Abstract
In this article, a complete analysis of the three muonic lepton-flavour violating processes μ → eγ, μ → 3e and coherent nuclear μ → e conversion is performed in the framework of an effective theory with dimension six operators defined below the electroweak symmetry breaking scale mW . The renormalisation-group evolution of the Wilson coefficients between mW and the experimental scale is fully taken into account at the leading order in QCD and QED, and explicit analytic and numerical evolution matrices are given. As a result, muonic decay and conversion rates are interpreted as functions of the Wilson coefficients at any scale up to mW . Taking the experimental limits on these processes as input, the phenomenology of the mixing effects is investigated. It is found that a considerable set of Wilson coefficients unbounded in the simplistic tree-level approach are instead severely constrained. In addition, correlations among operators are studied both in the light of current data and future experimental prospects.
Highlights
LFV processes have been studied in detail in many specific extensions of the SM
In this article, a complete analysis of the three muonic lepton-flavour violating processes μ → eγ, μ → 3e and coherent nuclear μ → e conversion is performed in the framework of an effective theory with dimension six operators defined below the electroweak symmetry breaking scale mW
We stress the fact that if NP is realised not too far above the EWSB scale, a reduced hierarchy between the NP and EWSB scales would not allow for potential large logarithms from the Standard Model Effective Field Theory (SMEFT) renormalisation-group evolution (RGE), while the hierarchy between the EWSB scale and the muon/nuclear scale is always sufficiently large to give rise to important effects
Summary
Following the Appelquist-Carazzone theorem [36], we consider an effective Lagrangian that is valid below some scale Λ with mW ≥ Λ mb. Dimension-four QED and QCD Lagrangians, it contains higher-dimensional operators multiplied by dimensionless Wilson coefficients C. Note that for f ∈ {e, μ}, the tensor OfTfLL, OfTfRR and scalar OfSfLR, OfSfRL operators can be reduced by Fierz transformations to other operators already present in Leff. This Lagrangian does not contain redundant operators and constitutes a minimal basis. These operators are phenomenologically relevant because, as shown in [37], they encode the effects of scalar operators with heavy quarks (i.e. c, b) below the heavy-quark mass scale mQ, after the matching has been performed In practical terms, these operators are suppressed by 1/(Λ2mQ) rather than 1/(Λ3). We stress the fact that if NP is realised not too far above the EWSB scale, a reduced hierarchy between the NP and EWSB scales would not allow for potential large logarithms from the SMEFT RGE, while the hierarchy between the EWSB scale (our matching scale) and the muon/nuclear scale is always sufficiently large to give rise to important effects
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