Unambiguously Testing Positivity at Lepton Colliders

TL;DR

This paper explores how positivity bounds derived from fundamental principles can be tested unambiguously at lepton colliders through the diphoton channel, providing a robust way to probe new physics and effective operators.

Contribution

It demonstrates that positivity bounds can be applied to the diphoton channel at lepton colliders, offering a novel, model-independent test of fundamental quantum field theory principles.

Findings

Positivity bounds can constrain dimension-eight operators in diphoton processes.

Future lepton colliders can effectively test these bounds and improve global analyses.

Positivity bounds also relate to Zγ and ZZ processes, despite added complexity.

Abstract

The diphoton channel at lepton colliders, $e^+e^- (\mu^+\mu^-) \to \gamma \gamma$, has a remarkable feature that the leading new physics contribution comes only from dimension-eight operators. This contribution is subject to a set of positivity bounds, derived from the fundamental principles of Quantum Field Theory, such as unitarity, locality, analyticity and Lorentz invariance. These positivity bounds are thus applicable to the most direct observable -- the diphoton cross section. This unique feature provides a clear, robust, and unambiguous test of these principles. We estimate the capability of various future lepton colliders in probing the dimension-eight operators and testing the positivity bounds in this channel. We show that positivity bounds can lift certain flat directions among the effective operators and significantly change the perspectives of a global analysis. We also discuss the positivity bounds of the $Z\gamma/ZZ$ processes which are related to the $\gamma\gamma$ ones, but are more complicated due to the massive $Z$ boson.