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The coupling of gravity to a scalar field raises a number of interestingquestions of principle since the usual minimal coupling obtained by replacingordinary derivatives with covariant derivatives is not available -- they arethe same operation on scalar fields. Conformal couplings in the Lagrangianproportional to $\phi^2 R$ have been suggested before, usually to maintainconformal invariance for massless scalar fields, but at the cost of breakingthe equivalence principle. Here we give intuitive arguments for the appearanceof such a term due to fluctuations of scalar particles about their classicalworld lines. Remarkably, these arguments give precisely a correction of theform required to maintain conformal invariance. We also show that such a termwould naturally be expected for the Higgs field in the Standard Model, making aperhaps surprising connection between weak-scale physics and gravity. Thenonminimal coupling, whether induced by quantum corrections or already presentas a bare term, can be constrained from measurements of the Higgs widthassuming the Higgs particle is to be detected.

An Argument for Nonminimal Higgs Coupling to Gravity