Zgryźliwość kojarzy mi się z radością, która źle skończyła.
acta physica slovaca vol. 51 No. 2, 139 149
April 2001
RESONANCES FROM STRONGLY-INTERACTING ELECTROWEAK SYMMETRY
BREAKING SECTOR AT FUTURE
e
e
COLLIDERS
M. Gintner
1
, I. Melo
2
Physics Dept.,University of Zilina, Vel'ky Diel, 010 26 Zilina, Slovakia
Received 21 December 2000, in nal form 3 March 2001, accepted 5 March 2001
We study new strong resonances associated with the physics responsible for the strong elec-
troweak symmetry breaking. We write down the lowest order effective chiral Lagrangians
describing the couplings of these new resonances to the Standard Model elds and calculate
signals for
-resonances and for
-resonances in the
scat-
1 Introduction
One of the most important problems of today's particle physics is the mechanism of electroweak
symmetry breaking (ESB). The mechanism of ESB is responsible for giving the W and Z bosons
their masses. Despite some progress in the experimental limits on the Higgs mass [1], the ESB
sector of the Standard Model (SM) is still rather weakly constrained by the experimental data
and the physics behind the mechanism of ESB remains unknown.
There are two major scenarios for the solutions to this problem. The rst scenario is a weakly-
coupled electroweak symmetry breaking sector. Its simplest version is the light SM Higgs bo-
son. More complicated alternatives of this scenario include supersymmetric theories. The second
scenario is a strongly-coupled ESB sector. In this scenario the symmetry breaking is triggered
by new non-perturbative strong forces. Typical representatives of this scenario are technicolor
models built in analogy to chiral symmetry breaking in QCD. In this work we study some phe-
nomenological consequences of strong ESB.
As a common feature of any plausible scenario, the originally massless
and
gauge
components. A direct consequence of this fact is the Equivalence Theorem (ET): in the large
energy limit (
) the interactions of the longitudinal
's become equal to those of
1
E-mail address: gintner@fel.utc.sk
2
E-mail address: melo@fel.utc.sk
0323-0465 /01 c
Institute of Physics, SAS, Bratislava, Slovakia
139
tering in the process
at the Next Linear Collider. We also nd low-energy
constraints on the
-resonance couplings to the top quark.
PACS:
12.60.Fr, 12.15.Ji
bosons become massive through the Higgs mechanism, by absorbing Goldstone bosons of the
ESB sector. The Goldstone bosons are the inevitable product of a spontaneous symmetry break-
ing. When eaten-up by the
and
bosons, the Goldstone bosons become their longitudinal
140
M. Gintner et al.
the ESB Goldstone bosons. Thus any collider process which involves the longitudinal weak
gauge bosons can in principle give us an access to the interactions connected to the mechanism
of ESB [2].
In QCD the spontaneous breaking of chiral symmetry gives rise to pions which are the bound
states of quarks. At energies of a few hundred MeV we cannot see their substructure we can
only study QCD interactions through the
scattering amplitudes which are unitarized by some
expect new strongly interacting ESB resonances to appear at or below this scale. We will not be
able to see the substructure of these new resonances and EW pions at the Large Hadron Colider
(LHC) and at the Next Linear Collider (NLC) operating at 1-3 TeV range, but the question is if
we can distinguish at least the resonances themselves and measure their masses and couplings.
A lot of attention has been devoted to the testing of the strongly-interacting scenario in the
longitudinal vector boson scattering
" # " # $ " # " #
[3]. The studies concentrated on signatures
of either a new
-resonance or a new
%
-resonance (parameters of the
the NLC or the LHC. The results have shown that it will be possible to establish the presence of
strong ESB at the LHC and the NLC and that, to a degree, it will be possible to distinguish new
strong resonances [2].
Another potentially powerful process for the study of strong ESB is the scattering of longitu-
dinal vector bosons to top quarks,
" # " # $ & &
. Its main appeal is in the possibility to test whether
the extraordinarily large top quark mass is generated by the same new strong interactions which
are responsible for ESB, or by yet additional new strong interactions introduced just for that sake.
In the former case (represented, e.g., by the extended technicolor theories [4]) we expect the top
quark to couple signicantly to the resonances which unitarize
" # " # $ " # " #
scattering [5, 6].
nism of the top mass generation is different from the
mass generation (as in topcolor-assisted
technicolor models [4]), we expect that the top quark does not couple signicantly to the new
resonances of the strong ESB sector. This would imply that the new resonances observed in the
top quark. Unlike all the other known quarks the top quark decays so rapidly that the information
about its spin is transferred directly to the nal state with negligible hadronization uncertainties.
