Drell-yan Process, The P-a Collisions. Target Rest Frame

Although cross sections are Lorentz invariants, the partonic interpretation of the microscopic process depends on the reference frame. B. Z. Kopeliovich et. al. first applies the color-dipole approach to Drell-Yan process, which says that in the target rest frame the Drell-Yan process can be viewed as bremsstrahlung .rather than parton annihilation. According to factorization theorem, the Drell-Yan cross section can be expressed in terms of the same dipole cross section that appears in deep inelastic scattering. It is found that unlike Drell-Yan model , color dipole approach to Drell-Yan process needs no K factor and it describes nuclear shadowing effect well in p-A Drell-Yan process. In p-A Drell-Yan process , the incident quark will experience multiple collisions with different nucleons in the nucleus, which leads to the suppressed Drell-Yan cross section , in another words, the nuclear shadowing effect. Gribov combined the nonrelativistic Glauber multiple collisions theory with quantum field theory and Feynman diagram technique so that relativistic kinematics could be included. Based on Glauber-Gribov theory , B. Z.Kopeliovich et.al. developed Green function method to calculate the shadowing effect in p-A Drell-Yan process. Whereas, as a crucial input in the color dipole approach , the color dipole cross section is largely unknown in theory, it is necessary for us to comparedifferent hadron-hadron dilepton production processes to test the appalicablity of this approach.In this paper, the color dipole approach in the target rest frame is presented and the ratio of the Drell-Yan cross section per nucleon for an 800 GeV proton beam incident on a variety of nuclear targets are calculated and the results are compared with Fermilab E772 and E866 experimental data .It is shown that without considering the energy loss effect, the calculated results can fit rather well with experimental data.