Sudakov double logs in single-inclusive hadron production in DIS at small $x$ from the Color Glass Condensate formalism

We investigate the high $Q^2$ (photon virtuality) limit of single-inclusive hadron production in DIS (SIDIS) at small $x$, using the color glass condensate formalism at next-to-leading order. We focus on the ${\mathrm{\Lambda }}_{QCD}^2\ll {\mathbf{p}}_h^2\ll Q^2$ kinematic regime where ${\mathbf{p}}_h$ is the produced hadron transverse momentum, and extract the Sudakov double logarithms. We further argue that compatibility between the CGC calculation and TMD factorization at one-loop order can only be achieved if the small-x evolution is kinematically constrained.