Electroweak flavour unification

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, ${\Psi }_L\sim (4,6,1)$ and ${\Psi }_R\sim (4,1,6)$, 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.

arXiv comment35 pages. v3: Matches published version

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• Toric 2-group anomalies via cobordism
• Flavour Deconstructing the Composite Higgs
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• The Standard Model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an $\mathrm{SU}(8)$ theory
• The gauge coupling evolutions of an $\mathrm{SU}(8)$ theory with the maximally symmetry breaking pattern
• The problem of flavour
• The standard HVM
• Natural neutrino mass hierarchy in a theory of gauge flavour deconstruction
• Precision Tests in $b\to s{\ell }^{+}{\ell }^{-}$ ($\ell =e,\mu$) at FCC-ee