  We study the semi-inclusive hadron production in deep inelastic scattering at
small $x$. A transverse momentum dependent factorization is found consistent
with the results calculated in the small-$x$ approaches, such as the
color-dipole framework and the color glass condensate, in the appropriate
kinematic region at the lowest order. The transverse momentum dependent quark
distribution can be studied in this process as a probe for the small-$x$
saturation physics. Especially, the ratio of quark distributions as a function
of transverse momentum at different $x$ demonstrates strong dependence on the
saturation scale. The $Q^2$ dependence of the same ratio is also studied by
applying the Collins-Soper-Sterman resummation method.
