The Higgs-Graviton Couplings: from Amplitudes to the Action

Abstract

In this paper we study the coupling of scalar (Higgs) particles (φ) with gravitons (h) and their possible effects. The general form of the 3-point interaction φ(p)h(1)h(2) can be derived using the scaling behavior of the spinor variables under the little group; the resulting vertices exhibit such simplicity, that some simplifications should be hidden in the expressions obtained from the extended scalar action. To investigate this, we study an extended Einstein-Hilbert action that besides the minimal coupling, it also includes terms of the form φR 2 , φR µν R µν and φR µνρσ R µνρσ , as well as the term µναβ φ 5 R µν ρσ R αβρσ for the case of a pseudo-scalar (φ 5 ). The resulting vertices satisfy KLT-type relations, i.e., they can be written as the square of the coupling of the Higgs with gluons. We find that the amplitude for the Higgs decay into a pair of gravitons (on-shell) only receives a contribution coming from the square of the Riemann

Scalar field couplings to quadratic curvature and decay into gravitons

“…This rate differs from the one in[36] by a factor of 16. We believe that this difference originates from that[36] does not properly normalize the graviton field 4.…”

“…This rate differs from the one in[36] by a factor of 16. We believe that this difference originates from that[36] does not properly normalize the graviton field 4. If the vacuum expectation value (VEV) of φ is zero, v φ in (3.2) should be regarded as v φ = m/λ.…”

“…The next simplest possibility is the couplings between φ and the quadratic curvature. Among them, φR 2 and φR µν R µν do not induce the decay in the flat spacetime [35,36]. This is probably most easily seen by noting that the on-shell graviton equation of motion gives R = 0 and R µν = 0 in the flat spacetime.…”

“…induce a decay of φ into graviton pairs (see, e.g., [35,36]), which is never realized in the Einstein gravity nor the nonminimal coupling to gravity [1,16,35,36].…”

Scalar field couplings to quadratic curvature and decay into gravitons

“…induce a decay of φ into graviton pairs (see, e.g., [37,38]), which is never realized in the Einstein gravity nor the nonminimal coupling to gravity [1,18,37,38].…”