Gravity and the Higgs boson mass

According to usual calculations, both in flat and curved spacetime, the mass m 2 of a scalar particle is quadratically sensitive to the ultimate scale of the theory, the UV physical cutoff Λ. Building on previous work [1–3], here we calculate the one-loop effective action Γ 1l for a scalar field on a spherical gravitational background, using the diffeomorphism invariant Fradkin-Vilkovisky path integral measure. This measure gives rise to an automatically dimensionless fluctuation determinant, that we calculate resorting to a numerical cut N on the number of eigenvalues. We show that the UV-sensitivity of the radiative correction δm 2 to m 2 depends crucially on the relation between N and the UV cutoff Λ. We find that if the transition from N to Λ is realized through the off-shell background radius, δm 2 presents the well-known quadratic sensitivity to Λ. If, instead, the transition is realized resorting to the on-shell radius that minimizes the classical action, the mass turns out to be only logarithmically sensitive to Λ.