Electroweak flavour unification

Abstract

We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6)L× Sp(6)R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, ΨL ∼ (4,6,1) and ΨR ∼ (4,1,6), 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 ‘flavour-deconstructed’ gauge groups; for instance, we propose a pattern Sp(6)L→$$ {\prod}_{i=1}^3\mathrm{SU}{(2)}_{L,i}\to \mathrm{SU}{(2)}_L $$ ∏ i = 1 3 SU 2 L , i → SU 2 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.

Anomalies of non-Abelian finite groups via cobordism

“…One can also study how these anomalies relate to the anomalies studied in this paper through a generalised version of anomaly interplay. 28 Another avenue to pursue concerns a higher-dimensional generalisation of the 2d 2-groups discussed in § 6, as follows. We saw that one can cancel (almost) all pure Up1q anomalies in 2d by enhancing the Up1q 0-form symmetry to a 2-group by making use of the top-form Up1q current.…”

“…This should be contrasted with the residual order 2 anomaly (6.7) that cannot be cancelled in this way for the theory defined with a spin structure. 27…”

“…For theories with symmetry type S " SpinˆG, where G is the internal symmetry group, we have that Ext 1 Z pπ d`1 pM T Sq, Zq -Hom ´Tor Ω Spin d`1 pBGq, R{Z ¯classifies global anomalies, where Ω Spin ‚ denotes spin bordism. A straightforward corollary is that if the group Tor Ω Spin d`1 pBGq vanishes there can be no global anomalies, which has been applied to various particle physics applications in recent years [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Third-Family Quark-Lepton Unification and Electroweak Precision Tests

“…An interesting way to combine these two general indications is realized by postulating new flavor non-universal gauge interactions at the TeV scale, with the non-universality distinguishing the third generation. This idea has received a lot of interest in the last few years in connection with a series of hints of deviations from the SM in Bmeson decays [1][2][3][4][5][6]. However, it is worth stressing that the appeal goes beyond the B-meson anomalies and connects to the older, more general idea of a (flavor-based) multi-scale structure in the UV completion of the SM [7][8][9][10].…”

“…The common aspect of all the recent flavor non-universal proposals in Ref. [1][2][3][4][5][6] is the hypothesis that TeV-scale dynamics is ruled by the extended gauge group SU (4) h × SU (3) l × SU (2) L × U (1) X . Commonly denoted the "4321" group, it was first proposed in a flavor universal version in [11] and then later in a non-universal version featuring quark-lepton unification à la Pati-Salam [12] for the third family SM fermions [1,2].…”