Left-right asymmetries and exotic vector-boson discovery in lepton-lepton colliders

Abstract

By considering left-right (L-R) asymmetries we study the capabilities of lepton colliders in searching for new exotic vector bosons. Specifically we study the effect of a doubly charged bilepton boson and an extra neutral vector boson appearing in a 3-3-1 model on the L-R asymmetries for the processes $e^-e^-\to e^-e^-$, $\mu^-\mu^-\to\mu^-\mu^-$ and $e^-\mu^-\to e^-\mu^-$ and show that these asymmetries are very sensitive to these new contributions and that they are in fact powerful tools for discovery this sort of vector bosons.

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arXiv:hep-ph/0003085v1 9 Mar 2000
IFT-P.026/2000
March 2000
Left-right asymmetries and exotic vector–boson discovery in
lepton-lepton colliders
J. C. Montero, V. Pleitez and M. C. Rodriguez
Instituto de F´ ısica Te´ orica
Universidade Estadual Paulista
Rua Pamplona, 145
01405-900– S˜ ao Paulo, SP
Brazil
Abstract
By considering left-right (L-R) asymmetries we study the capabilities of lep-
ton colliders in searching for new exotic vector bosons. Specifically we study
the effect of a doubly charged bilepton boson and an extra neutral vector
boson appearing in a 3-3-1 model on the L-R asymmetries for the processes
e−e−→ e−e−, µ−µ−→ µ−µ−and e−µ−→ e−µ−and show that these asym-
metries are very sensitive to these new contributions and that they are in fact
powerful tools for discovery this sort of vector bosons.
PACS numbers: 13.88.+e; 12.60.-i 12.60.Cn;
Typeset using REVTEX
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I. INTRODUCTION
Any extension of the electroweak standard model (ESM) [1] implies necessarily the exis-
tence of new particles. We can have a rich scalar-boson sector if there are several Higgs-boson
multiplets [2] or have more vector and scalar fields in models with a larger gauge symmetry
as in the left–right symmetric [3] and in 3-3-1 models [4], or we also can have at the same
time more scalar, fermion, and vector particles as in the supersymmetric extensions of the
ESM [5].
If in a given model all the new particles contribute to all observables, it will be very dif-
ficult to identify their contribution in the usual and exotic processes. In some models [4,6]
the contributions of the scalar-bosons can not be suppressed by the fermion mass and they
can have same strength of the fermion–vector-boson coupling. Hence, we can ask ourselves
if there exist observables and/or processes which allow us to distinguish between the con-
tributions of charged and neutral scalar-bosons from those of the vector-bosons. In Ref. [7]
it was noted that the left-right (L-R) asymmetries in the lepton–lepton diagonal scattering
are insensible to the contribution of doubly-charged scalar fields but are quite sensible to
doubly-charged vector field contributions. On the other hand, in non-diagonal scattering
(as µ−e−) those asymmetries are sensible to the existence of an extra neutral vector-boson
Z′[8,9].
Here we will extend our previous analysis by considering a detailed study of the L-R
asymmetries in order to analyse their capabilities in detecting new physics. The outline of
the paper is the following: In Sec. II we define the asymmetries; in Sec. III we show the
lagrangian interaction of the models we are considering here. The results and experimental
considerations are given in Sec. IV and our conclusions appear in the last section.
II. THE L-R ASYMMETRIES
The left-right asymmetry for the process l−l′−→ l−l′−with one of the particles being
unpolarized is defined as
ARL(ll′→ ll′) ≡ ARL(ll′) =dσR− dσL
dσR+ dσL,(1)
where dσR(L)is the differential cross section for one right (left)-handed lepton l scattering
on an unpolarized lepton l′and where l,l′= e,µ. That is
ARL(ll′) =(dσRR+ dσRL) − (dσLL+ dσLR)
(dσRR+ dσRL) + (dσLL+ dσLR),(2)
where dσijdenotes the cross section for incoming leptons with helicity i and j, respectively,
and they are given by
dσij∝
?
kl
|Mij;kl|2,i,j;k,l = L,R.(3)
Notice that when the scattering is diagonal, l = l′= e,µ, dσRL= dσLR, so the asymmetry
in Eq. (2) is equal to the asymmetry defined as (dσRR−dσLL)/(dσRR+dσLL). For practical
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purposes, for the non-diagonal (eµ → eµ) case of the ARLasymmetry, we will focus on the
scattering of polarized muons by unpolarized electrons.
