Electromagnetic and Gravitational Decay of the Higgs Boson

Abstract

The decays of a scalar particle, of either parity, into two photons or into two gravitons are evaluated. The effective interactions are of the form φ FF , φ FF ~ or φ RR , φ RR ~ ; in particular, the Higgs meson decay mode into gravitons is tiny and can be neglected. In two recent papers, Srivastava and Widom (2000 a , 2000 b ) have claimed that the decay width of the Higgs meson into two gravitons is given by �� 2 G F m 3 /16 π . In their result, which they say stems from an effective interaction φ R / � φ � , Newton's constant disappears and gets replaced by the Fermi constant, leading to a large magnitude for the process. If their result were true, it would be counter-intuitive to the notion that gravitational interactions are miniscule in particle physics and it would imply that the Higgs mesons disappears very quickly into a puff of gravitational plus electromagnetic radiation! In this paper we revisit this interesting problem and derive the correct magnitudes for the decay amplitudes, be the decaying particle scalar or pseudoscalar; our faith in the weakness of induced gravitational (and electromagnetic) effects is happily restored. We consider parity-conserving decays of a 0 + or 0 − particle into two photons γ or into two gravitons h . A simple helicity amplitude analysis (Delbourgo and Liu 1998) shows that either process is governed by just one reduced helicity amplitude, � k , λ ; k ′ , λ′ | S |0 � , where λ = λ′ = 1 or 2, because of parity conservation. The same conclusion is reached by a covariant amplitude analysis, using the twin principles of gauge and general covariance. If e represents the external wavefunction of an incoming massless particle ( γ or h ), we may write down the unique couplings: