The eikonal spin-dependent Odderon and gluon Sivers function of a proton, and its small-$x$ evolution

TL;DR

This paper models the gluon Sivers function of a proton at small x using a light-front approach, analyzing its properties and small-x evolution, including the impact of the eikonal Odderon and BFKL dynamics.

Contribution

It introduces a light-front model to compute the gluon Sivers function at moderate small x and explores its small-x evolution with BFKL anomalous dimension.

Findings

The model predicts the magnitude and peak position of the Sivers function.

The small-x tail of the Sivers function follows a power-law decay with exponent -3.3.

The BFKL anomalous dimension characterizes the small-x evolution of the gluon Sivers function.

Abstract

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small $x_0 \sim 0.1$ and transverse momentum $k_\perp \lesssim 1$~GeV. The model light-cone (LC) wave function predicts the properties of $x f_{1T}^{\perp g}(x,k_\perp)$ such as its overall magnitude, the position of its peak in $k_\perp$, and its behavior at small $k_\perp$. We then compute numerically the BFKL anomalous dimension characterizing the power-law tail at $k_\perp \gtrsim 1.5$~GeV of the gluon Sivers function at small LC momentum fractions, $\alpha_s \log x_0/x = 1$: $x f_{1T}^{\perp g}(x,k_\perp) \sim k_\perp^{-3.3}$.