References - Bogoliubov Laboratory of Theoretical Physics - JINR

to discriminate the spin-2 graviton resonance against the spin-1 hypothesis was discussed
in Refs. [1, 2].
It would be interesting to compare the LHC results for the Z ′ identification reaches [1]
with the foreseeable identification potential of the e + e − International Linear Collider
(ILC). In this case, with the mass expected to lie well above the available c.m. energy,
the Z ′ manifestations can be represented only by deviations of observables from the SM
predictions, to be searched for in precision measurements of cross sections. For this
discussion, we must utilize, as basic observables, the differential cross sections for the
processes
e + + e − → f + ¯ f, f = e, μ, τ, c, b. (2)
In a wide variety of electroweak theories, in particular those based on extended, spontaneously
broken, gauge symmetries, the existence of one (or more) new neutral gauge
bosons Z ′ is envisaged [3]. The three possible U(1) Z ′ scenarios originating from the
exceptional group E6 spontaneous breaking are Z ′ χ , Z′ ψ and Z′ η . Also, we consider the leftright
model with Z ′ LR originating from the breaking down of an SO(10) grand-unification
symmetry and the Z ′ ALR predicted by the so-called “alternative” left-right scenario. The
so-called sequential Z ′ SSM , where the couplings to fermions are the same as those of the
SM Z. Current Z ′ mass limits, from the Fermilab Tevatron collider, are in the range
500 − 900 GeV, depending on the model.
It is widely believed that new heavy vector bosons are “light” enough to be directly
produced at the LHC by means of the DY mechanism and discovered through e.g. the
leptonic decay mode. However, since the current limits on MZ ′ for the Z′ models under
study are well above the planned ILC energy of 0.5 TeV, it is expected to observe the
virtual effects of new gauge bosons with the ILC at least at this energy option. A scenario
we adopt in this section and the question we will address is that if the mass of a potential
Z ′ is known from the LHC, whether the Z ′ model can be resolved at the ILC.
In the following, we will try to quantitatively discuss the above issues in the framework
of the processes (2). In particular, our aim will be to assess the potential of electron and
positron longitudinal polarization at the ILC, in enhancing the discovery reaches on Z ′
masses and distinction of Z ′ models. We will take as basic observables the polarized
angular differential cross sections of the processes (2).
Expression of the polarized differential cross section for the process e + e − → f ¯ f with
f �= t can be found in [4]. We divide the angular range into bins. For Bhabha scattering,
the angular range | cos θ| < 0.90 is divided into ten equal-size bins. Similarly, for annihilation
into muon, tau and quark pairs we consider the analogous binning of the angular
range | cos θ| < 0.98. For the Bhabha process, we combine the cross sections with the following
initial electron and positron longitudinal polarizations: (P − ,P + )=(|P − |, −|P + |);
(−|P − |, |P + |;(|P − |, |P + |); (−|P − |, −|P + |). For the “annihilation” processes in Eq. (2),
with f �= e, t, we restrict ourselves to combining the (P − ,P + ) = (|P − |, −|P + |)and
(−|P − |, |P + |) polarization configurations. Numerically, we take the “standard” envisaged
values |P − | =0.8 and|P + | =0.5.
Regarding the ILC energy and time-integrated luminosity, for simplicity we assume
the latter to be equally distributed among the different polarization configurations defined
above. The explicit numerical results will refer to C.M. energy √ s = 0.5 TeVwith
time-integrated luminosity Lint = 500 fb −1 . The assumed reconstruction efficiencies,
that determine the expected statistical uncertainties, are 100% for e + e − final pairs; 95%
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