Spinning Sum Rules for the Dimension-Six SMEFT

TL;DR

This paper develops new dispersive sum rules for the dimension-six SMEFT that relate the spin of UV states to IR Wilson coefficients, with potential applications in phenomenology and constraints on new physics.

Contribution

It introduces spinning sum rules for the dimension-six SMEFT operators, linking UV spin information to IR Wilson coefficients, and discusses their phenomenological implications.

Findings

Sum rules encode UV spin information in IR coefficients.

Sign of Wilson coefficients reflects dominant UV spin.

Applications to Peskin-Takeuchi and oblique parameters.

Abstract

We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a memory of the dominant spin in the UV completion. The sum rules are constructed for operators containing scalars and fermions, although we consider the dimension-six SMEFT exhaustively, outlining why equivalent relations do not hold for the remaining operators. As with any dimension-six dispersive argument, our conclusions are contingent on the absence of potential poles at infinity, so-called boundary terms, and we discuss in detail where these are expected to appear. There are a number of phenomenological applications of spinning sum rules, and as an example we explore the connection to the Peskin-Takeuchi parameters and, more generally, the set of oblique parameters in universal theories.