This raises an interesting possibility to measure polarized cross sections in
" # " # $ & &
and use
When studying the
" # " # $ & &
process, we can make use of another unique property of the
combinations of the top quarks [2, 5].
For these reasons the
" # " # $ & &
process at the NLC has recently attracted growing inter-
est. There have been studies within the SM [79], within the Higgsless SM below the scale
of new physics (no-resonance model) [6, 10], and also within models above the scale of a new
-resonance and
-resonance [2, 5, 11, 12].
In this work we study the new
%
- and
-resonances in the process
#
# $ & &
which is
low-lying resonances such as
-resonance or
!
-resonance. We expect
an analogical situation in the case of the strong ESB scenario. The strong ESB results in the
appearance of massless Goldstone bosons electroweak (EW) pions which, just like QCD
pions, are assumed to be bound states of some more fundamental strongly interacting objects
(e.g. technifermions).
Since
" # " #
(
"
) scattering amplitudes start to violate unitarity at 1-3 TeV range we
-resonance can be tuned to immitate the SM Higgs boson SM-like
%
-resonance) at either
This could lead to signicant event rates in
" # " # $ & &
. In the latter case, when the mecha-
channel are suppressed in the
" # " # $ & &
channel [2, 5].
this information to distinguish between
%
- and
resonances which contribute to different helicity
Resonances from strongly-interactingESB sector
141
being considered as a subprocess of
(
( $ ) ) & &
at the NLC with the CM energy of
*+
TeV and
-resonance, and the
-resonance are considered with
various values of parameters. We show the importance of low energy constraints for
-resonance
signals at NLC. We calculate total and differential cross sections with polarized
,-./0 1 2/ 3 4
quarks in the nal state using the Effective-
Approximation and considering longitudinal weak
gauge bosons only. The number of events obtained is for the assumed integrated luminosity of
200 fb
5
.
This paper is organized as follows. In Section 2 we introduce the lowest order effective chi-
ral Lagrangians describing models with no resonance,
%
-resonance, and
-resonance. The La-
grangians describe interactions of these resonances with EW pions, gauge elds, and top quarks.
In Subsection 2.1 we discuss existing constraints on the parameters of the
Lagrangian. Our
calculations and results obtained for the models under consideration are presented in Section 3.
Finally, our conclusions can be found in Section 4.
Due to our ignorance of details of new strong physics behind ESB the most convenient approach
to the analysis of its possible consequences is the effective eld theory framework. Within this
framework a model-independent analysis of the strong ESB mechanism can be performed. Our
ignorance of the full theory will be reected in our inability to calculate values of free param-
eters that appear in an effective Lagrangian. These free parameters parameterize all possible
new physics which respects the given low-energy theory. They will have to be obtained from
experiment.
In this approach, if energy available is below the threshold of new resonances production,
one starts with EW pions as the only particles in the spectrum which are subject to new strong
interactions. The Lagrangian of EW pions is the familiar nonlinear
6
-model based on global
symmetry breaking pattern is supported by the relation
<
=3 > ?
which is satised to
high accuracy.
If we assume to have enough energy to produce a new resonance it must be added to the
set of building elements of the effective Lagrangian. In our work beside the no-resonance case
we also assume the production of either the
%
-resonance or
-resonance. They are added to the
Lagrangian respecting chiral
% 7 ,8 2
#
9 % 7 ,8 2
:
symmetry. For
%
-resonance it is a straight-
approach [14]. The gauge interactions of the SM are introduced by requiring the
%
and
La-
grangians to be gauge invariant under
% 7 ,8 2# 9 7 ,
2@
.
Let us begin with the no-resonance Lagrangian. The
% 7 ,8 2# 9 7 ,
2@
gauged non-renorma-
lizable effective Lagrangian responsible for the low energy interactions of the EW pions is given
by
Tr
,F G 7 H F
G
7 2 I
(1)
where
7
NO 4 ,8P Q
R
C
2
with
GeV,
Q
is the isospin triplet of the EW pions, and
are the
% 7 ,8 2
group generators with the normalization Tr
,
R T R W
2
X
T W
8
.
