Signs, Spin, SMEFT: Sum Rules at Dimension Six

TL;DR

This paper derives theoretical sum rules and constraints on dimension-six four-fermion operators in the Standard Model Effective Field Theory (SMEFT) using S-matrix principles, linking low-energy observables to high-energy new physics.

Contribution

It introduces new dispersion relations and sum rules that connect SMEFT operator coefficients with fundamental scattering amplitude properties, providing a novel diagnostic tool for emerging new physics.

Findings

Derived spin-dependent sum rules for fermionic operators.

Established inequalities linking low-energy measurements to high-energy theories.

Provided a framework to infer UV properties from flavor-violating decay observations.

Abstract

We place theoretical constraints on the leading deviations to four-fermion standard model interactions. Invoking S-matrix analyticity and partial wave unitarity, we develop new dispersion relations that yield either spin-dependent sum rules on dimension-six fermionic operators or information about the amplitude's behavior at large momentum. The pattern of SMEFT inequalities we find for theories obeying certain large-momentum constraints enables a diagnosis of properties of emerging new physics. These relations form a bridge between new physics searches: discovery of flavor-violating $\tau$ decays at Belle II would motivate the search for flavor-conserving new physics below 25 TeV, as the results would provide definitive information about the UV.