High Order QCD Correction To H?c(?) Process

The study on the interaction between Higgs boson and SM particles,becomes one of the hot topics of particle physics at the frontier since it was found.The experimental measurements of the interaction of the Higgs with the bottom quark at LHC are finished,and the experimental results are compatible with the prediction of the standard model.A preliminary study for the SM Higgs boson decaying to a charm quark pair is performed by CMS collaboration and ATLAS collaboration respectively,and the measurement er-ror is relatively large.High precision production for h?c(?),that is important to test the standard model accurately and searching for new physical signals.In this paper,We study the decay of the SM Higgs boson to massive charm quark pair:at the next-to-next-to leading order QCD,the process of h?c(?) is calculated accurately,including the exact results of flavour-singlet contributions where the Higgs boson couples to the internal top and bottom quark.Some helpful information on the running mass effects related to Yukawa coupling may be obtained by analyzing this process.According to our research results,We find that the flavour-singlet contributions where the Higgs bo-son couples to the internal top and bottom quark is an important part of the NNLO QCD correction and cannot be ignored.Using MS scheme to represent the running quark mass in the Yukawa coupling is necessary to offset large logarithm regarding mQ/mh effectively,making the theoretical prediction more reliable.The higher order correction of QCD reduces the dependence of the decay width on the renormalization scale.The results of this paper are helpful for the study ofh?c(?) processes in the Large Hadron Collider(LHC)and the future e+e-Collider to accurately test the standard model and find new physical signals beyond the Standard Model.