Investigation On The Form Factors Of η_c Electromagnetic Production

In this paper,the relativistic correction of γγ~*→η_c form factor in the process of the production of the heavy quarkonium is studied based on the theory of non-relativistic quantum chromodynamics(NRQCD).NRQCD is a very successful quantum chromodynamics of low energy efficient field theory.It can be used to study the production and annihilation processes of heavy quarks.The NRQCD factorization theorem factors a process into the product of a series of short-range coefficients and longrange matrix elements.The short-range coefficient contains the contribution of the scale,which is Greater than the m_Q,While the contribution of this scale that is less than m_Q is sucked into the non-perturbable long-range matrix element.The short-range coefficient can be calculated for perturbation,so it can be expanded by the coupling constant.And each long-range matrix element is expanded by the characteristic velocity in the heavy quarkonium system.In this way,the NRQCD factorization formula expands the amplitude or cross section of a process by the coupling constant and the characteristic velocity.The specific calculation to which order needs to be determined according to the convergence of the expansion.In this paper,we calculate the short-range coefficient(F)corresponding to the leading order and the short-range coefficient(G)corresponding to the subordinate matrix element.The process of γγ~*→η_c is now calculated in the literature to the two-loop diagram,and the experiment is done with the phenomenological discussion,and the results show that only consider F is not consistent with the experiment.In order to test the correctness of the NRQCD factorization formula and the ability to predict,this paper studies the other short-range coefficient G of the process.We expand the G to the next-leading order of the perturbation expansion,that is,one loop of the order,and combined with F and G through the appropriate parameters to do a detailed phenomenological analysis and discussion.In addition,the paper also studies the form factor of γγ~*→η_b.Future experiments can test the correctness of theoretical calculations to test NRQCD theory.In order to complete the calculation,the paper uses Feyn Arts to generate Feynman diagram,and uses Feyn Calc to analyze high energy physics.In addition,the paper also uses the Apart and FIRE software package to integrate the part of the loop.We will eventually get the main contribution to the physical process of the integral items,which greatly saves our computing time.In order to ensure the correctness of the calculation,we have repeated some of the original calculation.This includes: the correction of J/ψ→e~+e~-,η_c→γγ and e~+e~-→η_c+γ in order α_s andα_sν~2.We found that the results were consistent with the used literature.