  By defining dijet rapidity gap events according to interjet energy flow, we
treat the photoproduction cross section of two high transverse momentum jets
with a large intermediate rapidity region as a factorizable quantity in
perturbative QCD. We show that logarithms of soft gluon energy in the interjet
region can be resummed to all orders in perturbation theory. The resummed cross
section depends on the eigenvalues of a set of soft anomalous dimension
matrices, specific to each underlying partonic process, and on the
decomposition of the scattering according to the possible patterns of hard
color flow. We present a detailed discussion of both. Finally, we evaluate
numerically the gap cross section and gap fraction and compare the results with
ZEUS data. In the limit of low gap energy, good agreement with experiment is
obtained.
