$SU(2)_L$ deconstruction and flavour (non)-universality

Abstract: We study two-site deconstructions of the $SU(2)L$ gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global $U(2)_q\times U(3)_u\times U(3)_d$ flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with $U(2){\ell}$ or $U(3){\ell}$ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of $SU(2)_L$. We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient $C_9$ while naturally suppressing contributions to $C{10}$, as suggested by current $b\to s\ell^+\ell^-$ data, predicting simultaneously a mild positive shift in the $W$ boson mass.