  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) ${\rm Re}(F_{1,2})$ as, \begin{eqnarray} {\rm Re}(F_{1,2}) \sim
\left(\frac{1}{x}\right)^{{\bar \alpha}_s\left(4\ln2-8/3\right)} \left(\cos
3\phi_{k\Delta} +\cos \phi_{k\Delta}\right). \nonumber \end{eqnarray} This is
done by analytically solving the integro-differential evolution equation for
${\rm Re}(F_{1,2})$, recently proposed by Hatta and Zhou, in the dilute regime.
Interestingly, the surviving solution corresponds to conformal spin $n=2$ and
carries an explicit $\cos 3\phi_{k\Delta} + \cos \phi_{k\Delta}$ azimuthal
dependence. As the imaginary part of $F_{1,2}$, is related to the
spin-dependent odderon or gluon Siver function and scales as ${\rm Im}(F_{1,2})
\sim x^{0}$, the positive intercept for ${\rm Re}(F_{1,2})$, 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.
