Abstract
Motivated by the intriguing discrepancies in b → sℓℓ transitions, the fermion mass problem, and a desire to preserve the accidental symmetries of the Standard Model (SM), we extend the SM by an anomalous U(1)X gauge symmetry where X = Y3 + a(Lμ− Lτ)/6. The heavy Z′ boson associated with spontaneously breaking U(1)X at the TeV scale mediates the b → sℓℓ anomalies via {mathcal{O}}_9^{mu}sim frac{1}{Lambda^2}left(overline{s}{gamma}_{rho }{P}_Lbright)left(overline{mu}{gamma}^{rho}mu right) . We show that this model, which features mixed gauge anomalies involving U(1)X and hypercharge, can be made anomaly-free for any a ∈ ℤ by integrating in a pair of charged fermions whose masses naturally reside somewhere between 1 and 30 TeV. The gauge symmetry permits only the third family Yukawas at the renormalisable level, and so the light quark masses and mixings are controlled by accidental U(2)3 flavour symmetries which we assume are minimally broken alongside U(1)X. The lepton sector is not governed by U(2) symmetries, but rather one expects a nearly diagonal charged lepton Yukawa with me,μ « mτ. The model does not explain the hierarchy me « mμ, but it does possess high quality lepton flavour symmetries that are robust to the heavy physics responsible for generating me,μ. We establish the viability of these models by checking agreement with the most important experimental constraints. We comment on how the model could also explain neutrino masses and the muon g − 2.
Highlights
A frequent argument contrary to this scenario is that it is difficult to hide new chiral fermions at suitably high masses, without prematurely breaking electroweak symmetry. (Returning to our 5-flavour SM analogy, the top quark could not have been much heavier than it is, being chiral with respect to SU(2)L × U(1)Y .) While it is in general challenging to give heavy enough masses to some complicated set of charged chiral fermions needed for anomaly cancellation, in this paper we will consider a very particular anomalous U(1)X gauge symmetry that acts as X = Y3 + a(Lμ − Lτ )/6 on the SM fermions
In this paper we explore one simple way to tie all these observations together via a heavy Z boson that arises from spontaneously breaking a U(1)X gauge symmetry with family-dependent couplings
In this paper we have considered extending the SM gauge symmetry by U(1)X, where X acts as a linear combination of third family hypercharge and Lμ − Lτ on the SM fermions, X
Summary
The fact that we gauge an anomalous U(1)X symmetry, whose anomaly cancellation via chiral fermions is postponed until the TeV scale (section 4), leaves vestiges in the effective field theory (EFT) that describes the SM fields plus the Z boson. The Green-Schwarz terms (3.1), (3.5), which manifest the anomalous structure of our SM extension at low-energies, have a priori important phenomenological effects that distinguish this model from anomaly-free Z models Most notably, they give rise to triangle diagrams replicating each non-vanishing gauge anomaly, which, upon electroweak symmetry breaking and diagonalisation of the neutral gauge boson mass terms, give rise to Z → Zγ and Z → ZZ decays. A second hallmark of the fact that U(1)X is anomalous is that the heavy scale vΦ at which the anomalous gauge boson resides cannot be taken arbitrarily high, as can be done consistently for an anomaly-free spontaneously broken U(1)X symmetry ( by taking the vev to be as high as desired) This is possible because a massive anomaly-free abelian gauge theory is renormalisable, while the anomalous version is not. This new physics will come in the shape of heavy chiral fermions, to which we turn
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