Scattering Cross Section Of Two-photon To Pseudoscalar Meson Pair Based On Ads Model

Since the establishment of the Quantum chromodynamics(QCD)theory,many physicists have done a lot of theoretical prediction and practical verification for the two-photon exclusive processes in the Quantum chromodynamics framework.With the development of research and technology,more and more data have been measured and collected experimentally in the two-photon exclusive processes,this provides a detailed and reliable reference for the further study of the quantum chromodynamics two photon exclusive processes.Since the initial state of the two photon exclusive processes does not participate in the strong interaction,only the hadronic state of the final state is considered,which is a very clean process for studying the properties of the hadronic state,therefore,many theoretical researchers and experimental workers are attracted to carry out more in-depth research on this process.In the pQCD factorization framework,many researchers have done a lot of research on this process.The scattering amplitudes can be expressed in the form of the hard scattering amplitudes that can be calculated by perturbations and the convolution forms of the hadronic wave functions that can be calculated by non-perturbations,however,there are still many disputes between the results obtained and the experimental values,especially in the range of 1-4 Gev measured in the low energy region,and the experimental cross section data of two-photon-to-pseudoscalar meson pair scattering,is much higher than the theoreticalpredictions.We hope that by analyzing the experimental data and further theoretical calculation,the cross section of two-photon scattering from a pair of pseudoscalar mesons can also be in agreement with the experimental values in this energy region.Based on pQCD factorization,the hard scattering amplitudes of the two-photon to pseudoscalar meson pair process are calculated in this paper.The problem of end-point divergence in hard scattering amplitudes is eliminated by the Sudakov factor of the transverse momentum carried by quarks in the final mesons.We have made a new attempt to calculate the wave function and the distribution amplitude of the pseudoscalar meson by using the distribution amplitude of Ads model.We consider the effect of the evolution of energy scaling on the distribution amplitude of pseudoscalar mesons,the contribution of pion and kaon meson twist-2 and twist-3 amplitudes to the scattering cross section of two-photon to pseudoscalar meson pair is calculated respectively,the contribution of the amplitudes of the pseudoscalar meson distribution in the Ads model to the scattering cross section is also compared with that in the BHL(Brodsky-Huang-Lepage)framework.In the calculation of the contribution of this process to twist-3,we estimate that the transverse momentum of the fermion propagator is ignored,and only the transverse momentum of the main contributor gluon propagator is preserved.We hope that this method can improve the theoretical calculation value of this process in the low energy region.Finally,we calculate the scattering process of the final pseudoscalar meson by using the distribution amplitude of the Ads model,the Cross section of twist-2 wave function is lower than that of the experimental data at the initial energy level of 1 Gev,even though the twist-3 wave function is taken into account and the results are optimized,in the case of kaon mesons,the cross section of twist-2 wave function is highly consistent with the experimental value in the low energy region,when the contribution of twist-2 wave function is considered,taking into account the contribution of the twist-3 wave function,the calculated cross section is in good agreement with the experimental data in the whole energy region.The energy scaling evolution of pion twist-2 wave function and the contribution of another form of the distribution amplitude of the Ads model are taken into account,especially in the low energy region,the experimental data can be well matched.