Electroweak flavour unification

TL;DR

This paper proposes a unified high-energy gauge model combining electroweak and flavor symmetries, explaining fermion families, generating realistic Yukawa hierarchies, and fitting observed CKM matrix values.

Contribution

It introduces an anomaly-free $SU(4)\times Sp(6)_L \times Sp(6)_R$ gauge model unifying electroweak and flavor symmetries, with a natural mechanism for fermion family replication and Yukawa hierarchies.

Findings

Realistic quark Yukawa hierarchies naturally emerge.

The CKM matrix can be precisely fitted to observed values.

The model provides a framework for symmetry breaking down to the Standard Model.

Abstract

We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an $SU(4)\times Sp(6)_L \times Sp(6)_R$ anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, $\Psi_L \sim (\mathbf{4}, \mathbf{6}, \mathbf{1})$ and $\Psi_R\sim (\mathbf{4}, \mathbf{1},\mathbf{6})$, thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via `flavour-deconstructed' gauge groups; for instance, we propose a pattern $Sp(6)_L \to \prod_{i=1}^3 SU(2)_{L,i} \to SU(2)_L$ for the left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values.