Mapping the genuine bosonic quartic couplings

TL;DR

This paper provides a comprehensive classification of genuine quartic gauge-boson couplings (QGC) in the electroweak sector, considering both linear and nonlinear realizations of the gauge symmetry. It builds the full set of Lorentz structures for four-gauge-boson vertices with up to two derivatives and then derives the operator bases that generate these QGC in two effective theories: a linearly realized SU(2)L x U(1)Y with an elementary Higgs, and a nonlinear chiral Lagrangian with a dynamical Higgs. In the linear case, genuine QGC without a TGC arise at dimension eight, with three D_mu Phi operators and seven D_mu Phi plus field-strength operators leading to 23 of the 70 Lorentz structures, and linear gauge invariance imposes correlations among coefficients. In contrast, the nonlinear (chiral) framework yields QGC already at O(p^4) and O(p^6), producing 5 and 70 independent operators respectively, with no basis-independent correlations among coefficients. The results provide a unified mapping between operator bases and Lorentz structures, clarifying how to translate experimental bounds across notations and outlining the most sensitive channels, notably those with two photons, for probing genuine QGC at current and future colliders.

Abstract

The larger center-of-mass energy of the Large Hadron Collider Run 2 opens up the possibility of a more detailed study of the quartic vertices of the electroweak gauge bosons. Our goal in this work is to classify all operators possessing quartic interactions among the electroweak gauge bosons that do not exhibit triple gauge-boson vertices associated to them. We obtain all relevant operators in the non-linear and linear realizations of the $SU(2)_L \otimes U(1)_Y$ gauge symmetry.