Consistency of the Standard Model Effective Field Theory

TL;DR

This paper derives causality-based bounds on the couplings of dimension-eight operators in the Standard Model Effective Field Theory, constraining their signs and magnitudes to ensure consistency with fundamental principles like analyticity and signal causality.

Contribution

It provides the first set of analytic bounds on SMEFT couplings at dimension eight, linking causality and analyticity to experimental constraints.

Findings

27 independent bounds on SMEFT couplings derived

Bounds include positivity constraints and upper limits on CP-odd operators

Implications for collider experiments and electric dipole moment measurements

Abstract

We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion relation arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bounds also follow as a consequence of causality of signal propagation in nonvacuum SM backgrounds. These bounds come in two qualitative forms: i) positivity of (various linear combinations of) couplings of CP-even operators and ii) upper bounds on the magnitude of CP-odd operators in terms of (products of) CP-even couplings. We exhibit various classes of example completions, which all satisfy our EFT bounds. These bounds have consequences for current and future particle physics experiments, as part of the observable parameter space is inconsistent with causality and analyticity. To demonstrate the impact of our bounds, we consider applications both to SMEFT constraints derived at colliders and to limits on the neutron electric dipole moment, highlighting the connection between such searches suggested by infrared consistency.