Kavli Affiliate: David W. Miller
| Summary:
Understanding the origin of flavour hierarchies in the Standard Model remains an open problem, motivating extensions with non-trivial flavour symmetries. We unify deconstructed weak isospin $mathrmSU(2)_mathrmL^3$ into an $mathrmSp(6)_mathrmL$ symmetry at a high scale $v_S$. The three generations of Standard Model (SM) left-handed doublets are unified into a single fundamental representation of $mathrmSp(6)_mathrmL$. In addition to two BSM triplets from the breaking of $mathrmSU(2)_mathrmL^3$, the enlarged symmetry predicts six additional gauge bosons below the unification scale: three $mathrmSU(2)_mathrmL$ triplets and three singlets, which induce flavour transitions in both the quark and lepton sectors, even in the presence of mass-gauge alignment. We derive updated bounds on the intermediate breaking scale $v_12$ of $mathrmSU(2)_mathrmL^3$ in the presence of the unification scale $v_S$, mapping exclusions in the $(v_12, r)$ parameter space with $r = v_S^2 / v_12^2$. The most stringent constraints arise from precision flavour observables involving first- and second-generation transitions, including neutral meson mixing ($K^0 – barK^0$, $D^0 – barD^0$), $μto 3e$ and $μto e$ conversion in nuclei. These measurements probe scales well beyond direct collider reach and imply $v_12 gtrsim 550 ~mathrmTeV$ for small $r approx 1$, while for $rgtrsim100$ the bound relaxes to $v_12 gtrsim 150~mathrmTeV$, recovering the limits of the $mathrmSU(2)_mathrmL^3$ model. Additionally we include projections from Mu3e and COMET-I and -II experiments which show promising further reach into the parameter space.
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