Invisible Higgs Decays from Higgs Graviscalar Mixing

TL;DR

This paper recalculates the invisible Higgs decay width from Higgs-graviscalar mixing in the ADD model, clarifying the physics with a diagonal basis approach and exploring additional decay contributions.

Contribution

It provides a pedagogical derivation of the invisible Higgs width in a diagonal mass basis and compares it to previous methods, including new decay channel calculations.

Findings

The diagonal basis derivation confirms previous results, differing by a factor of 2 from earlier calculations.

The total width follows a single Breit-Wigner form with combined SM and invisible contributions.

Additional Higgs to graviscalar pair decays are generally small unless the Higgs mass is high.

Abstract

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.