2 TeV. Three cases, the no-resonance, the
2 No- ,
%
- and
-resonance models
spontaneously broken down to
% 7 ,8 2;
custodial or isospin symmetry. This
forward procedure, for
-resonance one can follow either Weinberg [13] or hidden symmetry
142
M. Gintner et al.
is the kinetic energy term of the
gauge elds,
, and the
gauge eld,
M G
. The covariant derivative
F G 7
is dened as follows
(2)
where
and
Z G
[ \ M G
R ]
.
In this model the interactions of EW pions with fermions are described by the following
Lagrangian
h.c.
2
R
]
(3)
where the
denotes fermion eld doublet,
,& i2
, the
b 1 c
is the baryon minus lepton number
operator, and the
diag
,j k j
W
2
is the fermion doublet mass matrix.
The gauged
%
-resonance model can be described by the following leading order effective
Lagrangian
Tr
,F G 7 H F
G
7 2% I
(4)
where
is given by (1), the
is the kinetic energy term of the
%
-resonance, the
%
denotes the scalar
,
2
resonance eld, the
l
is its mass. The
[ \\\
and
l
are free
parameters.
To include the interactions with fermions we have to add
h.c.
2
(5)
where
is a free parameter.
The gauged
-resonance model is given by
is given by (3), and
m
Tr
,o G o
G
2 I
(6)
where
is given by (1), the
is the kinetic energy term of the
-resonance, and
(7)
where
,
, and the
" G
[ \\ " G
R
denotes the vector
The fermionic part of the
-resonance model is described as follows
-resonance eld. The
U
and the
[ \\
are free parameters.
G
,
(8)
where the
i
5
,
i
D
are free parameters, and
r
diag
,
2
.
Resonances from strongly-interactingESB sector
143
This Lagrangian is
% 7 ,8 2# 9 7 ,
2@
gauge invariant. However, introduction of gauge elds
terms. The
custodial symmetry is also broken by the top-bottom quark mass splitting in the fermion mass
term. These two particular breakings of the custodial symmetry also occur in the SM. The third
custodial symmetry breaking originates in the projection matrix
r
in the coupling of the
to the
_
that got broken by the
right-handed bottom quark (to avoid constraints on the
couplings from the
ii
vertex), which
spoils the custodial symmetry in much the same fashion as does the top-bottom mass splitting.
The difference between our
-resonance Lagrangian and the BESS model of Ref. [15] is
is assumed to be universal for all fermion generations,
while here we assume coupling constants
i
5
i
D
and
i
5
to be specic (and possibly large) for the third
generation of quarks.
There are four new parameters in the
Lagrangian: couplings
U [ \\ i
5
i
D
. Since
n s
2.1 Constraints on the parameters of the
Lagrangian
the coupling
U
can be traded for the
mass. We do not have any experimental con-
(the theoretical expectation is that it should be around
1 V
TeV scale). We do,
however, have constraints on
[ \\
,
i
5
and
i
D
. These are due to the corrections that
[ \\
,
i
5
and
i
D
induce in the SM couplings of the
and the
to fermions at low energies (
t u
GeV) when the
-resonance is integrated-out from the particle spectrum. This leads to corrections to
v
param-
eters which conveniently parameterize new physics effects [16]. The BESS model studies [17]
have shown that
[ \\
corrects
v
]
by
X v
]
[
D
,
E
[ \\
D
2
, which implies for our model
(9)
parameters which are specic to our model.
We nd the low-energy couplings of the
and the
to fermions by taking
n s
and
i
D
the equation of motion for the
" G
eld (
Y
A n
Y " G
) has the solution
" G
1 ,
A
G I Z G 2
8
.
When we substitute this solution in the fermion Lagrangian in (8) and follow usual steps, we
eventually get for the low-energy
and
couplings to the top and bottom quarks
3
:
(10)
where
{ |
}
|
=3 > ?
>0. ?
, respectively. There is no modication of the
or
couplings
thus escapes the constraint from the
ii
coupling).
modies the
& i
,
&&
and
3
These couplings are also modied by the small terms
~
€ ‚‚€
which we neglect here for simplicity.
