence

From the middle of the last century to the present,a large number of data of the two-photon exclusive processes have been measured experimentally,which provides more detailed and reliable experimental data for the study of the two-photon exclusive processes by the perturbation quantum chromodynamics theory.So it has attracted many theoretical and experimental physicists to study the two-photon exclusive processes.In the theoretical framework of pQCD factorization scheme,the scattering amplitude of this process can be expressed as the convolution form of the hard scattering amplitude TH calculated by the perturbation and the hadron wave function calculated by the non?perturbation method.This kind of factorization scheme has been widely used in high energy region,but it is still controversial in the energy range of 1 Gev-4 Gev measured by experiment.The experimental data of the scattering cross sections of two photon to light pseudoscalar meson pairs measured experimentally are obviously higher than the predicted values given by the leading order in theory.Based on the analysis of experimental measurements and theoretical calculations,we consider that the contribution of the transverse momentum kT of quarks in the twist-3 distribution amplitude of the final meson to the scattering process cannot be ignored.In this paper,we use the kT factorization theorem to calculate the contribution of pion meson and kaon meson twist-2 and twist-3 distribution amplitude of the scattering cross section of the process ????+?-,K+K-and the ratio ?0(K+K-)/?0(?+?-)of the cross section.By means of the transverse momentum kT carried by quarks in the final meson,the problem of endpoint divergence can be eliminated.However,the estimation of the contribution of the process to twist-3,we ignore the transverse momentum of the Fermi propagator and only retain the transverse momentum in the gluon propagator which provides the main contribution,so twist-3 distribution amplitude of the pseudoscalar meson is given by the BHL model.The endpoint divergence problem to reduce the amplitude of this part.The results show that the contribution of the pseudoscale meson twist-2 distribution amplitude,which depends on the transverse momentum,to the scattering process is consistent with previous theoretical predictions in the two-photon scattering collision energy range of 1 Gev-7Gev.Compared with the experimental data,they are lower than the experimental values by about an order of magnitude.However,when the pseudoscale meson twist-3 distribution amplitude dependent on transverse momentum is considered,the scattering cross section is obviously increased to the same order of magnitude as the experimental value,and it is in good agreement with the experimental value.The ratio?0(K+K-)/?0(?+?-)of the contribution of the scattering cross section of the pion meson and kaon meson twist-2 distribution amplitude is quite different from the measured value,while the ratio of the scattering cross section contribution of the twist-3 distribution amplitude is in good agreement with the experimental measurement value.