When gluons go odd: how classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions

TL;DR

This paper demonstrates that in the saturation/Color Glass Condensate framework, odd azimuthal harmonics in two-gluon correlations arise from higher-order interactions involving multiple scatterings, providing a leading-order expression and confirming their non-zero contribution.

Contribution

The paper derives a leading-order expression for two-gluon production that includes all-order target interactions and three projectile interactions, revealing the origin of odd harmonics.

Findings

Odd harmonics require three scatterings in both projectile and target.

Derived an all-order interaction expression for two-gluon production.

Confirmed analytically and numerically that odd harmonics are non-zero.

Abstract

We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. We evaluate the obtained expression both analytically and numerically, confirming that the odd-harmonics contribution to the two-gluon production in the saturation framework is non-zero.