Gluon Sivers function from forward exclusive $\chi_{c1}$ photoproduction on unpolarized protons

TL;DR

This paper investigates the gluon Sivers function through exclusive $$ photoproduction on unpolarized protons, comparing Primakoff and Odderon exchange mechanisms to constrain gluon transverse momentum distributions.

Contribution

It introduces a method to extract the gluon Sivers function by analyzing $$ production and compares two models for the Sivers function using cross section ratios and angular distributions.

Findings

The ratio of Sivers to Primakoff cross sections varies with $x$.

Angular coefficient $mbda_ heta$ depends on the gluon Sivers function.

Observables can constrain the gluon Sivers function at small $x$.

Abstract

Exclusive production of a $\chi_{c1}$ axial vector quarkonia in photon-proton scattering at high energies requires a $C$-odd $t$-channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as $t \to 0$. Alternatively, a $C$-odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the $k_\perp$-moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient $\lambda_\theta$ governing the angular distribution of the $\chi_{c1} \to J/\psi + \gamma$ decay as functions of $x$. We point out that these observables constrain the magnitude of the gluon Sivers function at small $x$ which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions.