Comparative Study Of ???M~+M~- And ?M~±??M~±(M=?,K)

In recent decades,many physics experimenters have conducted a lot of research on the two-photon exclusive processes,and have obtained abundant experimental data,which has better promoted the theoretical research process of the two-photon exclusive processes.The perturbative QCD(PQCD)factorization method based on the kT factorization theorem by Li Xiangnan and others is one of the mainstream methods used in the study of the two-photon exclusive processes.Under the framework of the perturbative QCD theory,the scattering amplitude of the ???M+M-(M=?,K)process can be factored into the convolution of the hard scattering process amplitude TH and the hadron distribution amplitude.The non-perturbed part is absorbed into the hadron wave function,and we know that the hadron wave function is universal.it is independent of the process in which it is located,thus ensuring the feasibility of perturbation calculation.However,the theoretical results of the leading order obtained are quite different from the experimental data.In order to solve this problem and facilitate the follow-up comparative study of Compton scattering,we used the Mandelstam invariant to redefine the scalar product of the two-photon collision process,and under the perturbation QCD theoretical framework based on kT factorization,we considered the contribution of the twist-3 wave function of the pion and kaon meson,the hard scattering amplitude of the???M+M-(M=?,K)process is calculated.The end divergence problem in the calculation is solved by the Sudakov factor containing the lateral momentum.For the non-perturbed pseudoscalar meson wave function part,in addition to theoretical calculations with the distribution amplitude under the Ads model,we also used the asymptotic(Asy)model and the Chernyk-Zhitnitsky(CZ)model to compare the distribution amplitudes.Through these three models,the contribution of the distribution amplitude of pion and kaon meson twist-2 and twist-3 to the total scattering cross section of the ???M+M-(M=?,K)process is calculated.Finally,the theoretical numerical results obtained are compared and analyzed with the experimental data measured by the BELLE,TPC,and ALEPH experimental groups.The results show that for the two-photon to the pseudoscalar meson pair process,when the Twist-2 distribution amplitude is only considered in the total cross section,the numerical results are obviously lower than the experimental results.but when the contribution of the amplitude of twist-3 distribution is taken into account,the obtained numerical results have an order of magnitude increase,indicating that for the ???M+M-(M=?,K)process,the contribution of the twist-3 distribution amplitude becomes the dominant factor.Therefore,we must take this part of the contribution into account in the calculation process.And the result of the recalculation of the two-photon collision process is consistent with our previous research.After completing the theoretical analysis of the above two-photon collision process,since we choose the Mandelstam variant to define the scalar product,to study the Compton scattering process,we only need to exchange s and t in the above theoretical calculations and then calculate,the differential cross section data of the Compton scattering process can be obtained and compared with the results obtained by Li Xiangnan et al.The results show that:for the Compton scattering process,we have calculated the numerical results when s/t=-0.2 and s/t=-0.5.The numerical results of Li Xiangnan and others are obtained under the QCD sum rules,and This article is completed under the perturbation QCD theory,but the results obtained are consistent within the allowable range of error.And when s/t=-0.2,the scattering cross section when considering the amplitude contribution of the twist-3 distribution is calculated,and it is found that there is an order of magnitude improvement compared to when only considering the amplitude contribution of the twist-2 distribution.This also shows that in the Compton scattering process,the contribution of the twist-3 distribution amplitude has a greater impact on the differential cross section,so we have to consider it in the calculation.