Abstract
Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.
Highlights
The Standard Model Effective Field Theory (SMEFT) has become a cornerstone of LHC searches for physics beyond the Standard Model (SM)
In order to define the relevant terms of the Lagrangian for the calculation of the tadpole diagram, we follow the formulation of the geoSMEFT given in [10], as well as the gauge fixing of [9] and [12]
In doing so we have included, for the first time, the gauge fixing of the geoSMEFT and the all-orders Feynman rules related to gauge fixing which include a single background Higgs boson and two other particles
Summary
The Standard Model Effective Field Theory (SMEFT) has become a cornerstone of LHC searches for physics beyond the Standard Model (SM). The geometric SMEFT, or geoSMEFT, was born of an attempt to simplify the one loop calculation of H → γγ [7, 8] and the resulting background gauge fixing of the SMEFT [9] Within this context it was realized that the SMEFT could be formulated in terms of field-space connection matrices of the form: MI1···In ∼. By constructing all gauge-variant, but Lorentz invariant, products of up to any three of the field strengths, covariant derivatives of the scalar field, and products of fermions, the geoSMEFT was formulated to include all three-point functions of SM fields plus arbitrarily many products of scalar fields [10] This allowed for all-orders (in the SMEFT power counting) tree-level studies of the SMEFT in [11]. B demonstrates the importance of the Tadpole diagram both phenomenologically and in preserving the gauge symmetry of the theory beyond tree level
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