An Argument for Nonminimal Higgs Coupling to Gravity

Abstract

The coupling of gravity to a scalar field raises a number of interesting questions of principle since the usual minimal coupling obtained by replacing ordinary derivatives with covariant derivatives is not available -- they are the same operation on scalar fields. Conformal couplings in the Lagrangian proportional to $\phi^2 R$ have been suggested before, usually to maintain conformal invariance for massless scalar fields, but at the cost of breaking the equivalence principle. Here we give intuitive arguments for the appearance of such a term due to fluctuations of scalar particles about their classical world lines. Remarkably, these arguments give precisely a correction of the form required to maintain conformal invariance. We also show that such a term would naturally be expected for the Higgs field in the Standard Model, making a perhaps surprising connection between weak-scale physics and gravity. The nonminimal coupling, whether induced by quantum corrections or already present as a bare term, can be constrained from measurements of the Higgs width assuming the Higgs particle is to be detected.