SMEFT

SMEFT stands for the Standard Model Effective Field Theory. It is a framework for describing the effects of heavy new physics beyond the Standard Model at energies below a cutoff scale Λ by extending the SM Lagrangian with higher‑dimensional, gauge‑invariant operators built from Standard Model fields. The approach preserves the SM gauge symmetries and treats the Higgs field as part of a linear SU(2) doublet, i.e., the usual linear realization of electroweak symmetry breaking.

The SMEFT Lagrangian is written as L_SMEFT = L_SM + sum_i (C_i^(6)/Λ^2) O_i^(6) + sum_j (C_j^(8)/Λ^4) O_j^(8) + ... The dimension‑6 operators are the most studied, as they provide the leading corrections to SM processes, modifying Higgs and gauge boson couplings, fermion interactions, and flavor processes. Higher‑dimension terms are increasingly suppressed by Λ.

Operators are organized into bases; the Warsaw basis is a widely used set of dimension‑6 operators. The choice of basis is a matter of convention, and operator redundancy and flavor structure must be handled carefully. Wilson coefficients C_i encode information about the ultraviolet completion and can be derived by matching a UV theory onto the SMEFT at the scale Λ; their values evolve with energy through renormalization group running and operator mixing.

Applications include global fits to collider data and precision measurements to constrain potential new physics scales, and SMEFT serves as a bridge between experimental observations and UV theories. Limitations include the validity of the expansion (E ≪ Λ, small C_i/Λ^2), truncation effects, and basis dependence of intermediate steps, though physical observables remain basis‑independent.