Discriminating Z′ from anomalous trilinear gauge coupling signatures in e ⁺ e ⁻→W ⁺ W ⁻ at ILC with polarized beams

Abstract

New heavy neutral gauge bosons Z′ are predicted by many models of physics beyond the Standard Model. It is quite possible that Z′s are heavy enough to lie beyond the discovery reach of the CERN Large Hadron Collider LHC, in which case only indirect signatures of Z′ exchanges may emerge at future colliders, through deviations of the measured cross sections from the Standard Model predictions. We discuss in this context the foreseeable sensitivity to Z′s of W ^±-pair production cross sections at the e ⁺ e ⁻ International Linear Collider (ILC), especially as regards the potential of distinguishing observable effects of the Z′ from analogous ones due to competitor models with anomalous trilinear gauge couplings (AGC) that can lead to the same or similar new physics experimental signatures at the ILC. The sensitivity of the ILC for probing the Z–Z′ mixing and its capability to distinguish these two new physics scenarios is substantially enhanced when the polarization of the initial beams and the produced W ^± bosons are considered. A model-independent analysis of the Z′ effects in the process e ⁺ e ⁻→W ⁺ W ⁻ allows to differentiate the full class of vector Z′ models from those with anomalous trilinear gauge couplings, with one notable exception: the sequential SM (SSM)-like models can in this process not be distinguished from anomalous gauge couplings. Results of model-dependent analysis of a specific Z′ are expressed in terms of discovery and identification reaches on the Z–Z′ mixing angle and the Z′ mass.

Appendix: Helicity amplitudes

In this appendix, we collect the helicity amplitudes for the different initial (e ⁺ e ⁻) and final-state (W ⁺ W ⁻) polarizations. In Table 5 we quote the amplitudes for the case of Anomalous Gauge Couplings [20, 21], whereas in Table 6 we give the corresponding results for the case of a Z′.

Table 5 Helicity amplitudes for e ⁺ e ⁻→W ⁺ W ⁻ in the presence of AGC [20, 21]. To obtain the amplitude F _λττ′(s,cosθ) for definite helicity λ=±1/2 and definite spin orientations τ(W ⁻) and τ′(W ⁺) of the W ^±, the elements in the corresponding column have to be multiplied by the common factor on top of the column. Subsequently, the elements in a specific column have to be multiplied by the corresponding elements in the first column and the sum over all elements is to be taken. In the last column, the amplitude for the case of τ=±1, τ′=0 is obtained by replacing τ′ by −τ in the elements of this last column

Table 6 Helicity amplitudes for e ⁺ e ⁻→γ,Z ₁,Z ₂→W ⁺ W ⁻

Note that the quantity δ _Z appearing in Table 5 is different from, but plays a role similar to that of Δ _Z entering in the parametrization of Z′ effects. Furthermore, in analogy with the Δ _γ which enters the description of Z′ effects, one could imagine a factor (1+δ _γ ) multiplying the photon-exchange amplitudes in Table 5. Such a term could be induced by dimension-8 operators, but δ _γ would have to vanish as s→0, due to gauge invariance.