Abstract
We investigate the flavour alignment conditions that New Physics (NP) models need to satisfy in order to address the (g − 2)μ anomaly and, at the same time, be consistent with the tight bounds from μ → eγ and τ → μγ. We analyse the problem in general terms within the SMEFT, considering the renormalisation group evolution of all the operators involved. We show that semileptonic four-fermion operators, which are likely to generate a sizeable contribution to the (g − 2)μ anomaly, need to be tightly aligned to the lepton Yukawa couplings and the dipole operators in flavour space. While this tuning can be achieved in specific NP constructions, employing particular dynamical assumptions and/or flavour symmetry hypotheses, it is problematic in a wide class of models with broken flavour symmetries, such as those proposed to address both charged- and neutral-current B anomalies. We quantify this tension both in general terms, and in the context of explicit NP constructions.
Highlights
On the other hand, the B physics anomalies involve fermions of different generations, necessarily implicate flavour changing dynamics, and point to New Physics above the electroweak scale
We investigate the flavour alignment conditions that New Physics (NP) models need to satisfy in order to address the (g −2)μ anomaly and, at the same time, be consistent with the tight bounds from μ → eγ and τ → μγ
While this tuning can be achieved in specific NP constructions, employing particular dynamical assumptions and/or flavour symmetry hypotheses, it is problematic in a wide class of models with broken flavour symmetries, such as those proposed to address both charged- and neutral-current B anomalies
Summary
The key point we want to investigate is the interplay between the evidence of a non-vanishing value for (some of) the Wilson coefficients of these operators, following from the aμ anomaly, and the tight constraints derived by the non-observation of μ → eγ and τ → μγ. The tree-level expression for ∆aμ in terms of the Wilson coefficient of the dipole operator is. The Wilson coefficient is understood to be evaluated at the weak scale (we neglect the small effect of running below the weak scale) and the prime indicates the flavour basis corresponding to the mass-eigenstate basis of charged leptons.. Taking into account eq (2.4), the requirement of fitting the aμ anomaly and, at the same time, being consistent with the B μ+ → e+γ bound, leads to the following tight constraints on off-diagonal over diagonal entries in the 2 × 2 light lepton sector:.
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