Abstract
We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavour violation, by aligning the mass and weak eigenbases. For quarks, all the SM Yukawa couplings responsible for their observed masses and mixings arise at the renormalisable level. We perform fits to show that models in this class can explain $R_{K^{(\ast)}}$ and the other neutral current $B$ anomaly data if we introduce a heavy vector-like quark to mediate the required quark flavour violation, while simultaneously satisfying other constraints from direct $Z^\prime$ searches at the LHC, $B_s$ meson mixing, a number of electroweak precision observables, and neutrino trident production. Within this symmetry-motivated framework of models, we find interesting implications for the flavour anomalies; notably, any axial couplings of the $Z^\prime$ to electrons and muons must be flavour universal, with the flavour universality violation arising solely from the vector-like couplings. We also comment on the generation of neutrino masses in these models.
Highlights
The renormalizable Standard Model (SM) Lagrangian possesses a number of accidental continuous global symmetries, namely baryon number symmetry, Uð1ÞB, and three individual lepton number symmetries, Uð1Þe, Uð1Þμ, and Uð1Þτ
The second and more intriguing possibility is that, in some extended beyond the Standard Model (BSM) theory that arises due to new physics at a scale ΛLFUV, these global symmetries remain accidental at the level of the renormalizable Lagrangian
We have proposed a new framework of Z0 models based on gauging an almost arbitrary linear combination of the accidental Uð1Þ symmetries of the SM, i.e., baryon number and individual lepton numbers, as well as global hypercharge
Summary
The renormalizable Standard Model (SM) Lagrangian possesses a number of accidental continuous global symmetries, namely baryon number symmetry, Uð1ÞB, and three individual lepton number symmetries, Uð1Þe, Uð1Þμ, and Uð1Þτ. The second and more intriguing possibility is that, in some extended BSM theory that arises due to new physics at a scale ΛLFUV, these global symmetries remain accidental at the level of the renormalizable Lagrangian If this is the case, one would expect a natural separation between the scale ΛLFUV of those higher-dimension operators which respect to these global symmetries, and the scale ΛLFV ≫ ΛLFUV of those operators which violate them (where the reason for these names shall soon be apparent).. If one allows the addition of three SM singlet states to “soak up” anomalies, the most general anomaly-free Uð1ÞX charge assignment for the SM fermions, which allows a fully generic quark Yukawa sector and a strictly diagonal charged lepton Yukawa matrix, corresponds to gauging an almost arbitrary linear combination of the (otherwise accidental) global symmetries of the SM (including the “global part” of hypercharge symmetry). This involves a more in-depth examination of the dark sector of the theory, for the more enthusiastic of our readers
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