Spin-flip gluon generalized transverse-momentum-dependent parton distribution F1,2 at small x

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) Re(F1,2) as Re(F1,2)∼(1x)α¯s(4 ln2−8/3)(cos3ϕkΔ+cosϕkΔ). This is done by analytically solving the integro-differential evolution equation for Re(F1,2), recently proposed by Hatta and Zhou, in the dilute regime. Interestingly, the surviving solution corresponds to conformal spin n=2 and carries an explicit cos3ϕkΔ+cosϕkΔ azimuthal dependence. As the imaginary part of F1,2, is related to the spin-dependent odderon or gluon Siver function and scales as Im(F1,2)∼x0, the positive intercept for Re(F1,2) 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. Published by the American Physical Society 2024