Deconstructed weak isospin from a symplectic symmetry

A bstract 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 $$ \\mathrm{SU}{(2)}_{\\mathrm{L}}^3 $$ SU 2 L 3 into an Sp(6) 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 Sp(6) L . In addition to two BSM triplets from the breaking of $$ \\mathrm{SU}{(2)}_{\\mathrm{L}}^3 $$ SU 2 L 3 , the enlarged symmetry predicts six additional gauge bosons below the unification scale: three SU(2) 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 $$ \\mathrm{SU}{(2)}_{\\mathrm{L}}^3 $$ SU 2 L 3 in the presence of the unification scale v S , mapping exclusions in the ( v 12 , r ) parameter space with $$ r={v}_S^2/{v}_{12}^2 $$ 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 $$ \\left({K}^0-{\\overline{K}}^0,{D}^0-{\\overline{D}}^0\\right) $$ K 0 − K ¯ 0 D 0 − D ¯ 0 , μ → 3 e and μ → e conversion in nuclei. These measurements probe scales well beyond direct collider reach and imply v 12 ≳ 550 TeV for small r ≈ 1, while for r ≳ 100 the bound relaxes to v 12 ≳ 150 TeV, recovering the limits of the $$ \\mathrm{SU}{(2)}_{\\mathrm{L}}^3 $$ SU 2 L 3 model. Additionally we include projections from Mu3e and COMET-I and -II experiments which show promising further reach into the parameter space.