Bosonic Quartic Couplings at LEP2

We list the set of C and P conserving anomalous quartic vector bosons self-couplings which can be tested at LEP2 through triple vector boson production. We show how this set can be embedded in manifestly SU(2) × U(1) gauge invariant operators exhibiting an SU(2)c global symmetry. We derive bounds on these various couplings and show the most relevant distributions that can enhance their contribution. We also find that an e+e− collider running at 500 GeV can improve the LEP2 limits by as much as three-orders of magnitude. KEK-CP-087 LAPTH-744/99 1 Photonic Quartic Couplings LEP has now crossed the threshold for Z pair production and therefore experiments can now study triple boson production like e+e− → W+W−γ, ZZγ, beside e+e− → γγγ, γγZ which may be studied at lower energies. These processes have the potential to study new quartic photonic couplings, photonic in the sense that at least one of the vector bosons is a photon. One should refer to these quartic couplings as genuine quartic couplings [1, 2, 3] contrary to quartic couplings that may emerge from an operator that induces for instance both a tri-linear WWγ coupling as well as a possible WWγγ, as required by gauge invariance. The latter (non-genuine) couplings can therefore be investigated much more efficiently through their tri-linear counterpart in, for instance, e+e− → W+W−. An example of such a coupling is the much studied operator described by λγ in the by now classic classification [4] , λγ is sometimes referred to as the anomalous quadrupole moment of the W . From this perspective genuine quartic couplings can only be studied in triple vector boson production or through boson-boson fusion, the latter becoming a more efficient means at TeV energies [3]. Let us note that quartic neutral couplings, 4−γ , Z−3γ, contributing to e+e− → 3γ have already been studied in [2] and could be explored for energies below those presently available. Since these quartic couplings involve at least three photons, electromagnetic gauge invariance alone allows these couplings only if they emerge from dimension-eight (or higher) operators. On the other hand, anomalous couplings such as WWγγ or WWZγ that contribute to e+e− → W+W−γ may be associated to dim-6 operators and are hence a more likely signal of a possible residual effects of New Physics. As a matter of fact WWγγ and WWZγ are present in the SM at tree-level and as a consequence these types of couplings are more important to study. These quartic photonic couplings were first introduced in [1] in view of studying their effects on γγ → W+W− in the laser mode of the Linear Collider. They were derived by only appealing to electromagnetic gauge invariance and SU(2)c custodial symmetry. The phenomenology of these couplings has since then been studied in the next linear collider both in the e+e− [3, 5], γγ [1] and eγ [6] modes. Very recently these couplings have been re-investigated for LEP2 energies [7]. Unfortunately, as we will show, when studying the effect of genuine quartic couplings in e+e− → W+W−γ and e+e− → Zγγ, one needs to consider a larger set of structures than the two that have been written down for γγ → W+W− . The aim of this paper is to generalize the study we performed in [1, 3] and to review and clarify some of the issues related to the photonic quartic couplings. The plan of the paper is as follows. In the next section, we start by first listing the leading quartic operators that contribute to e+e− → W+W−γ (and Zγγ). In writing