Positivity constraints on aQGC: carving out the physical parameter space

TL;DR

The authors derive polarization-independent positivity bounds for 18 dim-8 quartic gauge boson operators within SMEFT by analyzing forward-limit vector boson scattering under fundamental QFT principles. They solve the polarisation dependence to obtain 19 linear, 3 quadratic, and 1 quartic inequalities that define the physically allowed QGC parameter space, which geometryically forms pyramids, prisms, and cones. The resulting allowed region reduces to about 2–3% of the total parameter space, significantly sharpening guidance for experimental searches and global EFT analyses. They also illustrate benchmark scenarios with one, two, or three operators active and discuss the role of UV completions in shaping these bounds, including a simplified resonant model that satisfies positivity.

Abstract

Searching for deviations in quartic gauge boson couplings (QGCs) is one of the main goals of the electroweak program at the LHC. We consider positivity bounds adapted to the Standard Model, and show that a set of positivity constraints on 18 anomalous QGC couplings can be derived, by requiring that the vector boson scattering amplitudes of specific channels and polarisations satisfy the fundamental principles of quantum field theory. We explicitly solve the positivity inequalities to remove their dependence on the polarisations of the external particles, and obtain 19 linear inequalities, 3 quadratic inequalities, and 1 quartic inequality that only involve the QGC parameters and the weak angle. These inequalities constrain the possible directions in which deviations from the standard QGC can occur, and can be used to guide future experimental searches. We study the morphology of the positivity bounds in the parameter space, and find that the allowed parameter space is carved out by the intersection of pyramids, prisms, and (approximately) cones. Altogether, they reduce the volume of the allowed parameter space to only 2.1% of the total. We also show the bounds for some benchmark cases, where one, two, or three operators, respectively, are turned on at a time, so as to facilitate a quick comparison with the experimental results.

Figures (27)

• Figure 1: Limits on pairs of QGC operator coefficients from CMS $WZjj$ analysis CMS:2018ysc. Green shaded area represents positivity bounds.
• Figure 2: Dispersion relation contours in the forward limit.
• Figure 3: Tree level dispersion relation contour in the forward limit.
• Figure 4: Examples of BSM contribution arising from heavy particle loops. Double lines represent BSM particles.
• Figure 5: If the leading BSM loop contribution contains SM fields in the loop, the diagram needs to be matched to both tree-level and loop-level diagrams in the EFT. Red blobs represent higher-dimensional vertices.