Semisimple extensions of the Standard Model gauge algebra

Allanach, B. C.; Gripaios, Ben; Tooby-Smith, Joseph

doi:10.1103/physrevd.104.035035

Cited by 19 publications

(35 citation statements)

References 13 publications

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“…Here G vert breaks to the SM gauge symmetry, while G horiz breaks ultimately to nothing, giving rise to heavy gauge bosons that mediate very weak flavour-changing forces. Curiously, if we want to fit all 48 Weyl fermions of the SM+3ν R into a single irrep R of a unified gauge group G that acts faithfully on matter, assuming G is connected and semi-simple, then the only options are G " Spinp10q tSU p2q or SOp3qu with R " p16, 3q [4]. 2 Both these are horizontal extensions of the Spinp10q GUT.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Ref. [4] classified all semi-simple Lie algebras g in which the SM+3ν R gauge algebra can be embedded without needing extra fermions. This list of algebras enumerates all possible ways in which flavour could be intertwined with the SM gauge interactions, albeit subject to the (not insignificant) assumption that there are no extra fermions beyond those of the SM+3ν R .…”

Section: Introductionmentioning

confidence: 99%

“…One might judge the 'most unified' of these gauge algebras to be those in which the SM fermions are packaged into the smallest number N rep of irreps. If we moreover insist that the flavour symmetry does not just act horizontally, thereby removing the N rep " 1 options discussed above, then three gauge algebras from [4] emerge as especially interesting, each with N rep " 2. These are sup12q ' sup2q L ' sup2q R , sup4q ' spp6q L ' spp6q R , and sup4q ' spp6q L ' sop6q R .…”

Section: Introductionmentioning

confidence: 99%

“…for which the corresponding fermion representations are properly anomaly-free (of both local 2 Interestingly, there is no simple gauge group in which one can 'faithfully embed' the SM+3νR with all 48 Weyls sitting in a single representation -Ref. [4] amounts to a proof-by-exhaustion of this fact. Such is life!…”

Section: Introductionmentioning

confidence: 99%

“…For n f generations of SM fermions, the relevant embeddings in each case are: (a) colour and complex SU pn f q flavour symmetry are unified via the natural embedding of SU p4qˆSU pn f q ãÑ SU p4n f q; (b) Spp2q LpRq and real SOpn f q flavour symmetry are unified via the natural embedding Spp2q ˆSOpn f q ãÑ Spp2n f q; (c) SOp2qR hypercharge and real SOpn f q flavour symmetry are unified via the natural embedding SOp2qR ŜOpn f q ãÑ SOp2n f q. See Refs [4,9]…”

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Electroweak flavour unification

Davighi¹,

Tooby-Smith²

2022

Preprint

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We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU p4q ˆSpp6q L ˆSpp6q R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L " p4, 6, 1q and Ψ R " p4, 1, 6q, thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via 'flavourdeconstructed' gauge groups; for instance, we propose a pattern Spp6q L Ñ ś 3 i"1 SU p2q L,i Ñ SU p2q L for the left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Electroweak flavour unification

Davighi¹,

Tooby-Smith²

2022

Preprint

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Higher Flavor Symmetries in the Standard Model

Córdova

Koren

2023

Annalen der Physik

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A study of the generalized global flavor symmetries of the Standard Model is initiated. The presence of nonzero triangle diagrams between the U(3)5 flavor currents and the hypercharge current intertwines them in the form of a higher‐group which mixes the zero‐form flavor symmetries with the one‐form magnetic hypercharge symmetry. This higher symmetry structure greatly restricts the possible flavor symmetries that may remain unbroken in any ultraviolet completion that includes magnetic monopoles. In the context of unification, this implies tight constraints on the combinations of fermion species which may be joined into multiplets. Three of four elementary possibilities are reflected in the classic unification models of Georgi–Glashow, , and Pati–Salam. The final pattern is realized non‐trivially in trinification, which exhibits the sense in which Standard Model Yukawa couplings which violate these flavor symmetries may be thought of as spurions of the higher‐group. Such modifications of the ultraviolet flavor symmetries are possible only if new vector‐like matter is introduced with masses suppressed from the unification scale by the Yukawa couplings.

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Ising Machines for Diophantine Problems in Physics

Abel

2022

Fortschritte der Physik

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Diophantine problems arise frequently in physics, in for example anomaly cancellation conditions, string consistency conditions and so forth. We present methods to solve such problems to high order on annealers that are based on the quadratic Ising Model. This is the intrinsic framework for both quantum annealing and for common forms of classical simulated annealing. We demonstrate the method on so-called Taxicab numbers (discovering some apparently new ones), and on the realistic problem of anomaly cancellation in U(1) extensions of the Standard Model.

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Semisimple extensions of the Standard Model gauge algebra

Cited by 19 publications

References 13 publications

Electroweak flavour unification

Electroweak flavour unification

Higher Flavor Symmetries in the Standard Model

Ising Machines for Diophantine Problems in Physics

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