The standard model as an effective field theory

The geometric Standard Model Effective Field Theory

“…Our remaining notation is largely consistent with Ref. [9]. Field space metrics have been studied and developed outside the SMEFT in many works.…”

“…The propagating degrees of freedom, including the Higgs field, then interact on field manifolds, which encode the effects of higher-dimensional operators. The scalar field space is curved, and the degree of curvature is linked to the size of the ratio of scalesv T /Λ [5][6][7][8][9][10][11]. This curved field space modifies correlation functions, and the definition of SM Lagrangian parameters such as gauge couplings, mixing angles, and masses.…”

“…The direct meaning of this assumption of including a SU(2)L scalar doublet in the theory, is that the local operators are analytic functions of the field H. The analyticity of the operator expansion was reviewed in Ref [9]…”

“…Such a basis also offers a number of other benefits when calculating in the SMEFT, that are most apparent beyond leading order in the operator expansion; see the review[9] for more details.…”

Off-shell renormalization in the presence of dimension 6 derivative operators. Part I. General theory

“…Indeed while it has been known since a long time that there is ultraviolet (UV) mixing between gauge invariant and gauge variant (unphysical) operators (also known as 'alien' operators [2]), it has also been shown that such mixing can be made to vanish by a suitable choice of the basis in the space of local operators [3][4][5][6]; additionally, alien operators have been shown to be cohomologically trivial and therefore have vanishing on-shell correlators [3] (for a review see also [7]). This fact is at the basis of recent computations in the literature [8][9][10][11] as it implies that for certain purposes, e.g., when evaluating anomalous dimensions and/or S-matrix elements, one can consider only on-shell inequivalent operators [12].…”