The μ → eγ decay in a systematic effective field theory approach with dimension 6 operators

Abstract

We implement a systematic effective field theory approach to the benchmark process µ → eγ, performing automated one-loop computations including dimension 6 operators and studying their anomalous dimensions. We obtain limits on Wilson coefficients of a relevant subset of lepton-flavour violating operators that contribute to the branching ratio µ → eγ at one-loop. In addition, we illustrate a method to extract further constraints induced by the mixing of operators under renormalisation-group evolution. This results in limits on the corresponding Wilson coefficients directly at the high scale. The procedure can be applied to other processes as well and, as an example, we consider also lepton-flavour violating decays of the τ .

Y and ψ leptonic decays as probes of solutions to the R(D (*)) puzzle

“…Typically, the resulting contribution to the vector meson decay rate is O(αv/m V ) compared to the contribution arising from the tensor operator. Yet, the Wilson coefficients generated in the mixing are y c V cb suppressed [69,70]. Numerically, we find that this effect on R Υ(1S) τ / is always below the per-mil level and can be neglected.…”

$$\mu \rightarrow e \gamma $$ μ → e γ in the 2HDM: an exercise in EFT

“…So although these extra operators are required below m W to obtain all the O(1/M 2 ) terms, they are not necessary for getting a reasonable approximation to the answer. 6 2. There are two-loop contributions involving a top or Wloop, initially discussed by Bjorken and Weinberg [3], and illustrated in Fig.…”

“…This running should be performed with electroweak RGEs, which are given in [6,41]. However, since CHK separate photon and Z diagrams, and only the photon contributions were retained in the previous section, the running from M → m W is performed with the RGEs of QED.…”

“…The operators of Eq. (47) are not included in the EFT analysis of μ → eγ performed by Pruna and Signer [6], who make the restriction to dimension-six SU(2)-invariant operators. From the diagrams illustrated in Fig.…”

“…Pruna and Signer [6] studied μ → eγ in an EFT consisting of the SM extended by a complete set of SU(2)-invariant operators, but they focused on the electroweak running above m W , rather than the matching at m W , so they did not extend the oper-ator basis below m W . In the context of B physics, Alonso et al [7] and Aebischer et al [8] calculated the coefficients of the enlarged operator basis below m W , given a selection of SU(2)-invariant operators above m W .…”