Until recently the spin-flip processes in the deep inelastic scatterings are thought to be suppressed in the high energy. We found a positive intercept for the spin-flip generalized transverse momentum-dependent parton distribution (GTMDs) $\mathrm{Re}(F_{1,2})$ as $\mathrm{Re}(F_{1,2})\sim {(\frac{1}{x})}^{{\overline{\alpha }}_s(4\ln 2-8/3)}(\cos 3{\varphi }_{k\mathrm{\Delta }}+\cos {\varphi }_{k\mathrm{\Delta }}).$ This is done by analytically solving the integro-differential evolution equation for $\mathrm{Re}(F_{1,2})$, recently proposed by Hatta and Zhou, in the dilute regime. Interestingly, the surviving solution corresponds to conformal spin $n=2$ and carries an explicit $\cos 3{\varphi }_{k\mathrm{\Delta }}+\cos {\varphi }_{k\mathrm{\Delta }}$ azimuthal dependence. As the imaginary part of $F_{1,2}$, is related to the spin-dependent odderon or gluon Siver function and scales as $\mathrm{Im}(F_{1,2})\sim x^0$, the positive intercept for $\mathrm{Re}(F_{1,2})$ implies that it is expected to dominate over the gluon Siver function in the small-$x$ limit and may directly impact the modeling of unpolarized GTMDs and associated spin-flip processes.

• Received 15 December 2023
• Accepted 7 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.074039

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Published by the American Physical Society