Consistency of the Standard Model Effective Field Theory

TL;DR

Remmen and Rodd derive 27 causality- and analyticity-based bounds on the 64 dimension-eight bosonic four-derivative SMEFT operators, splitting into CP-even positivity constraints and CP-odd discriminants. They construct a complete operator basis (including Higgs and gauge-field quartics) and demonstrate how forward dispersion relations constrain forward amplitudes, with explicit bounds across SU(3), SU(2), and U(1) sectors. The bounds are validated against UV completions (one-loop heavy states, Born-Infeld, and tree-level $(DH)^4$ completions) and shown to have tangible phenomenological consequences for anomalous quartic gauge couplings and neutron EDM measurements. The work provides strong theoretical priors on SMEFT parameter space, connects infrared consistency to high-energy UV physics, and suggests avenues for future refinements involving operator mixtures, superpositions, and fermionic sectors.

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.

Figures (10)

• Figure 1: Schematic depiction of bounds derived in this work. For the example of an observable sensitive to two SMEFT operators, $\mathcal{O}_1$ and $\mathcal{O}_2$, data can weigh directly on the allowed parameter space for these operators, as shown by the yellow contours in the figure. However, much of the parameter space is inconsistent with fundamental underlying properties of quantum field theory, and any theory with couplings in the forbidden region would depart significantly from standard assumptions about the form of UV physics (causality, unitarity, etc.). Consequently, our bounds can be viewed as placing strong theoretical priors on the parameter space of the SMEFT.
• Figure 2: A schematic depiction of the analytic structure of the amplitude in the complex $s$ plane, as well as the two contours we will use to establish our positivity bounds. The zigzag lines denote the discontinuity in the amplitude, which can include poles and branch cuts.
• Figure 3: A representative interaction between a small perturbation $\varphi$ and the background scalar condensate $\bar{\phi}$ in which it is propagating. As shown in the text, in a theory where this interaction is mediated by a term $c (\partial \phi)^4$, unless $c > 0$, these interactions will lead to the superluminal propagation of $\varphi$.
• Figure 4: One-loop diagram involving a heavy state $\Phi$, which when integrated out will generate a set of CP-even $F^4$ operators, the coefficients of which must obey our bounds. Here $\Phi$ can be a complex scalar, Dirac fermion, or complex vector field.
• Figure 5: General form of the bounds derived in Sec. \ref{['sec:bounds']}. CP-conserving terms (or linear combinations thereof) have coefficients $c_1$ and $c_2$ bounded to be positive, while the corresponding CP-breaking term has coefficient $\widetilde{c}$ satisfying $\widetilde{c}^2 < 4c_1 c_2$.