Abstract

The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an---asymptotically---vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted.

Highlights

  • We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity

  • If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value

  • The quantum effective potential for the Higgs field is the central quantity for understanding the electroweak symmetry breaking in the Standard Model of particle physics (SM)

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Summary

INTRODUCTION

The quantum effective potential for the Higgs field is the central quantity for understanding the electroweak symmetry breaking in the Standard Model of particle physics (SM). The size of A depends strongly on the fixed-point value of the dimensionless Planck mass This value depends, in turn, on the precise particle content of the model and requires a computation of the flow equation with similar detail as the one for the effective potential investigated here. Once this task is accomplished, a definite statement on the predictive power of asymptotic safety for the gauge hierarchy will be possible.

FLOW OF THE SCALAR POTENTIAL
FIXED POINT AND CRITICAL EXPONENTS FOR THE SCALAR POTENTIAL
Critical exponents
Fixed point as a function of the Planck mass
Critical exponent
PREDICTIONS OF ASYMPTOTIC SAFETY FOR THE PROPERTIES OF THE HIGGS SCALAR
Effective low-energy theory
Scalar mass term
Scalar mass flow and gauge hierarchy problem
Quantum gravity effects
Quartic scalar coupling
ROBUSTNESS OF RESULTS
Extension of truncation
Regulator dependence
DISCUSSION
Physical metric fluctuations
Flow generator from physical fluctuations
Measure contribution
Flow of the scalar potential
Full Text
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