broke the original
chiral invariance, namely by the terms with the weak
hypercharge. More precisely, it is the custodial
. The
r
matrix ensures that the
only couples to the right-handed top quark but not to the
that in the BESS model
i
D
straints on
n s
We will now derive constraints on the
i
5
, which is
accomplished by
U $ x
while keeping
[ \\
xed, as in the BESS model studies [17]. In this limit
to leptons and the rst and second generation quarks. Note that
i
5
couplings, while
i
D
, due to the matrix
r
in the
" G
_
:
_
:
coupling in (8) modies only
&&
coupling (
i
D
zanotowane.pl doc.pisz.pl pdf.pisz.pl hannaeva.xlx.pl
April 2001
RESONANCES FROM STRONGLY-INTERACTING ELECTROWEAK SYMMETRY
BREAKING SECTOR AT FUTURE
e
e
COLLIDERS
M. Gintner
1
, I. Melo
2
Physics Dept.,University of Zilina, Vel'ky Diel, 010 26 Zilina, Slovakia
Received 21 December 2000, in nal form 3 March 2001, accepted 5 March 2001
We study new strong resonances associated with the physics responsible for the strong elec-
troweak symmetry breaking. We write down the lowest order effective chiral Lagrangians
describing the couplings of these new resonances to the Standard Model elds and calculate
signals for
-resonances and for
-resonances in the
scat-
1 Introduction
One of the most important problems of today's particle physics is the mechanism of electroweak
symmetry breaking (ESB). The mechanism of ESB is responsible for giving the W and Z bosons
their masses. Despite some progress in the experimental limits on the Higgs mass [1], the ESB
sector of the Standard Model (SM) is still rather weakly constrained by the experimental data
and the physics behind the mechanism of ESB remains unknown.
There are two major scenarios for the solutions to this problem. The rst scenario is a weakly-
coupled electroweak symmetry breaking sector. Its simplest version is the light SM Higgs bo-
son. More complicated alternatives of this scenario include supersymmetric theories. The second
scenario is a strongly-coupled ESB sector. In this scenario the symmetry breaking is triggered
by new non-perturbative strong forces. Typical representatives of this scenario are technicolor
models built in analogy to chiral symmetry breaking in QCD. In this work we study some phe-
nomenological consequences of strong ESB.
As a common feature of any plausible scenario, the originally massless
and
gauge
components. A direct consequence of this fact is the Equivalence Theorem (ET): in the large
energy limit (
) the interactions of the longitudinal
's become equal to those of
1
E-mail address: gintner@fel.utc.sk
2
E-mail address: melo@fel.utc.sk
0323-0465 /01 c
Institute of Physics, SAS, Bratislava, Slovakia
139
tering in the process
at the Next Linear Collider. We also nd low-energy
constraints on the
-resonance couplings to the top quark.
PACS:
12.60.Fr, 12.15.Ji
bosons become massive through the Higgs mechanism, by absorbing Goldstone bosons of the
ESB sector. The Goldstone bosons are the inevitable product of a spontaneous symmetry break-
ing. When eaten-up by the
and
bosons, the Goldstone bosons become their longitudinal
140
M. Gintner et al.
the ESB Goldstone bosons. Thus any collider process which involves the longitudinal weak
gauge bosons can in principle give us an access to the interactions connected to the mechanism
of ESB [2].
In QCD the spontaneous breaking of chiral symmetry gives rise to pions which are the bound
states of quarks. At energies of a few hundred MeV we cannot see their substructure we can
only study QCD interactions through the
scattering amplitudes which are unitarized by some
expect new strongly interacting ESB resonances to appear at or below this scale. We will not be
able to see the substructure of these new resonances and EW pions at the Large Hadron Colider
(LHC) and at the Next Linear Collider (NLC) operating at 1-3 TeV range, but the question is if
we can distinguish at least the resonances themselves and measure their masses and couplings.
A lot of attention has been devoted to the testing of the strongly-interacting scenario in the
longitudinal vector boson scattering
" # " # $ " # " #
[3]. The studies concentrated on signatures
of either a new
-resonance or a new
%
-resonance (parameters of the
the NLC or the LHC. The results have shown that it will be possible to establish the presence of
strong ESB at the LHC and the NLC and that, to a degree, it will be possible to distinguish new
strong resonances [2].
Another potentially powerful process for the study of strong ESB is the scattering of longitu-
dinal vector bosons to top quarks,
" # " # $ & &
. Its main appeal is in the possibility to test whether
the extraordinarily large top quark mass is generated by the same new strong interactions which
are responsible for ESB, or by yet additional new strong interactions introduced just for that sake.
In the former case (represented, e.g., by the extended technicolor theories [4]) we expect the top
quark to couple signicantly to the resonances which unitarize
" # " # $ " # " #
scattering [5, 6].
nism of the top mass generation is different from the
mass generation (as in topcolor-assisted
technicolor models [4]), we expect that the top quark does not couple signicantly to the new
resonances of the strong ESB sector. This would imply that the new resonances observed in the
top quark. Unlike all the other known quarks the top quark decays so rapidly that the information
about its spin is transferred directly to the nal state with negligible hadronization uncertainties.
