References - Bogoliubov Laboratory of Theoretical Physics - JINR

We shall call this model the “secluded” model because the electric charge has no component
in U(1)z, this happens even if z �= B − L. It has also three right-handed neutrinos
with L =1.
Both models have the same scalar sector: one doublet, H, withY = +1; and one
complex singlet, φ, withY = 0. However, in general, depending on the z value, the
doublet in the secluded model has to carry U(1)z charge. Only in this case there is
mixing between Z and Z ′ in the mass square matrix. The difference between (2) and (3)
distinguishes both models. Only when zH = 0 the factor U(1)z corresponds to U(1) B−L
and this is the case to be considered here. For the secluded model see also Ref. [7]. In
most of the paper we compare both models assuming that the breaking of the B − L
symmetry occurs at an energy above the TeV scale.
These models have two massive neutral vector bosons that we will denote Z1 and Z2
and we will parameterize their neutral currents as follows:
L NC = − g �
ψiγ
2cW
μ [(g i V − gi Aγ5)Z1μ +(f i V − f i Aγ5)Z2μ]ψi, (4)
i
with Z1 ≈ Z and Z2 ≈ Z ′ .
At ILC, the phenomenological constraints on extra neutral gauge bosons can be investigated
with the use of polarization. These bosons can be detected by measuring some
observables, as Z ′ decay partial widths, and Z ′ mass and several kinds of asymmetries
and some cross sections as well.
In the recent past, the precision of electroweak measurements was achieved at electronpositron
colliders SLC and LEP. Although the SLC data statistics were smaller than the
LEP one, the presence of longitudinal polarization allowed complementary and competitive
measurements of Z couplings. The ILC is been planed to have both electron and
positron beams polarized and we shall see that the polarization is a useful tool to distinguish
different kinds of models. Here we present and analyze some polarization asymmetries
for the two models discussed above. We study the decay channel e + e − → μ + μ − .
Bhabha and Møller scattering can also be used as additional observables in e + e − collisions
but these kind of processes are sensitive only to the Z ′ couplings to electron. Møller
scattering has an advantage of profiting from two highly polarized electron beams.
So we work with left-right asymmetry, polarization asymmetry and a mix asymmetry
that combines the forward-backward and left-right asymmetries. The definition of
these asymmetries are as follows: AFB =3NFB/4σT , ALR =3NLR/4σT ,andALR,F B =
3NLR,F B/4σT ,whereNFB = σLL − σLR + σRR − σRL, NLR = σLL + σLR − σRR − σRL,
and NLR,F B = σLL − σRR + σRL − σLR, andσT = σLL + σLR + σRR + σRL. We are not
considering the effects of transverse polarization in this situation because they suffer from
experimental difficulties.
For the case of e + e − → μ + μ − at high energies, the polarization asymmetry is just the
left-right asymmetry with the opposite sign. The left-right and polarization asymmetries
are very sensitive to the weak mixing angle and the combined left-right and forwardbackward
asymmetry is a very important statistical tests. At SLC, this kind of asymmetry
had given an statistical precision equivalent to the measurements of unpolarized forwardbackward
asymmetry at LEP [8]. In Fig. 1(a) we show the cross section at the Z ′ peak
as a function of center of mass energy, s; and in Fig. 1(b), we show the forward-backward
asymmetry also in terms of s. Notice that the cross section is more sensitive to the
presence of Z ′ at the peak, but the asymmetry can be relevant even out of the pole.
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