| Heavy quarkonium is a frontier of particle physics.The research of heavy quarko-nium mainly includes the spectrum,decay,production of heavy quarkonium and the property of heavy quarkonium in media.A new approach,the quantum chromody-namics?QCD?factorization approach to take care of heavy quarkonium production was proposed recently.In this paper,the cross section for the partonic scattering channel? +q ?QQ???+q at e6eq6 order and the cross section for the partonic scattering chan-nel ?+g?QQ???+g at e2eq2g4 order are calculated.In the process of calculation,firstly,the Feynman diagrams for the partonic scattering channel ? +q? QQ???,+q at e6eq6 order and the Feynman diagrams for the partonic scattering channel ? + g ? QQ???+g at e2eq2g4 order are drawn.Next according to the Feynman rules of QCD in momen-turn space,the invariant amplitudes corresponding to above-mentioned Feynman di-agrams are written out.The square of absolute value of the invariant amplitude is|M|2 = MaMa???+ MaMb???+ Mb+Ma???+ MbMb?.Averaging MaMa???,MaMb???,MbMa???,MbMb???over spin and color of the initial state and summing MaMa???,MaMb???,MbMa???,MbMb???over spin and color of the final state are transformed into the product of the color factor and averaging them over spin of the initial state and summing them over spin of the final state.Then their color factors are calculated by the color projection operators.Averag-ing MaMa???,MaMb???,MbMa???,MbMb???over spin of the initial state and summing them over spin of the final state are transformed into the traces of matrixes by the techniques of spin projection and summing over the spin of a photon and a gluon.Finally,the traces of matrixes are calculated by some properties and trace formulas of y matrix.Thus the above-mentioned partonic cross sections are calculated.Taking the partonic cross sec-tions we calculate and those which have been calculated in previous literatures together will give the complete partonic cross sections for heavy quarkonium production. |
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