Diapositiva 1

1
PHENOMENOLOGY OF A THREE-FAMILY MODEL WITH GAUGE
SYMMETRY
Villada Gil, Stiven svillad_at_unalmed.edu.co
Sánchez Duque, Luis Alberto lasanche_at_unalmed.edu.c
o Theoretical Physics Group, School of Physics,
National University of Colombia
An extension of the Standard Model to the gauge
group SU(3)C ? SU(4)L ? U(1)X as a three-family
model is presented. The model does not contain
exotic electric charges and anomaly cancellation
is achieved with a family of quarks transforming
differently from the other two, thus leading to
FCNC. By introducing a discrete Z2 symmetry we
obtain a consistent fermion mass spectrum, and
avoid unitarity violation of the CKM mixing
matrix arising from the mixing of ordinary and
exotic quarks. The neutral currents coupled to
all neutral vector bosons are studied, and by
using CERN LEP and SLAC Linear Collider data at
Z-pole and APV data, we bound the relevant
parameters of the model. These parameters are
further constrained by using experimental input
from neutral meson mixing in the analysis of
sources of FCNC present in the model.
INTRODUCTION
One intriguing puzzle completely unanswered in
modern particle physics concerns the number of
fermion families in nature. The SU(3)C ? SU(4)L ?
U(1)X extension (3-4-1 for short) of the gauge
symmetry SU(3)C ? SU(2)L ? U(1)Y of the standard
model (SM) provides an interesting attempt to
answer the question of family replication, in the
sense that anomaly cancellation is achieved when
Nf Nc 3, Nc being the number of colors of
SU(3)c . A systematic study of possible
extensions for three-family anomaly free models,
based on the gauge group 3-4-1, was carried out
by our group in reference 1, leading to
different models. Three of them have been studied
in reference 2 and the other one has not been
yet analyzed in the literature and will be
presented in a paper, which is the base for this
poster.
The couplings between the flavor diagonal mass
eigenstates .. and , and the
fermion fields are obtained from
FERMION CONTENT
The expresions for giV and giA with i 1,2 are
listed in Tables 2 and 3, where
Bounds on MZ3 from FCNC processes
where i1,2 and a1,2,3 are generation indexes.
From current we can see that the
couplings of Z to the third family of quarks
are different from the ones to the first two
families. This induces FCNC at tree level
transmitted by the Z boson. The flavor changing
interaction can be written, for ordinary up- and
down-type quarks in the weak basis, as
SCALARS
To avoid unnecessary mixing in the electroweak
gauge boson sector and to give masses for all the
fermion fields (except for the neutral leptons),
we introduce the following four Higgs scalars and
its vacuum expectation values (VEV)
This Lagrangian produces the following efective
Hamiltonian for the tree-level neutral meson
mixing interactions
Note that in the limit the couplings of
to the ordinary quarks and leptons are the
same in the SM. This allows us to test the new
physics beyond the SM predicted by this
particular model.
where (a,ß) must be replaced by (d,s), (d,b),
(s,b) and (u,c) for the
and systems,
respectively, and VL must be replaced by UL for
the neutral system.
This set of scalars break the symmetry in three
steps
FERMION SPECTRUM
Mixing between ordinary and exotic fermions and
violation of unitarity of the Cabibbo-Kobayashi-Ma
skawa (CKM) mixing matrix is avoided by
introducing a discrete Z2 symmetry with
assignments of Z2 charge qz given by
The effective Hamiltonian gives the following
contribution to the mass differences ?mK, ?mB and
?mD
When the 3-4-1 symmetry is broken to the SM, we
get the gauge matching conditions
and
After the symmetry breaking, the Yukawa couplings
allowed by the gauge invariance and the Z2
symmetry produces for up- and down-type quarks,
in the basis (u1,u2,u3,U1,U2,U3) and (d1,d2,d3,
D1,D2,D3) respectively, block diagonal mass
matrices of the form
where g and g are the gauge coupling constants
of the SU(2)L and U(1)Y gauge groups of the SM
respectively, and g4 and gX are associated with
the groups SU(4)L and U(1)X respectively.
where B stands for Bd or Bs. Bm and fm (m
K,Bd,Bs,D) are the bag parameter and decay
constant of the corresponding neutral meson. The
?'s are QCD correction factors which, at leading
order, can be taken equal to the ones of the SM,
that is
9.
