We present a model to explain LHCb's recent measurements of R K and R K * based on an anomaly-free, spontaneously-broken U (1) F gauge symmetry, without any fermionic fields beyond those of the Standard Model (SM). The model explains the hierarchical heaviness of the third family and the smallness of quark mixing. The U (1) F charges of the third family of SM fields and the Higgs doublet are set equal to their respective hypercharges. A heavy Z particle with flavour-dependent couplings can modify the [b L γ ρ s L ][µ L γ ρ µ L ] effective vertex in the desired way. The Z contribution to B s − B s mixing is suppressed by a small mixing angle connected to V ts , making the constraint coming from its measurement easier to satisfy. The model can explain R K and R K * whilst simultaneously passing other constraints, including measurements of the lepton flavour universality of Z couplings.
Spontaneously broken, flavour-dependent, gauged U(1) extensions of the Standard Model (SM) have many phenomenological uses. We chart the space of solutions to the gauge anomaly cancellation equations in such extensions, for both the SM chiral fermion content and the SM plus (up to) three right-handed neutrinos (SMν R). Methods from Diophantine analysis allow us to efficiently index the solutions arithmetically, and produce the complete solution space in particular cases. In order to solve the general case, we build a computer program which cycles through possible U(1) charge assignments, providing all solutions for charges up to some pre-defined maximum absolute charge. Lists of anomaly-free U(1) charge assignments result, which corroborate the results of our Diophantine analysis. We make these lists, which may be queried for further desirable properties, publicly available. This previously uncharted space of anomaly-free charge assignments has been little explored until now, paving the way for future model building and phenomenological studies.
We consider a deformation of the Third Family Hypercharge Model, which arguably makes the model more natural. Additional non-zero charges of the spontaneously broken, family-dependent U (1) F gauge symmetry are assigned to the second family leptons, and the third family leptons' charges are deformed away from their hypercharges in such a way that the U (1) F gauge symmetry remains anomaly-free. Second family U (1) F lepton charges allow a Z coupling to muons without having to assume large charged lepton mixing, which risks violating tight lepton flavour violation bounds. In this deformed version, only the bottom and top Yukawa couplings are generated at the renormalisable level, whereas the tauon Yukawa coupling is absent. The Z mediates a beyond the Standard Model contribution to an effective (bs)(μµ) vertex in the combination C 9 = −9C 10 and is able to fit the apparent discrepancy between Standard Model predictions in flavour changing neutral-current B−meson decays and their measurements, whilst simultaneously avoiding current constraints from direct Z searches and other measurements, when 0.8 TeV < M Z < 12.5 TeV.
We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be G = G SM /Γ n , with G SM = SU(3) × SU(2) × U(1) and Γ n isomorphic to Z/n where n ∈ {1, 2, 3, 6}. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups Ω Spin 5 (BG) using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific fermion content of the SM by embedding the SM in an anomaly-free SU(5) GUT, our results here remain true when the SM fermion content is extended arbitrarily. Going beyond the SM gauge groups, we show that there are no new global anomalies in extensions of the (usual) SM gauge group by U(1) m for any integer m, which correspond to phenomenologically well-motivated BSM theories featuring multiple Z bosons. Nor do we find any new global anomalies in various grand unified theories, including Pati-Salam and trinification models. We also consider global anomalies in a family of theories with gauge group SU(N) × Sp(M) × U(1), which share the phase structure of the SM for certain (N, M). Lastly, we discuss a BSM theory in which the SM fermions are defined using a spin c structure, for example by gauging B − L. Such a theory may be extended to all orientable four-manifolds, and we find no global anomalies.
We discuss anomaly cancellation in U(2) gauge theories in four dimensions. For a U(2) gauge theory defined with a spin structure, the vanishing of the bordism group Ω Spin 5 (BU(2)) implies that there can be no global anomalies, in contrast to the related case of an SU(2) gauge theory. We show explicitly that the familiar SU(2) global anomaly is replaced by a local anomaly when SU(2) is embedded in U(2). There must be an even number of fermions with isospin 2r +1/2, for r ∈ Z ≥0 , for this local anomaly to cancel. The case of a U(2) theory defined without a choice of spin structure but rather using a spin-U(2) structure, which is possible when all fermions (bosons) have half-integer (integer) isospin and odd (even) U(1) charge, is more subtle. We find that the recently-discovered 'new SU(2) global anomaly' is also equivalent, though only at the level of the partition function, to a perturbative anomaly in the U(2) theory, which is this time a combination of a mixed gauge anomaly with a gauge-gravity anomaly. This perturbative anomaly vanishes if there is an even number of fermions with isospin 4r + 3/2, for r ∈ Z ≥0 , recovering the condition for cancelling the new SU(2) anomaly. Alternatively, this perturbative anomaly can be cancelled by a Wess-Zumino term, leaving a low-energy theory with a global anomaly, which can itself be cancelled by coupling to topological degrees of freedom.
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