We demonstrate by performing a global fit on Higgs signal strength data that
large invisible branching ratios Br_{inv} for a Standard Model (SM) Higgs
particle are currently consistent with the experimental hints of a scalar
resonance at the mass scale m_h ~ 124 GeV. For this mass scale, we find
Br_{inv} < 0.64 (95 % CL) from a global fit to individual channel signal
strengths supplied by ATLAS, CMS and the Tevatron collaborations. Novel tests
that can be used to improve the prospects of experimentally discovering the
existence of a Br_{inv} with future data are proposed. These tests are based on
the combination of all visible channel Higgs signal strengths, and allow us to
examine the required reduction in experimental and theoretical errors in this
data that would allow a more significantly bounded invisible branching ratio to
be experimentally supported. We examine in some detail how our conclusions and
method are affected when a scalar resonance at this mass scale has couplings
deviating from the SM ones.Comment: 32pp, 15 figures v2: JHEP version, ref added & comment added after
Eq.