  We analytically and numerically study the effect of perturbative gluons
emission on the "Filtering analysis", which is part of a subjet analysis
procedure proposed two years ago to possibly identify a low-mass Higgs boson
decaying into b\bar{b} at the LHC. This leads us to examine the non-global
structure of the resulting perturbative series in the leading single-log
large-N_c approximation, including all-orders numerical results, simple
analytical approximations to them and comments on the structure of their series
expansion. We then use these results to semi-analytically optimize the
parameters of the Filtering analysis so as to suppress as much as possible the
effect of underlying event and pile-up on the Higgs mass peak reconstruction
while keeping the major part of the perturbative radiation from the b\bar{b}
dipole.
