Deconstructed Weak Isospin from a Symplectic Symmetry

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 ($K^0-{\bar{K}}^0$, $D^0-{\bar{D}}^0$), $\hat{I}¼\to 3e$ and $\hat{I}¼\to e$ 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 $r\gtrsim 100$ 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.

47 pages, 7 figures, 1 table. v2: version accepted by JHEP. Added section 2.6 discussing limitations of the model regarding the rank of the Yukawa matrices; fixed typos