GAUGE BOSONS
For our purposes, we will be mainly interested in
the neutral gauge boson sector which consists of
four physical fields the massless photon
and the massive gauge bosons and
. In terms of the electroweak basis, they
are given by
Similary for the charged leptons, in the basis
(e1,e2,e3,E1, E2,E3), we find the following
block diagonal mass matrix
Because there are various sources that may
contribute to the mass differences, it is
impossible to disentangle the Z3 contribution
from the other effects. Due to this, several
authors consider reasonable to assume that the Z3
exchange contribution must not be larger than the
experimental values 10.
These three mass matrices show that all the
charged fermions in the model acquire masses at
the three level.
Bounds on MZ2 and ? from Z-pole observables and
APV data
To get bounds on the parameter space (?-MZ2) we
use experimental parameters measured at the
Z-pole from CERN ee- collider (LEP), SLAC
Linear Collider (SLC), and atomic parity
violation data which are given in Table 4.
Since the complex numbers VLij and ULij can not
be estimated from the present experimental, we
assume the Fritzsch ansatz for the quark mass
matrices 11, which implies (for ij)
, and similary for UL .
where
is the field to be identified as the Y
hypercharge associated with the SM abelian gauge
boson.
To obtain bounds on MZ3, we use updated
experimental and theoretical values for the input
parameters as shown in Table 5, where the quark
masses are given at Z-pole. The results are
For convenience we choose V V and v v,
for which the current decouples from
the other two and acquires a squared mass
. The remaining mixing
between and is parametrized
by the mixing angle ? as
This shows that the strongest constraint comes
from the d system, which puts
on MZ3 the lower bound 6.65 TeV.
where and are the mass eigenstates and
NEUTRAL CURRENTS
The partial decay width for is
given by 4,5
The neutral currents are given by
where f is an ordinary SM fermion, is the
physical gauge boson observed at LEP.
The prediction of the SM for the value of the
nuclear weak charge QW in Cesium atom is given
by 6
CONCLUSIONS
?QW, which includes the contribution of new
physics, can be written as 7
This model has the particular feature that,
notwithstanding two families of quarks transform
differently under the SU(4)L group, the three
families have the same hypercharge X with respect
to the U(1)X group. Therefore, the couplings of
the fermion fields to the neutral currents Z1 and
Z2 are family universal. Thus, the allowed region
in the parameter space (? - MZ2) is MZ2 gt0.89
TeV and -0.00039 ? 0.00139. Additionally,
FCNC present for this Model in the left-handed
couplings of ordinary quarks to the Z3 gauge
boson allows us to conclude that the
strongest constraint on MZ3 comes from the
system and turns to be MZ3
gt 6.65 TeV. These values show that the 3-4-1
model studied here could be tested at the LHC
facility.
The term is model dependent. In
particular, is a function of the couplings g(q)2V
and g(q)2A (qu,d) of the first family of quarks
to the new neutral gauge boson Z2. So, the new
physics in depends on which family of
quarks transform dierently under the gauge group.
Taking the third generation being diferent the
value we obtain is
where the left-handed currents are
REFERENCES
which is 1.1s away from the SM predictions.
The diference between the experimental value and
that predicted by the SM for ?QW is given by 6
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Introducing the expressions for Z-pole
observables in the partial decay width for ,
with ?QW in terms of new physics and using
experimental data from Table 4, we do fit
and find the best allowed region in the (?-MZ2)
plane at 95 condence level. In Fig. 1 we display
this region which gives us the constraints
where is the third
component of the weak isospin,
and
are convenient 4x4 diagonal matrices, acting
both of them on the representation 4 of SU(4)L.
The current is clearly recognized as
the generalization of the neutral current of the
SM. This allows us identify as the neutral
gauge boson of the SM.
As we can see the mass of the new neutral gauge
boson is compatible with the bound obtained in
collisions at the Fermilab Tevatron 8.