Full positivity bounds for anomalous quartic gauge couplings in SMEFT

TL;DR

This paper derives comprehensive positivity bounds for dimension-8 anomalous quartic gauge couplings in SMEFT, incorporating all electroweak boson modes and providing tools for practical bound verification.

Contribution

It extends previous bounds by including all electroweak modes, constructs the positivity cone's extremal rays using group theory, and offers a Python package for bound analysis.

Findings

Positivity bounds restrict parameter space to about 0.0313% of the naive total.

Two independent methods confirm the extremal rays of the positivity cone.

The paper provides linear bounds and a Python tool for practical bound verification.

Abstract

Electroweak boson scattering at the LHC provides a crucial avenue for probing physics beyond the Standard Model, particularly regarding deviations in quartic gauge couplings. We derive the complete set of positivity bounds for the $22$ dimension-$8$ anomalous quartic gauge coupling (aQGC) coefficients within the Standard Model Effective Field Theory (SMEFT). Moving beyond previous studies limited to transverse vector bosons, our analysis incorporates all electroweak boson modes, explicitly constructing the extremal rays (ERs) of the positivity cone through a group theoretic framework. We utilize two independent methods--direct construction and Casimir operator analysis--to determine these rays, addressing complexities such as parity-violating operators and continuous parameter degeneracies. Our results indicate that the positivity bounds impose severe constraints, restricting the physically viable parameter space to approximately $0.0313\%$ of the naive total space. Furthermore, we derive linear analytical bounds for various operator combinations and provide an easy-to-use Python package, {\tt SMEFTaQGC}, which implements algorithms to numerically verify positivity and compute the optimized positivity bounds for general aQGC configurations.