  It has been known for many years that jet cross sections at hadron colliders
exhibit double-logarithmic corrections starting at four-loop order, arising
from two soft Glauber-gluon interactions between the two colliding partons. The
resummation of these "super-leading logarithms" has been achieved only recently
by means of a renormalization-group treatment in soft-collinear effective
theory. We generalize this result and, within the same framework and for
quark-initiated processes, resum the double logarithms arising in the presence
of an arbitrary number of Glauber-gluon exchanges. For typical choices of
parameters, the higher-order Glauber terms give rise to corrections which are
expected to be numerically of the same magnitude as the super-leading
logarithms. However, we find that the Glauber series for jet cross sections is
dominated by the two-Glauber contribution, if the colliding partons are quarks
or anti-quarks.
