  The Higgs mass determination from diphoton events at the LHC can be affected
by interference between the Higgs resonant and continuum background amplitudes
with the same initial and final states. For the leading order gluon fusion
process, this shift was previously found to exceed 100 MeV, with some
dependence on the diphoton mass resolution and the methods used to extract and
fit the peak from data. In this paper, I consider the mass shift for the
process pp --> j\gamma\gamma\ that includes an additional central jet in the
final state. For cuts on the transverse momentum of the jet of 25 GeV or more,
the diphoton Higgs peak mass shift due to interference is found to be very
small, due in part to less interference for the gluon-gluon initiated
subprocess, and in part to a cancellation between it and the quark-gluon
initiated subprocess.
