Signs, spin, SMEFT: Sum rules at dimension six

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 standard model effective theory 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.

Automated summary

In this study, we place theoretical constraints on the leading deviations to four-fermion standard model interactions and 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. These relations serve as a bridge between new physics searches, providing definitive information about the UV and enabling a diagnosis of properties of emerging new physics.