  We consider di-jet production in hadron collisions where a transverse veto is
imposed on radiation for (pseudo-)rapidities in the central region only, where
this central region is defined with rapidity cutoff. For the case where the
transverse measurement (e.g., transverse energy or min $p_T$ for jet veto) is
parametrically larger relative to the typical transverse momentum beyond the
cutoff, the cross section is insensitive to the cutoff parameter and is
factorized in terms of collinear and soft degrees of freedom. The virtuality
for these degrees of freedom is set by the transverse measurement, as in
typical transverse-momentum dependent observables such as Drell-Yan, Higgs
production, and the event shape broadening. This paper focuses on the other
region, where the typical transverse momentum below and beyond the cutoff is of
similar size. In this region the rapidity cutoff further resolves soft
radiation into (u)soft and soft-collinear radiation with different rapidities
but identical virtuality. This gives rise to rapidity logarithms of the
rapidity cutoff parameter which we resum using renormalization group methods.
We factorize the cross section in this region in terms of soft and collinear
functions in the framework of soft-collinear effective theory, then further
refactorize the soft function as a convolution of the (u)soft and
soft-collinear functions. All these functions are calculated at one-loop order.
As an example, we calculate a differential cross section for a specific
partonic channel, $q q' \to q q'$, for the jet shape angularities and show that
the refactorization allows us to resum the rapidity logarithms and
significantly reduce theoretical uncertainties in the jet shape spectrum.
