$\mathrm{Sp}(6)$ Unifying Deconstructed $\mathrm{SU}(2)$'s

TL;DR

This paper unifies deconstructed weak isospin symmetries into an $ ext{Sp}(6)$ framework, predicting new gauge bosons and deriving bounds from flavor observables, with implications for future experiments.

Contribution

It introduces an $ ext{Sp}(6)$ unification of deconstructed $ ext{SU}(2)_L^3$, predicting additional gauge bosons and analyzing flavor constraints and experimental prospects.

Findings

Bounds on the intermediate breaking scale $v_{12}$ are established, with $v_{12} ext{ } extgreater 550$ TeV for small $r$.

Flavor observables constrain the model, with the most stringent bounds from meson mixing and lepton flavor violation.

Future experiments like Mu3e and COMET could further probe the parameter space.

Abstract

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 $\mathrm{SU}(2)_\mathrm{L}^3$ into an $\mathrm{Sp}(6)_\mathrm{L}$ 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 $\mathrm{Sp}(6)_\mathrm{L}$. In addition to two BSM triplets from the breaking of $\mathrm{SU}(2)_\mathrm{L}^3$, the enlarged symmetry predicts six additional gauge bosons below the unification scale: three $\mathrm{SU}(2)_\mathrm{L}$ 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 $\mathrm{SU}(2)_\mathrm{L}^3$ 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 ($K^0 - \bar{K}^0$, $D^0 - \bar{D}^0$), $\mu \to 3e$ and $\mu \to e$ conversion in nuclei. These measurements probe scales well beyond direct collider reach and imply $v_{12} \gtrsim 550 ~\mathrm{TeV}$ for small $r \approx 1$, while for $r\gtrsim100$ the bound relaxes to $v_{12} \gtrsim 150~\mathrm{TeV}$, recovering the limits of the $\mathrm{SU}(2)_\mathrm{L}^3$ model. Additionally we include projections from Mu3e and COMET-I and -II experiments which show promising further reach into the parameter space.