Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models

TL;DR

This paper analyzes how gravitational corrections influence the Higgs self-coupling's renormalization group flow, using hypergeometric functions to solve the resulting equations, and discusses implications for Higgs mass predictions in spectral action models.

Contribution

It introduces a novel approach to solving the RG flow equations with gravitational corrections using hypergeometric functions and explores their impact on Higgs mass estimates.

Findings

Explicit solutions for RG equations via hypergeometric functions

Gravitational corrections significantly affect Higgs mass predictions

Provides a new mathematical framework for spectral action models

Abstract

We study the renormalization group flow for the Higgs self coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.