The twist-3 gluon contribution to $A_N$ in $J/\psi$ production in $pp$ collisions

TL;DR

This paper calculates the twist-3 gluon contribution to the single transverse-spin asymmetry in J/psi production in proton-proton collisions, providing a rigorous collinear factorization approach and numerical predictions relevant for RHIC and LHC.

Contribution

It offers the first rigorous collinear factorization calculation of the dominant gluonic contribution to J/psi SSA, linking it to gluon TMD distributions and highlighting its potential as a gluon structure probe.

Findings

Only C-even twist-3 gluon distribution contributes to J/psi SSA.

Numerical simulations suggest sizable SSA at RHIC and LHC energies.

The mechanism differs from SSA in light hadron and D-meson production.

Abstract

We present our results for the twist-3 gluon contribution to the single transverse-spin asymmetry(SSA) in $J/\psi$ production in proton-proton collisions. Although the data were reported by the RHIC experiment more than a decade ago, a theoretical calculation based on rigorous collinear factorization has remained unavailable for the dominant gluonic contribution. Our results show that only the $C$-even type twist-3 gluon distribution, which has a direct relationship with the gluon TMD distribution function, contributes to the $J/\psi$ SSA. Therefore, this observable serves as a key probe to understand the three-dimensional motion of gluons inside the proton. We also perform numerical simulations of the $J/\psi$ SSA at RHIC and LHC energies. Our simulations indicate that a sizable SSA could be generated through a mechanism different from that responsible for the SSA in light hadron and $D$-meson production.