  It is well known that understanding the structure of jet radiation can
significantly improve Higgs analyses. Using Fox--Wolfram moments we
systematically study the geometric patterns of additional jets in weak boson
fusion Higgs production with a decay to photons. First, we find a significant
improvement with respect to the standard analysis based on an analysis of the
tagging jet correlations. In addition, we show that replacing a jet veto by a
Fox-Wolfram moment analysis of the extra jet radiation almost doubles the
signal-to-background ratio. Finally, we show that this improvement can also be
achieved based on a modified definition of the Fox--Wolfram moments which
avoids introducing a new physical scale below the factorization scale. This
modification can reduce the impact of theory uncertainties on the Higgs rate
and couplings measurements.