This raises an interesting possibility to measure polarized cross sections in
" # " # $ & &
and use
When studying the
" # " # $ & &
process, we can make use of another unique property of the
combinations of the top quarks [2, 5].
For these reasons the
" # " # $ & &
process at the NLC has recently attracted growing inter-
est. There have been studies within the SM [79], within the Higgsless SM below the scale
of new physics (no-resonance model) [6, 10], and also within models above the scale of a new
-resonance and
-resonance [2, 5, 11, 12].
In this work we study the new
%
- and
-resonances in the process
#
# $ & &
which is
low-lying resonances such as
-resonance or
!
-resonance. We expect
an analogical situation in the case of the strong ESB scenario. The strong ESB results in the
appearance of massless Goldstone bosons electroweak (EW) pions which, just like QCD
pions, are assumed to be bound states of some more fundamental strongly interacting objects
(e.g. technifermions).
Since
" # " #
(
"
) scattering amplitudes start to violate unitarity at 1-3 TeV range we
-resonance can be tuned to immitate the SM Higgs boson SM-like
%
-resonance) at either
This could lead to signicant event rates in
" # " # $ & &
. In the latter case, when the mecha-
channel are suppressed in the
" # " # $ & &
channel [2, 5].
this information to distinguish between
%
- and
resonances which contribute to different helicity
Resonances from strongly-interactingESB sector
141
being considered as a subprocess of
(
( $ ) ) & &
at the NLC with the CM energy of
*+
TeV and
-resonance, and the
-resonance are considered with
various values of parameters. We show the importance of low energy constraints for
-resonance
signals at NLC. We calculate total and differential cross sections with polarized
,-./0 1 2/ 3 4
quarks in the nal state using the Effective-
Approximation and considering longitudinal weak
gauge bosons only. The number of events obtained is for the assumed integrated luminosity of
200 fb
5
.
This paper is organized as follows. In Section 2 we introduce the lowest order effective chi-
ral Lagrangians describing models with no resonance,
%
-resonance, and
-resonance. The La-
grangians describe interactions of these resonances with EW pions, gauge elds, and top quarks.
In Subsection 2.1 we discuss existing constraints on the parameters of the
Lagrangian. Our
calculations and results obtained for the models under consideration are presented in Section 3.
Finally, our conclusions can be found in Section 4.
Due to our ignorance of details of new strong physics behind ESB the most convenient approach
to the analysis of its possible consequences is the effective eld theory framework. Within this
framework a model-independent analysis of the strong ESB mechanism can be performed. Our
ignorance of the full theory will be reected in our inability to calculate values of free param-
eters that appear in an effective Lagrangian. These free parameters parameterize all possible
new physics which respects the given low-energy theory. They will have to be obtained from
experiment.
In this approach, if energy available is below the threshold of new resonances production,
one starts with EW pions as the only particles in the spectrum which are subject to new strong
interactions. The Lagrangian of EW pions is the familiar nonlinear
6
-model based on global
symmetry breaking pattern is supported by the relation
<
=3 > ?
which is satised to
high accuracy.
If we assume to have enough energy to produce a new resonance it must be added to the
set of building elements of the effective Lagrangian. In our work beside the no-resonance case
we also assume the production of either the
%
-resonance or
-resonance. They are added to the
Lagrangian respecting chiral
% 7 ,8 2
#
9 % 7 ,8 2
:
symmetry. For
%
-resonance it is a straight-
approach [14]. The gauge interactions of the SM are introduced by requiring the
%
and
La-
grangians to be gauge invariant under
% 7 ,8 2# 9 7 ,
2@
.
Let us begin with the no-resonance Lagrangian. The
% 7 ,8 2# 9 7 ,
2@
gauged non-renorma-
lizable effective Lagrangian responsible for the low energy interactions of the EW pions is given
by
Tr
,F G 7 H F
G
7 2 I
(1)
where
7
NO 4 ,8P Q
R
C
2
with
GeV,
Q
is the isospin triplet of the EW pions, and
are the
% 7 ,8 2
group generators with the normalization Tr
,
R T R W
2
X
T W
8
.
