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arXiv · 2603.09630

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

Sanjin Benić·Adrian Dumitru·Florian Hechenberger·Tomasz Stebel
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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 (but pre-asymptotic) LC momentum fractions, $\alpha_s \log x_0/x = 1$: $x f_{1T}^{\perp g}(x,k_\perp) \sim k_\perp^{-3.3}$.

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Sanjin Benić, Adrian Dumitru, Florian Hechenberger, Tomasz Stebel. 2026-03-10. The eikonal spin-dependent Odderon and gluon Sivers function of a proton, and its small-$x$ evolution. https://arxiv.org/abs/2603.09630

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