Spin-flip gluon GTMD $F_{1,2}$ at small-$x$

Abstract

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, \begin{eqnarray} {\rm Re}(F_{1,2}) \sim \left(\frac{1}{x}\right)^{{\bar α}_s\left(4\ln2-8/3\right)} \left(\cos 3ϕ_{kΔ} +\cos ϕ_{kΔ}\right). \nonumber \end{eqnarray} 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 $\cos 3{\varphi }_{k\Delta }+\cos {\varphi }_{k\Delta }$ 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 unpolarised GTMDs and associated spin-flip processes.

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Cited by in corpus (3)

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• Off forward non-SCHC contributions to exclusive vector quarkonium production from the "spin dependent BFKL Pomeron"
• Small-$x$ evolution of dipole amplitude in momentum space: forward--off-forward correspondence