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 & eth;F1;2 & THORN; as Re & eth;F1;2 & THORN; similar to & eth;1x & THORN;alpha<overline>s & eth;4 ln 2-8=3 & THORN;& eth;cos 3 phi k Delta & thorn; cos phi k Delta & THORN;: This is done by analytically solving the integro-differential evolution equation for Re & eth;F1;2 & THORN;, recently proposed by Hatta and Zhou, in the dilute regime. Interestingly, the surviving solution corresponds to conformal spin n 1/4 2 and carries an explicit cos 3 phi k Delta & thorn; cos phi k Delta azimuthal dependence. As the imaginary part of F1;2, is related to the spin-dependent odderon or gluon Siver function and scales as Im & eth;F1;2 & THORN; similar to x0, the positive intercept for Re & eth;F1;2 & THORN; 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.