Bosonic Quartic Couplings at LEP2

TL;DR

The paper addresses the classification and testing of genuine CP/C-conserving bosonic quartic couplings involving photons at LEP2 through triple vector boson production, embedding them in manifestly $SU(2) imes U(1)$ gauge-invariant, $SU(2)_c$-symmetric operators. It constructs a complete set of dimension-6 photonic quartic operators, derives their Feynman rules, and maps them onto both nonlinear and linear (Higgs-containing) realizations, revealing relations among $WW\, ext{gamma} ext{gamma}$, $WWZ\gamma$, and $ZZ\gamma\gamma$ structures. The phenomenological analysis of $e^{+}e^{-} o W^{+}W^{-}\gamma$ and $e^{+}e^{-} o Z\gamma\gamma$ at LEP2 yields bounds on the anomalous couplings, with high-energy extrapolations showing improvements up to ~$3$ orders of magnitude at a 500 GeV linear collider. The work clarifies the gauge-invariant basis of quartic photonic operators, discusses the interplay with custodial symmetry, and provides a framework for constraining non-renormalizable quartic interactions at current and future $e^{+}e^{-}$ colliders.

Abstract

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)xU(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.

Figures (7)

• Figure 1: Dependence of the $e^+ e^-\rightarrow W^+ W^- \gamma \;$ cross section at $\sqrt{s}=200$ GeV on the anomalous parameters a) $k_0$, b) $a_0$ with the constraint Eq. (\ref{['nowwz']}) c) $k_c$ and d) $k_{1,2,3}^w$. For the cuts on the photon refer to the text. The horizontal line indicates the $3\sigma$ increase of the cross section. $\Lambda$ has been set to $M_W$.
• Figure 2: $2\sigma$ and $3\sigma$ contours from $e^+ e^-\rightarrow W^+ W^- \gamma \;$ at $\sqrt{s}=200$ GeV in $k_0^m-k_2^w$ and the $k_0^b-k_c^w$ planes.
• Figure 3: Distribution in the energy of the photon in $e^+ e^-\rightarrow W^+ W^- \gamma \;$ due to the anomalous couplings $k_0^b$ and $k_c^b$ as compared to the tree-level ${\cal{S}} {\cal{M}}\;$. We have taken $k_i$ values that lead to a $3\sigma$ increase of the cross section as explained in the text. The $\pm$ are the positive and negative values given by Eq. (\ref{['eewwglep2limit']}).
• Figure 4: As in Fig. \ref{['dis_eg']} but for the $p_T$ of one of the $W$'s.
• Figure 5: Dependence of the $e^{+} e^{-}\; \rightarrow Z\gamma \gamma$ cross section at $\sqrt{s}=200$ GeV on the anomalous parameters $k_{0,c}$ with $\Lambda=M_W$. For the cuts on the photon refer to the text.