Causal vs. Analytic constraints on anomalous quartic gauge couplings

TL;DR

This work addresses how to bound anomalous quartic gauge couplings in the electroweak sector by two complementary methods. It develops dispersive, analyticity-based bounds from a non-forward elastic scattering amplitude and contrasts them with causality-based bounds derived from requiring subluminal propagation of fluctuations around a background. Applying the analytic approach to the electroweak chiral Lagrangian yields scale-dependent constraints on $\alpha_4$ and $\alpha_5$ that are weaker than the causal bounds, especially in the Higgsless scenario, while the causal analysis yields robust bounds such as $\alpha_4+\alpha_5 \gtrsim 3.8\times10^{-3}$ and $\alpha_4 \gtrsim 2.5\times10^{-3}$ at the $Z$ pole with $\Lambda\sim 1$ TeV. These results tighten the allowed parameter space for anomalous quartic interactions and provide theoretical guidance for collider investigations at the LHC and future linear colliders.

Abstract

We derive one loop constraints on the anomalous quartic gauge couplings using a general non-forward dispersion relation for the elastic scattering amplitude of two longitudinally polarized vector bosons. We compare this result with another one derived by the assumption that the underlying theory satisfies the causality principle of Special Relativity and show that this latter is more constraining.