Abstract
We explore the constraints imposed by the cancellation of triangle anomalies on models in which the flavour anomalies reported by LHCb and other experiments are due to an extra U(1)^prime gauge boson Z^prime . We assume universal and rational U(1)^prime charges for the first two generations of left-handed quarks and of right-handed up-type quarks but allow different charges for their third-generation counterparts. If the right-handed charges vanish, cancellation of the triangle anomalies requires all the quark U(1)^prime charges to vanish, if there are either no exotic fermions or there is only one Standard Model singlet dark matter (DM) fermion. There are non-trivial anomaly-free models with more than one such ‘dark’ fermion, or with a single DM fermion if right-handed up-type quarks have non-zero U(1)^prime charges. In some of the latter models the U(1)^prime couplings of the first- and second-generation quarks all vanish, weakening the LHC Z^prime constraint, and in some other models the DM particle has purely axial couplings, weakening the direct DM scattering constraint. We also consider models in which anomalies are cancelled via extra vector-like leptons, showing how the prospective LHC Z^prime constraint may be weakened because the Z^prime rightarrow mu ^+ mu ^- branching ratio is suppressed relative to other decay modes.
Highlights
Rather than take a top-down based on some postulated ultraviolet scenario, we proposed some minimal benchmark models with desirable characteristics such as suppressed leptonic couplings or axial coupling to quarks
We have scanned for all possible triangle anomaly-free models with charges that can be expressed in the form p/q with p, q ∈ [− 4, 4] when we normalise the left-handed dark matter (DM) charge YχL = 1
We have explored in this paper the constraints on Z interpretations of the flavour anomalies in B → K (∗) + − decays imposed by the cancellation of triangle anomalies, namely the conditions (a) to (f) stated at the beginning of Section 2
Summary
In the wake of this recent report of μ–e non-universality in B → K ∗ + − decay [1,2], several phenomenological analyses favour an anomalous non-SM contribution to the coefficient of the dimension-6 operator O9μ ≡ (sγμ PL b)(μγ μμ), but do not exclude a smaller non-SM contribution to the coefficient of (sγμ PRb)(μγ μOμ)1μ0[13≡–19(,s2 ̄γ7μ].PAL bp)o(μpuγlμarγ5inμt)erporretaOti9μon. The reported μ–e non-universality and LEP constraints lead us to assume that the electron has vanishing U(1) couplings [54], but we allow arbitrary U(1) charges for the left- and right-handed μ and τ , generalizing the anomaly-free models discussed previously that assumed a Lμ − Lτ charge in the lepton sector [33,34,35,36]. We explore models in which anomalies are cancelled by extra vector-like leptons [54], exhibiting an example in which the LHC Z → μ+μ− signal is suppressed because of a small Z → μ+μ− branching ratio Such a model may be able to explain the discrepancy between SM calculations and the experimental measurement of the anomalous magnetic moment of the muon, gμ − 2 [56].
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