Goldstone Bosons in Effective Theories with Spontaneously Broken Flavour Symmetry

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. In addition, one encounters Goldstone modes for every broken flavour symmetry generator. In this paper, we discuss the implications of interpreting these Goldstone modes as longitudinal modes for massive gauge bosons of a local flavour symmetry. Because of the chiral nature of the SM flavour symmetry, we encounter gauge anomalies which can be consistently treated within an effective-field theory framework. On the other hand, 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. In this dynamical picture of flavour symmetry breaking, one encounters 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.