# Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking

## TL;DR

This paper investigates how pseudo-Goldstone boson masses behave in chiral Yukawa theories with explicit symmetry breaking, revealing stable mass ratios and a limiting behavior linked to an ultraviolet fixed point, using nonperturbative renormalization group methods.

## Contribution

It demonstrates the existence of a stable mass ratio for pseudo-Goldstone and fermions under quadratic explicit symmetry breaking and generalizes the findings to higher chiral symmetries.

## Key findings

- Mass ratio of fermion and pseudo-Goldstone remains stable as explicit breaking diminishes.
- Bosonic excitation mass ratio approaches a limit depending on infrared parameters.
- Results are obtained using nonperturbative functional renormalization group techniques.

## Abstract

The symmetry breakdown pattern is studied in models containing one fermion flavor multiplet and a multicomponent scalar field, supplemented with a chiral Yukawa-interaction, and in presence of an explicit symmetry breaking source quadratic in the scalar field. In a detailed investigation of the model with $U_L(1) \times U_R(1)$ chiral symmetry it is shown that by diminishing the strength of quadratic explicit symmetry breaking one can still keep stable the mass ratio of the fermionic and the pseudo-Goldstone excitation. At the same time the mass ratio of the two bosonic excitations appears to approach a limiting value depending only on the infrared value of the first ratio, but not on the microscopic (ultraviolet) coupling values. The observations receive a general interpretation by the existence of an ultraviolet fixed point located in the symmetric phase. Understanding the general conditions for its existence allows the construction of a similar theory with $U_L(2) \times U_R(2)$ chiral symmetry. All results of the present investigation were obtained with nonperturbative functional renormalisation group technique making use of the first two approximations to the gradient expansion of the effective action.