Relativistic corrections to prompt J/ψ photo- and hadroproduction

We systematically calculate the relativistic corrections to prompt J/ψ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the ³S₁^[1] and ³P_J^[1] color-singlet and the ³S₁^[8], ¹S₀^[8], and ³P_J^[8] color-octet channels as well as the effects due to the mixing between the ³S₁^[8] and ³D₁^[8] channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the NRQCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, except in the ³S₁^[1] color-singlet channel of hadroproduction. We also observe significant differences in the lineshapes of the relativistic corrections between photoproduction and hadroproduction.