$\mathrm{Sp}(6)$ Unifying Deconstructed $\mathrm{SU}(2)$'s
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| Format: | Preprint |
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2026
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| _version_ | 1866910082138112000 |
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| author | Gosnay, Alastair Miller, David J |
| author_facet | Gosnay, Alastair Miller, David J |
| contents | 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 ($K^0 - \bar{K}^0$, $D^0 - \bar{D}^0$), $μ\to 3e$ and $μ\to e$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $\mathrm{Sp}(6)$ Unifying Deconstructed $\mathrm{SU}(2)$'s Gosnay, Alastair Miller, David J High Energy Physics - Phenomenology 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 ($K^0 - \bar{K}^0$, $D^0 - \bar{D}^0$), $μ\to 3e$ and $μ\to e$ 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. |
| title | $\mathrm{Sp}(6)$ Unifying Deconstructed $\mathrm{SU}(2)$'s |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2603.27359 |