Another interesting possibility is the case when both leptons are polarized. We can
define an asymmetry AR;RLin which one beam is always in the same polarization state, say
right-handed, and the other is either right- or left-handed polarized (similarly we can define
AL;LR):
AR;RL=dσRR− dσRL
dσRR+ dσRL,AL;RL=dσLR− dσLL
dσLL+ dσLR. (4)
In this case, when the non-diagonal scattering is considered, we will assume that the muon
beam has always the same polarization and the electron one can have both, the left and the
right polarizations.
We can integrate over the scattering angle and define the asymmetry
?ARLas
?
ARL=(?dσRR+?dσRL) − (?dσLL+?dσLR)
(?dσRR+?dσRL) + (?dσLL+?dσLR),
?175o
(5)
where
?dσij≡
5o
dσij. A similar expression can be written for AR;RL.
III. THE MODELS
We are studying here the asymmetries defined above in the context of two models: the
electroweak standard model (ESM) and in a model having a doubly charged bilepton vector
field (U−−
charged scalar bileptons but since their contributions cancel out in the numerator of the
asymmetries we are not consider them on this study. We identify the case under study by
using the {ESM}, {ESM + U}, and {ESM + Z′} labels in cross sections and asymmetries.
In the context of the electroweak standard model, at the tree level, the relevant part of
the ESM lagrangian is
µ ) and an extra neutral vector boson Z′[4]. The latter model has also two doubly
LF= −
?
i
g mi
2MW
¯ψiψiH0− e
?
i
qi¯ψiγµψiAµ−
g
2cosθW
ψiγµ(gi
V− gi
Aγ5)ψiZµ,(6)
θW≡ tan−1(g′/g) is the weak mixing angle, e = gsinθWis the positron electric charge with
g such that
g2=8GFM2
W
√2
;org2/α = 4πsin2θW,(7)
with α ≈ 1/128; and the vector and axial neutral couplings are
gi
V≡ t3L(i) − 2qisin2θW,gi
A≡ t3L(i),(8)
where t3L(i) is the weak isospin of the fermion i and qiis the charge of ψiin units of e.
The charged current interactions in a model having a doubly charged vector boson [4],
in terms of the physical basis, are given by
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−
g
√2
?
¯ νLEν†
LEl
LlLW+
µ+¯lc
LγµElT
REν
LνLV+
µ−¯lc
LElT
REl
LlLU++
µ
?
+ H.c.,(9)
with l′
try (mass) eigenstates. We see from Eq. (9) that for massless neutrinos we have no mixing in
the charged current coupled to W+
to V+
the charged currents coupled to V+
µ
are not diagonal in flavor space and the mixing
matrix K = ElT
has three angles and six phases. In the present case, however, the matrix K is determined
entirely by the charged lepton sector, so we can rotate only three phases [10]).
The total width of the U-boson (Γtotal
U
) is a calculable quantity in the model once we
know all the U-boson couplings which are derived from the 3-3-1 gauge-invariant lagrangian.
However, we find that a complete computation of ΓUis out of the scope of this paper because
in this case some realistic hypotheses concerning the masses of the exotic scalars and quarks
should be made. Thus, we will only consider the partial width due to the U−−→ l−l−
decay. In the limit where all the lepton masses are negligible we have:
L= El
LlL,l′
R= El
RlR,ν′
L= Eν
LνL, the primed (unprimed) fields denoting symme-
µbut we still have mixing in the charged currents coupled
µ . That is, if neutrinos are massless we can always chose Eν†
µand U++
REν
µand U++
LEl
L= 1. However,
Lhas three angles and three phases. (An arbitrary 3 × 3 unitary matrix
Γtotal
U
∼ Γ(U−−→ leptons) =
?
i,j
GF
6√2πM2
WMU|Kij|2
(10)
where i,j run over the e,µ, and τ leptons and Kijis a mixing matrix in the flavor space. For
the expression above we can write Γtotal
U
=?
K is almost diagonal we can neglect Γijfor i ?= j and consider for practical purposes that
Γtotal
U
mass. For instance, for MU= 300 GeV we have Γtotal
In the model there is also a Z′neutral vector boson which couples with the leptons as
follows
g
2cW
W)1/2/√3 and Rl= 2Ll. Notice the leptophobic character of Z′
[11]. In this case we have no concerns about the Z′–width because this neutral boson is only
exchanged in the t–channel.
