Electroweak flavour unification
Joe Davighi, Joseph Tooby‐Smith
Abstract
A bstract We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6) L × Sp(6) R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L ∼ ( 4 , 6 , 1 ) and Ψ R ∼ ( 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 → $$ {\prod}_{i=1}^3\mathrm{SU}{(2)}_{L,i}\to \mathrm{SU}{(2)}_L $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mo>∏</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>3</mml:mn> </mml:msubsup> <mml:mi>SU</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>SU</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mi>L</mml:mi> </mml:msub> </mml:math> 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.