Relativistic corrections to prompt $J/\psi$ photo- and hadroproduction

Abstract

We systematically calculate the relativistic corrections to prompt $J/\psi$ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the ${}^3{S}_1^{[1]}$ and ${}^3{P}_J^{[1]}$ color-singlet and the ${}^3{S}_1^{[8]}$, ${}^1{S}_0^{[8]}$, and ${}^3{P}_J^{[8]}$ color-octet channels as well as the effects due to the mixing between the ${}^3{S}_1^{[8]}$ and ${}^3{D}_1^{[8]}$ channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the nonrelativistic-QCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, except in the ${}^3{S}_1^{[1]}$ color-singlet channel of hadroproduction. We also observe significant differences in the line shapes of the relativistic corrections between photoproduction and hadroproduction.

Comments: 26 pages, 3 figures, matches journal version