Goldstone Bosons in Effective Theories with Spontaneously Broken Flavour Symmetry

TL;DR

This paper explores the spontaneous breaking of flavour symmetry in the Standard Model, highlighting the role of Goldstone bosons as gauge modes, axions, and sources of flavor-changing processes within an effective theory framework.

Contribution

It provides a dynamical interpretation of Goldstone bosons in flavour symmetry breaking, linking them to gauge bosons, axions, and flavor-changing neutral currents.

Findings

Goldstone bosons act as longitudinal modes for massive gauge bosons.

Goldstone modes behave as axions resolving the strong CP problem.

New flavor-changing neutral currents arise from heavy scalar and gauge bosons.

Abstract

The Flavour Symmetry of the Standard Model (SM) gauge sector is broken by the fermion Yukawa couplings. Promoting the Yukawa matrices to scalar spurion fields, one can break the flavour symmetry spontaneously by giving appropriate vacuum expectation values (VEVs) to the spurion fields, and one encounters Goldstone modes for every broken flavour symmetry generator. In this paper, we point out various aspects related to the possible dynamical interpretation of the Goldstone bosons: (i) In an effective-theory framework with local flavour symmetry, the Goldstone fields represent the longitudinal modes for massive gauge bosons. The spectrum of the latter follows the sequence of flavour-symmetry breaking related to the hierarchies in Yukawa couplings and flavour mixing angles. (ii) Gauge anomalies can be consistently treated by adding higher-dimensional operators. (iii) Leaving the U(1) factors of the flavour symmetry group as global symmetries, the respective Goldstone modes behave as axions which can be used to resolve the strong CP problem by a modified Peccei-Quinn mechanism. (iv) The dynamical picture of flavour symmetry breaking implies new sources of flavour-changing neutral currents, which arise from integrating out heavy scalar spurion fields and heavy gauge bosons. The coefficients of the effective operators follow the minimal-flavour violation principle.