We will consider the process
iΓii+1
2
?
i?=jΓijand assuming that the matrix
= 3 × Γii. In our numerical applications Γtotal
U
is a varying function of the U-boson
∼ 2.5 GeV.
U
LZ′
NC= −
?¯laLγµLllaL+¯laRγµRllaR+ ¯ νaLγµLννaL
?
Z′
µ,(11)
with Ll= Lν = −(1 − 4s2
l−(p1,λ) + l′−(q1,Λ) → l−(p2,λ′) + l′−(q2,Λ′),
where q = p2−p1= q2−q1is the transferred momentum. As we said before, we will neglect
the electron mass but not the muon mass i.e., E = |? pe| for the electron and K2−|? qµ|2= m2
for the muon. In the non-diagonal elastic scattering in the standard model we have only the
t-channel contribution. The relevant amplitudes for the ESM, {ESM + U} and {ESM + Z′}
models are in the appendices of Ref. [7] (Ref. [8]) for the diagonal (non-diagonal) case.
(12)
µ
IV. RESULTS
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A. The U boson
We start this section by considering the contributions of the doubly charged vector boson
U to the asymmetries which contributes uniquely via the s-channel for a doubly charged
initial state. In Fig. 1 we see that the angular dependence of the ARLasymmetry, taken
into account the U contribution, presents a relatively different behavior with respect to the
ESM for a wide range of U-masses. Notice that the lines are considerably separated even for
those values of the U-mass that are not close to√s. Notice also that for U-mass lower than
√s we basically reproduce the ESM result for θ ≈ 0 and π/2; the largest difference with the
ESM occurs for θ in the interval 0.5–1. The behavior of ARLfor ESM+U as a function of
MUis showed in Fig. 2 for a fixed scattering angle and for several values of√s. We see that
this asymmetry is essentially negative and that its maximum value is zero and occurs at the
resonance point MU=√s. This is due to the fact that at the resonance the numerator of
ARL, as defined in Eq. (1), cancels out no mater the value of MU. On the other hand the
value of MU governs the width of the curves around the resonance point. This particular
feature is better seen in Fig. 3. In this figure we show the ARLasymmetry as a function of
the center-of-mass energy ECM =√s for some values of the U-mass and it is clearly seen
that not only at the peak but also for a considerably large range of masses around the peak,
the curves representing the respective U contribution are significantly separated from the
ESM one. It means that this asymmetry is very sensitive to the U-boson even in the case
where the U-mass is larger than√s; when the U-mass is lower than√s we reproduce the
ESM results.
In Fig. 4 and Fig. 5 we show the effects of the U-boson on the AR;RLasymmetry, defined
in Eq. (4), and as it behaves qualitatively like ARL we come to the same conclusions we
did for ARL. We must note that near the U-resonance the AR;RLasymmetry is negative.
However, in this case, polarization for both beams must be available.
The integrated asymmetry
?ARLdefined in Eq. (5) is shown in Fig. 6. There we can see
that while the ESM curve keeps an almost constant value (0.025-0.031) for 0.5 <√s < 2
TeV, the ESM+U curves go from zero, for MU?=√s, to a very pronounced peak (∼ −0.25)
at the resonance points. In Fig. 7, for the sake of detectability, we show the quantity δ%
defined by:
δ % =
?AESM+U
RL
−?AESM
?AESM
RL
RL
× 100, (13)
which in this case stands for the percent deviation of
can see that there is a wide range of U-masses that can be probed at e−e−colliders.
Next we study the effect of non-negligible initial and final fermion masses by considering
the µ−µ−→ µ−µ−process in a muon collider. The results are given in Fig. 8. There
we can see that, for MU = 500 GeV, below 300 GeV the muon mass effect is in evidence
differing sensibly from the electron-electron case, independently of the U-contribution for
higher energies the lepton mass has no effect at all for both models. Between 300 and
400 GeV all the curves are coincident and we cannot distinguish among both models or
leptons. Above 400 GeV it is the U-effect which dominates and it is the same for electrons
and muons. The effect of the U-resonance is well evident and even above the resonance
there is an almost constant difference between the ESM+U and ESM asymmetries showing
?AESM+U
RL
from
?AESM
RL . There we
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