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.

References in corpus (9)

• Generalized parton correlation functions for a spin-1/2 hadron
• Gluon and Wilson loop TMDs for hadrons of spin $\le$ 1
• The elliptic gluon GTMD inside a large nucleus
• Nucleon Energy Correlators for the Color Glass Condensate
• Signature of the gluon orbital angular momentum
• Gluon distributions in the proton in a light-front spectator model
• Computing the gluon Sivers function at small-$x$
• Harmonics of Parton Saturation in Lepton-Jet Correlations at the EIC
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution

Cited by in corpus (3)

• Gluon generalized transverse momentum dependent parton distributions and Wigner functions of the Proton
• 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