Eta_c Meson Electromagnetic Transition Form Factor With QCD Correction

Quantum chromodynamics(QCD)is the theory describing the strong interaction between quarks.Since the establishment of QCD theory,it has been proved by many experiments,and widely used to study various types of processes on hadrons.After G.P.Lepage and S.J.Brodsky used perturbation QCD to study of hadronic electromagnetic form factors and electromagnetic transition form factors,a lot of theoretical research works of the meson(for example,?0,?,?',?c...)transition form factor FM? have been done in the framework of perturbation QCD,lattice QCD,non-relativistic QCD(NRQCD)and k? factorization,etc.The light meson(?0,?,?')electromagnetic transition form factor and the heavy meson(?c,?b)electromagnetic transition form factor are calculated to the QCD two-loop correction in the perturbed QCD and non-relativistic QCD,respectively.However,the theoretical calculation in NRQCD has a large deviation from the latest experimental data,this requires a new theoretical calculation of the heavy meson electromagnetic transition form factor.In this paper,we study the ?c? transition form factor F?c? in the perturbation QCD theory,in analogy to the case of the ?? case,at large momentum transfer Q2,the ?c?transition form factor F?c? can be defined as a convolution of a hard scattering amplitude TH(x,Q)and the meson distribution amplitude ?(x).The meson distribution amplitude?(x)is universal and independent of the process.The calculation of the heavy meson My transition form factor has some differences with the light meson My transition form factor,because it is the P-wave charmonium.The mass of ?c(M?c)and that of the charm quark(mc)cannot be neglected in calculation for the ?c? transition form factor.In the QCD next-leading-order correction of the hard scattering amplitude TH(x,Q),we take the longitudinal momentum fraction of valence quarks for ?c meson as xp and(1-x)p respectively,p is the momentum of the ?c meson.That point is an important difference between our work with the work on the ?c? transition form factor in NRQCD theory.We have made some model-dependent analysis for the ?c meson and they are the BSW model wave function ?BSW(x,k?),asymptotic distribution amplitude ?asy(x)and so on.Finally,we give the numerical results of the transition form factor F?c?.We calculate the value of F?c?(Q2)at Q2 ?0 in leading-order and next-leading-order,and extract the value F?c?(0)=0.07 from the experimental process ?c???.Our results are that F?c?(0)is equal to 0.09 in tree level,but F?c?(0)with one-loop level is larger than that in tree level.So the value of F?c?(0)in tree level is more consistent with the experimental value than that in one-loop level.Our theoretical calculations give the relation between[F(Q2)/F(0)]and the transfer momentum Q2,which avoids the influence of the uncertainty of the ?c decay constant f?c,and is also easy to compare with the experimental data given by BABAR.The theoretical calculated value[F(Q2)/F(0)]in tree level are slightly larger than the value of the curve fitted from the experimental date,The error between the value of[F(Q2)/F(0)]in tree level and the value of the curve fitted from the experimental data is very small in the low momentum region where Q2 approaches zero,and it is well agreement with the fitted curve value in the large momentum region 22Gev<Q2<50Gev,the differences is about 9.0%of the fitted curve value.The theoretical calculated value[F(Q2)/F(0)]in one-loop level is lower than the value in the tree level,and then it is also slightly lower than the fitted curve value from the experimental data.The differences between the value of[F(Q2)/F(0)]in one loop level and the value of the fitted curve is about 7.3%of the fitted curve value.In the large momentum region,comparing with the result of tree level,the error between the results in one loop level with the fitted curve value become smaller.Our work confirms that it is feasibly and correct by applied the perturbation QCD to study the ?c? transition form factor.