Phenomenology of a Deconstructed Electroweak Force

Abstract: We study an effective theory of flavour in which the $SU(2)L$ interaction is `flavour-deconstructed' near the TeV scale. This arises, for example, in UV models that unify all three generations of left-handed fermions via an $Sp(6)_L$ symmetry. Flavour-universality of the electroweak force emerges accidentally (but naturally) from breaking the $\prod{i=1}^3 SU(2)_{L,i}$ gauge group to its diagonal subgroup, delivering hierarchical fermion masses and left-handed mixing angles in the process. The heavy gauge bosons transform as two $SU(2)_L$ triplets that mediate new flavour non-universal forces. The lighter of these couples universally to the light generations, allowing consistency with flavour bounds even for a TeV scale mass. Constraints from flavour, high mass LHC searches, and electroweak precision are then highly complementary, excluding masses below 9 TeV. The heavier triplet must instead be hundreds of TeV to be consistent with meson mixing constraints. Because only the lighter triplet couples to the Higgs, we find radiative Higgs mass corrections of a few hundred GeV, meaning this model of flavour is arguably natural. The natural region will, however, be almost completely covered by the planned electroweak programme at FCC-ee. On shorter timescales, significant parameter space will be explored by the High-Luminosity LHC measurements at high-$p_T$, and upcoming lepton flavour violation experiments, principally Mu3e.