Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes

TL;DR

This paper derives and classifies sum rules for dimension-6 operators in the Standard Model Effective Field Theory using helicity amplitudes, linking low energy parameters to high energy physics insights.

Contribution

It systematically formulates sum rules for SMEFT operators based on helicity amplitude classification, including some previously unreported relations.

Findings

Sum rules connect low energy SMEFT coefficients to high energy observables.

Some sum rules are applicable beyond tree level, aiding in loop calculations.

Provides new insights into custodial symmetries of the SM Higgs and fermions.

Abstract

The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.