Boundaries of Universal Theories

TL;DR

This paper explores the constraints on universal electroweak theories imposed by unitarity and analyticity, revealing positivity bounds on parameters and implications for interpreting collider data, with novel insights into Wilson coefficient cancellations.

Contribution

It demonstrates how fundamental principles restrict electroweak parameters and uncovers a surprising Wilson coefficient cancellation at very small levels.

Findings

W and Y parameters are positive and dominant in low energy expansion

Unitarity constrains the interpretation of Drell-Yan data

Wilson coefficient cancellation occurs at the 10^{-3} level

Abstract

Universal theories are a broad class of well-motivated microscopic dynamics of the electroweak sector that go beyond the Standard Model description. The long distance physics is described by electroweak parameters which correspond to local operators in the Effective Field Theory. We show how unitarity and analyticity constrain the space of parameters. In particular, the $W$ and $Y$ parameters are constrained to be positive and are necessarily the leading terms in the low energy expansion. We assess the impact of unitarity on the interpretation of Drell-Yan data. In passing, we uncover an unexpected Wilson coefficient transcendental cancellation at the $\mathcal{O}(<10^{-3})$ level.