  We study the change in the di-photon invariant mass distribution for Higgs
boson decays to two photons, due to interference between the Higgs resonance in
gluon fusion and the continuum background amplitude for gluon pair to photon
pair. Previously, the apparent Higgs mass was found to shift by around 100 MeV
in the Standard Model in the leading order approximation, which may potentially
be experimentally observable. We compute the next-to-leading order QCD
corrections to the apparent mass shift, which reduce it by about 40%. The
apparent mass shift may provide a way to measure, or at least bound, the Higgs
boson width at the Large Hadron Collider through "interferometry." We
investigate how the shift depends on the Higgs width, in a model that maintains
constant Higgs boson signal yields. At Higgs widths above 30 MeV the mass shift
is over 200 MeV and increases with the square root of the width. The apparent
mass shift could be measured by comparing with the ZZ* channel, where the shift
is much smaller. It might be possible to measure the shift more accurately by
exploiting its strong dependence on the Higgs transverse momentum.
