Positivity bounds on vector boson scattering at the LHC

TL;DR

The paper derives a new set of theoretical positivity bounds on the 18 dimension-8 QGC operators in SMEFT for vector boson scattering at the LHC, grounded in forward dispersion relations and fundamental S-matrix principles. By examining the $ ext{O}(rac{1}{\,\Lambda^4})$ contributions, it shows that certain linear combinations of the dimension-8 coefficients and a quadratic form of dimension-6 terms must be positive, with dimension-6 pieces being negative-definite, thus constraining allowed SMEFT directions. Consequently, the physically viable region of the 18-dimensional QGC parameter space is drastically reduced—Monte Carlo estimates place the remaining fraction at about 2–2.3% of the naive volume—and several coefficients cannot be nonzero by themselves. These positivity bounds provide a model-independent theoretical guide for VBS analyses and, if violated by data, would signal a breakdown of fundamental principles such as unitarity, locality, or analyticity.

Abstract

Weak vector boson scattering (VBS) is a sensitive probe of new physics effects in the electroweak symmetry breaking. Currently, experimental results at the LHC are interpreted in the effective field theory approach, where possible deviations from the Standard Model in the quartic-gauge-boson couplings are often described by 18 dimension-8 operators. By assuming that a UV completion exists, we derive a new set of theoretical constraints on the coefficients of these operators, i.e. certain combinations of coefficients must be positive. These constraints imply that the current effective approach to VBS has a large redundancy: only about $2\%$ of the full parameter space leads to a UV completion. By excluding the remaining unphysical region of the parameter space, these constraints provide guidance for future VBS studies and measurements.

Figures (3)

• Figure 1: Positivity constraints on $F_{S,0}\equiv f_{S,0}$ and $F_{S,1}\equiv f_{S,0}$, compared with the CMS results Khachatryan:2014sta. The green shaded area is allowed by positivity. A specific combination of $F_{S,0}$ and $F_{S,1}$ roughly rescales the Standard Model distribution, and so the measurement is insensitive to this direction.
• Figure 2: Positivity constraints on $\alpha_4$ and $\alpha_5$, compared with the ATLAS results Aaboud:2016uukAaboud:2016ffvAad:2016ett. The green shaded area is allowed by positivity. The difference between the expected limits and the observed ones are due to fluctuations in the observed events.
• Figure 3: Positivity constraints on $f_{M,0}$, $f_{M,1}$, and $f_{M,5}$.