  We derive a factorization theorem that allows for resummation of small-$x$
logarithms by exploiting Glauber operators in the soft collinear effective
field theory. Our analysis is carried out for the hadronic tensor $W^{\mu\nu}$
in deep inelastic scattering, and leads to the definition of a new gauge
invariant soft function $S^{\mu\nu}$ that describes quark and gluon emission in
the central region. This soft function provides a new framework for extending
resummed calculations for coefficient functions to higher logarithmic orders.
Our factorization also defines impact factors by universal collinear functions
that are process independent, for instance being identical in small-$x$ DIS and
Drell-Yan.
