Constructing Dimension-8 SMEFT from Conserved Currents

TL;DR

This work introduces a currents-first, noether-current–driven framework to construct dimension-8 SMEFT operators, yielding the Kinematically Diagonalized Current Basis (KDCB) in the electroweak sector. By building operators from conserved SM currents and their derivatives, the approach eliminates kinematic mixing and makes the energy growth of scattering amplitudes manifest as $E^4$, $E^2$, or $E^0$, enhancing S-matrix positivity diagnostics and UV interpretation. The framework partitions operators into two sectors (source-dependent and pure gauge) and three energy-growth classes, with explicit generators and IBP/EOM reductions that connect to standard aQGC bases while preserving physical interpretation. It also provides practical advantages for phenomenology, including a stable auxiliary-field Monte Carlo implementation, RG-consistent treatment, and clear avenues for UV-model discrimination through current decomposition. The methodology offers a transparent bridge from high-energy collider data to the structure of new physics, improving global SMEFT fits and the extraction of UV information from experimental observables.

Abstract

Effective Field Theories (EFTs) are the primary tool for interpreting precision collider data in the absence of new resonances. However, in the dimension-8 Standard Model Effective Field Theory (SMEFT), the utility of traditional algebraically minimal bases is fundamentally limited by kinematic mixing: multiple operators contribute to a single high-energy amplitude, creating degeneracies that obscure ultraviolet interpretations and complicate the application of theoretical constraints. We introduce a generative framework that resolves this by constructing operators directly from the conserved Noether currents of the Standard Model. The resulting Kinematically Diagonalized Current Basis (KDCB) ensures that each operator maps to a unique asymptotic energy scaling ($E^4$, $E^2$, $E^0$) in scattering amplitudes. This organization makes S-matrix positivity bounds manifest, enables a stable auxiliary-field formulation for Monte Carlo simulation, and provides direct diagnostics for universal versus non-universal ultraviolet completions through current decomposition. By rotating the operator space into physically interpretable sectors, the KDCB offers a transformative framework for global fits and a clear pathway from high-energy data to the structure of new physics.