Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems

TL;DR

This paper investigates the possibility of asymptotic safety in a chiral Yukawa system as a simplified model for the standard model Higgs sector, finding non-Gaussian fixed points that could address triviality and hierarchy problems.

Contribution

It demonstrates the existence of non-Gaussian fixed points in a chiral Yukawa system using functional RG, offering insights into potential solutions for the triviality and hierarchy problems.

Findings

Admissible non-Gaussian fixed points found for 1 ≤ N_L ≤ 57

Fixed points could solve triviality if present in the full theory

Destabilization at higher order due to Goldstone and fermion fluctuations

Abstract

We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Ga\ssian fixed-points for $1 \leq N_L \leq 57$ which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed-point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.