Invisible Higgs Decays from Higgs Graviscalar Mixing

We recompute the invisible Higgs decay width arising from Higgs-graviscalar mixing in the ADD model, comparing the original derivation in the non-diagonal mass basis to that in a diagonal mass basis. The results obtained are identical (and differ by a factor of 2 from the original calculation) but the diagonal-basis derivation is pedagogically useful for clarifying the physics of the invisible width from mixing. We emphasize that both derivations make it clear that a direct scan in energy for a process such as $WW\to WW$ mediated by Higgs plus graviscalar intermediate resonances would follow a {\it single} Breit-Wigner form with total width given by $\Gamma^{tot}=\Gamma_h^{SM}+\Gamma_{invisible}$. We also compute the additional contributions to the invisible width due to direct Higgs to graviscalar pair decays. We find that the invisible width due to the latter is relatively small unless the Higgs mass is comparable to or larger than the effective extra-dimensional Planck mass.