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

TL;DR

This paper calculates relativistic corrections to the polarization of prompt J/psi particles produced in photon- and hadron-induced processes, aiming to improve understanding of polarization data and resolve existing puzzles.

Contribution

It provides a comprehensive calculation of relativistic corrections for J/psi polarization including multiple channels and mixing effects within the nonrelativistic QCD framework.

Findings

Relativistic corrections are significant at low transverse momentum and high inelasticity.

All squared hard-scattering amplitudes are provided in analytic form.

Results support more complete global analyses of J/psi production data.

Abstract

We systematically calculate the relativistic corrections to the polarization variables of 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, especially at small transverse momentum $p_T$ and large inelasticity $z$. The results obtained here and in our previous work on the unpolarized yield [Phys. Rev. D 90, 014045 (2014)] will help to render global analyses of prompt $J/\psi$ production data more complete and hopefully to shed light on the $J/\psi$ polarization puzzle.