Abstract
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.