Abstract
Abstract We calculate one loop contributions to Γ(h → γγ) from higher dimensional operators in the Standard Model Effective Field Theory (SMEFT). Some technical challenges related to determining Electroweak one loop “finite terms” are discussed and overcome. Although we restrict our attention to Γ(h → γγ), several developments we report have broad implications. Firstly, the running of the vacuum expectation value (vev) modifies the log(μ) dependence of processes in a manner that is not captured in some past SMEFT Renormalization Group (RG) calculations. Secondly, higher dimensional operators can source ghost interactions in R ξ gauges due to a modified gauge fixing procedure. Lastly, higher dimensional operators can contribute with pure finite terms at one loop in a manner that is not anticipated in a RG analysis. These results cast recent speculation on the nature of one loop corrections in the SMEFT in an entirely new light.
Highlights
Invariant SM fields, are added to the renormalizable SM interactions
The running of the vacuum expectation value modifies the log(μ) dependence of processes in a manner that is not captured in some past Standard Model Effective Field Theory (SMEFT) Renormalization Group (RG) calculations
Higher dimensional operators can contribute with pure finite terms at one loop in a manner that is not anticipated in a RG analysis
Summary
The one loop improvement of Γ(h → γ γ), due to the Oi of the SMEFT, is given in part by the Effective Lagrangian. + Ce(W0) Oe(0W) + Ce(B0) Oe(0B) + Cu(0W) Ou(0W) + Cu(0B) Ou(0B) + Cd(0W) Od(0W) + Cd(0B) Od(0B) + h.c. The operator notation used here follows that in ref. The bare operators considered in detail in this paper are normalized as OH(0B) = g12 H† H Bμ ν Bμ ν , OH(0W) B = g1 g2 H† σaH Bμ ν Waμ ν. The gauge coupling normalization of the operators in eq (2.1) is chosen so that. The notation gi is used for the canonically normalized couplings in ref. We choose to consider in detail the subset of operators in eq (2.2), as these operators illustrate the basic issues involved with determining the Electroweak finite terms in the SMEFT. Our results are a first step in this direction, when considering finite terms
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