Transcript Diapositiva 1

PHENOMENOLOGY OF A THREE-FAMILY MODEL WITH GAUGE SYMMETRY
SU(3) C  SU(4) L  U (1) X
Villada Gil, Stiven [email protected]
Sánchez Duque, Luis Alberto [email protected]
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.
FERMION CONTENT
The couplings between the flavor diagonal mass eigenstates ..
and
, and the fermion fields are obtained from
The expresions for giV and giA with i = 1,2 are listed in Tables 2 and
3, where:
Bounds on MZ3 from FCNC processes
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
where i=1,2 and α=1,2,3 are generation indexes.
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 set of scalars break the symmetry in three steps:
When the 3-4-1 symmetry is broken to the SM, we get the gauge
matching conditions:
and
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.
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.
This Lagrangian produces the following efective Hamiltonian for
the tree-level neutral meson mixing interactions
FERMION SPECTRUM
where (α,β) 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.
The effective Hamiltonian gives the following contribution to the
mass differences ΔmK, ΔmB and ΔmD:
Mixing between ordinary and exotic fermions and violation of
unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix
is avoided by introducing a discrete Z2 symmetry with assignments
of Z2 charge qz given by:
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
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
These three mass matrices show that all the charged fermions in
the model acquire masses at the three level.
where:
is the field to be identified as the Y hypercharge associated with
the SM abelian gauge boson.
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 θ as:
where
and
Bounds on MZ2 and θ from Z-pole observables and APV data
To get bounds on the parameter space (θ-MZ2) we use
experimental parameters measured at the Z-pole from CERN e+ecollider (LEP), SLAC Linear Collider (SLC), and atomic parity
violation data which are given in Table 4.
This shows that the strongest constraint comes from the
system, which puts on MZ3 the lower bound 6.65 TeV.
are the mass eigenstates and
NEUTRAL CURRENTS
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 η's are QCD correction factors which, at leading order,
can be taken equal to the ones of the SM, that is:
[9].
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].
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 i≤j)
, and
similary for UL .
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
The partial decay width for
d
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]
ΔQW, which includes the contribution of new physics, can be written
as [7]:
where the left-handed currents are:
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.
The term
is model dependent. In particular, is a function of
the couplings g(q)2V and g(q)2A (q=u,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
which is 1.1σ away from the SM predictions.
The diference between the experimental value and that predicted
by the SM for ΔQW is given by [6]:
Introducing the expressions for Z-pole observables in the partial
decay width for , with ΔQW in terms of new physics and using
experimental data from Table 4, we do
fit and find the best
allowed region in the (θ-MZ2) plane at 95% condence level. In Fig.
1 we display this region which gives us the constraints
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].
CONCLUSIONS
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 (θ − MZ2) is: MZ2
>0.89 TeV and −0.00039 ≤ θ ≤ 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 > 6.65 TeV. These values show that the
3-4-1 model studied here could be tested at the LHC facility.
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