Abstract
Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question, which parameters of the Higgs potential can be predicted in the asymptotic safety scenario for quantum gravity? For the standard model and a large class of theories with additional particles the quartic Higgs coupling is an irrelevant parameter at the ultraviolet fixed point. This makes the ratio between the Higgs boson and the top-quark mass predictable.
Highlights
The asymptotic safety scenario [1,2] realizes quantum gravity as a nonperturbatively renormalizable quantum field theory, as summarized in [3,4,5,6,7,8,9,10]
If a particle physics model coupled to quantum gravity can be extended to an infinitely short distance, the free parameters of the model correspond to the relevant parameters at the ultraviolet (UV) fixed point
One can predict every renormalizable coupling of the effective low energy theory of particle physics at length scales much larger than the Planck length that corresponds to an irrelevant parameter at the fixed point
Summary
The asymptotic safety scenario [1,2] realizes quantum gravity as a nonperturbatively renormalizable quantum field theory, as summarized in [3,4,5,6,7,8,9,10]. We want to know for which type of particle physics models, specified by the number of (almost) massless scalars, fermions, and gauge bosons at the fixed point, the quartic Higgs coupling is an irrelevant parameter. Within the Einstein-Hilbert truncation for gravity we compute the critical exponents in dependence on the number of massless scalars, fermions, and gauge bosons at the fixed point. This issue depends on the particle physics model coupled to quantum gravity. For microscopic GUTs with a large number of scalar NS the gravity induced anomalous dimension for the scalar mass term and quartic coupling increases due to the graviton propagator moving close to the onset of instability This is the region where our truncation becomes doubtful.
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