2 TeV. Three cases, the no-resonance, the
2 No- ,
%
- and
-resonance models
spontaneously broken down to
% 7 ,8 2;
custodial or isospin symmetry. This
forward procedure, for
-resonance one can follow either Weinberg [13] or hidden symmetry
142
M. Gintner et al.
is the kinetic energy term of the
gauge elds,
, and the
gauge eld,
M G
. The covariant derivative
F G 7
is dened as follows
(2)
where
and
Z G
[ \ M G
R ]
.
In this model the interactions of EW pions with fermions are described by the following
Lagrangian
h.c.
2
R
]
(3)
where the
denotes fermion eld doublet,
,& i2
, the
b 1 c
is the baryon minus lepton number
operator, and the
diag
,j k j
W
2
is the fermion doublet mass matrix.
The gauged
%
-resonance model can be described by the following leading order effective
Lagrangian
Tr
,F G 7 H F
G
7 2% I
(4)
where
is given by (1), the
is the kinetic energy term of the
%
-resonance, the
%
denotes the scalar
,
2
resonance eld, the
l
is its mass. The
[ \\\
and
l
are free
parameters.
To include the interactions with fermions we have to add
h.c.
2
(5)
where
is a free parameter.
The gauged
-resonance model is given by
is given by (3), and
m
Tr
,o G o
G
2 I
(6)
where
is given by (1), the
is the kinetic energy term of the
-resonance, and
(7)
where
,
, and the
" G
[ \\ " G
R
denotes the vector
The fermionic part of the
-resonance model is described as follows
-resonance eld. The
U
and the
[ \\
are free parameters.
G
,
(8)
where the
i
5
,
i
D
are free parameters, and
r
diag
,
2
.
Resonances from strongly-interactingESB sector
143
This Lagrangian is
% 7 ,8 2# 9 7 ,
2@
gauge invariant. However, introduction of gauge elds
terms. The
custodial symmetry is also broken by the top-bottom quark mass splitting in the fermion mass
term. These two particular breakings of the custodial symmetry also occur in the SM. The third
custodial symmetry breaking originates in the projection matrix
r
in the coupling of the
to the
_
that got broken by the
right-handed bottom quark (to avoid constraints on the
couplings from the
ii
vertex), which
spoils the custodial symmetry in much the same fashion as does the top-bottom mass splitting.
The difference between our
-resonance Lagrangian and the BESS model of Ref. [15] is
is assumed to be universal for all fermion generations,
while here we assume coupling constants
i
5
i
D
and
i
5
to be specic (and possibly large) for the third
generation of quarks.
There are four new parameters in the
Lagrangian: couplings
U [ \\ i
5
i
D
. Since
n s
2.1 Constraints on the parameters of the
Lagrangian
the coupling
U
can be traded for the
mass. We do not have any experimental con-
(the theoretical expectation is that it should be around
1 V
TeV scale). We do,
however, have constraints on
[ \\
,
i
5
and
i
D
. These are due to the corrections that
[ \\
,
i
5
and
i
D
induce in the SM couplings of the
and the
to fermions at low energies (
t u
GeV) when the
-resonance is integrated-out from the particle spectrum. This leads to corrections to
v
param-
eters which conveniently parameterize new physics effects [16]. The BESS model studies [17]
have shown that
[ \\
corrects
v
]
by
X v
]
[
D
,
E
[ \\
D
2
, which implies for our model
(9)
parameters which are specic to our model.
We nd the low-energy couplings of the
and the
to fermions by taking
n s
and
i
D
the equation of motion for the
" G
eld (
Y
A n
Y " G
) has the solution
" G
1 ,
A
G I Z G 2
8
.
When we substitute this solution in the fermion Lagrangian in (8) and follow usual steps, we
eventually get for the low-energy
and
couplings to the top and bottom quarks
3
:
(10)
where
{ |
}
|
=3 > ?
>0. ?
, respectively. There is no modication of the
or
couplings
thus escapes the constraint from the
ii
coupling).
modies the
& i
,
&&
and
3
These couplings are also modied by the small terms
~
€ ‚‚€
which we neglect here for simplicity.
broke the original
chiral invariance, namely by the terms with the weak
hypercharge. More precisely, it is the custodial
. The
r
matrix ensures that the
only couples to the right-handed top quark but not to the
that in the BESS model
i
D
straints on
n s
We will now derive constraints on the
i
5
, which is
accomplished by
U $ x
while keeping
[ \\
xed, as in the BESS model studies [17]. In this limit
to leptons and the rst and second generation quarks. Note that
i
5
couplings, while
i
D
, due to the matrix
r
in the
" G
_
:
_
:
coupling in (8) modies only
&&
coupling (
i
D