Towards a bound on the Higgs mass in causal set quantum gravity

TL;DR

This paper explores how spacetime discreteness in causal set quantum gravity affects the Landau pole in scalar field theories, revealing that nonlocal modifications accelerate the onset of new physics near the nonlocality scale.

Contribution

It introduces the first application of continuum functional Renormalization Group methods to causal-set inspired models, analyzing the impact of nonlocality on the Landau pole.

Findings

Nonlocality speeds up the Landau pole onset.

The scale of new physics aligns with the nonlocality scale.

Challenges the assumption of scale separation in causal set quantum gravity.

Abstract

In the Standard Model of particle physics, the mass of the Higgs particle can be linked to the scale at which the Standard Model breaks down due to a Landau pole/triviality problem: for a Higgs mass somewhat higher than the measured value, the Standard Model breaks down before the Planck scale. We take a first step towards investigating this relation in the context of causal set quantum gravity. We use a scalar-field propagator that carries the imprints of spacetime discreteness in a modified ultraviolet behavior that depends on a nonlocality scale. We investigate whether the modification can shift the scale of the Landau pole in a scalar field theory with quartic interaction. We discover that the modifications speed up the onset of the Landau pole considerably, so that the scale of new physics occurs roughly at the nonlocality scale. Our results call into question, whether a separation between the nonlocality scale and the discreteness scale, which is postulated within causal set quantum gravity, and which has been argued to give rise to phenomenological consequences, is in fact achievable. Methodologically, our paper is the first to apply continuum functional Renormalization Group techniques in the context of a causal-set inspired setting.