Lepton number violations in the economical 331 model

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Lepton number violations in the economical 3-3-1
model
(E331)
Hoang Ngoc Long
Phys. Rev. D (2006) 73, 035004, 075005 74,
053003, Phys. Lett. B 639, 527 (2006)
hep-ph/0610381

• YongPyong Astro Particle CPV 21 -24/02/07

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• I. Motivation
• .Problem of fermion generation number,
• .why top quark is uncharacteristically heavy
• Previous SU(3) X SU(3) X U(1)
• (3-3-1) Models
• .Minimal Pisano Pleitez (Phys. Rev. D 46, 410
  (1992), Frampton (Phys. Rev. Lett, 69, 2889
  (1992)
• The Higgs sector contains 3 triplets one sextet

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Minimal 3-3-1 Model
Particle content
There are RH quark singlets, q_T 5/3, q_D -4/3
Electric charge operator

• No exotic lepton
• The Weinberg mixing angle s2_w lt ¼
• Require Higgs three triplets and one sextet

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3-3-1 Model with Right-Handed Neutrinos
Particle content
e_R
Electric charge operator
Foot, Tran H. N. L PR D 50, R34 (1994)

• There are 2 triplets with the same quantum
  numbers

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Yukawa couplings
These couplings give exotic quarks masses
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Yukawa couplings
VEVs of
give masses for all ordinary fermions
These couplings posses new conserved charge
Applying to lepton triplet we get
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Another conserved charge is
(D. Chang H. N. L, PRD 73, 053006 (2006)
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• Model with right-handed neutrinos
• The Higgs sector contains 3 triplets
• General Higgs potential is very complicate 20
  parameters

where
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Proposal of Economical 3-3-1 Model

• Two Higgs triplets of the 3-3-1 model with RH
  neutrinos

• The 3-3-1 model with two Higgs triplets
• (Economical 3-3-1 model)

P.V. Dong, D.T.N, D.V.Soa H. N. L PRD
73,035004 (2006)
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Gauge Bosons
Covariant derivative of a triplet
Adjoint SU(3)_L X U(1)_X representations
Combinations
X and Y are bilepton (L2)
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Gauge boson mass Lagrangian
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W-Y Mixing
Physical gauge bosons, the SM W and the new Y
Masses for the W and Y bosons
The SM weak scale for the VEV v
This mixing happens In L-R symmetric model
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Z-Z-X Mixing
The imaginary part of X boson is decoupled
whereas, Its real part as well as Z, Z bosons
are mixing
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Identification (masses of the real and imaginary
parts are equal)
The law of Pythagoras
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Higgs Potential
(only 6 parameters)

• The most general Higgs potential has very simple
  form

• Potential minimum condition, u-\omega
  degeneration

P. V. Dong,D. V. Soa H. N. L.Phys.Rev. D 73,
075005 (2006)

• Higgs and Goldstone bosons

• There are 4 physical Higgs bosons, two neutral
  and other two charged
• One of the neutral Higgs scalars is the SM-Higgs
  boson, h
• 8 Goldstone bosons are eaten by 8 massive gauge
  bosons

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and
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Higgs content

• Full content of scalar sector is recognized

Majoron

• G_1 is decoupled whereas, G_4 has the mixing in
  the same way in the gauge boson sector

• G_X is also a majoron field for Majorana masses

• Higgs bosons h, H0_1 do not carry lepton-number

• H,-_2 is bilepton and mainly coupled to WZ to
  be searched at LHC

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Yukawa couplings
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Lepton and baryon numbers in E331
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Charged Currents
New terms (LNV) exist in the charged currents
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New interactions are lepton-number violating and
weak

• New couplings are proportional to sin(\theta) or
  its square sin2(\theta)

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Neutral Currents

• Unnormal terms exist in the neutral currents

• Electromagnetic currents

• Weak neutral currents

• Lepton number violating interactions mediated by
  Z, Z bosons

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Bound on the masses of the exotic gauge bosons

• Wrong muon decay

- Lower limit for M_Y

• Parity violation in the 133 isotope of Cesium atom

- Lower limit for M_Z, and Upper one for the
Z-Z mixing angle
- Typical values for M_Z and the Z-Z mixing
angle
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Phenomenology

• Lepton family number violating processes

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Lepton number violating processes
Feynman diagram for lepton number violating decay
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Lepton number violating kaon decay
The above process in our model is mediated by SM
W and Y bosons!
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• Neutrino mass and LFV in E331

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One loop diagram for muon to electron gamma
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We have a constraint
Similarly
for
and
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• Leptogenesis in E331

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Diagrams contributing to leptogenesis in E331
model
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• Summary
• E331 model has the following advantages
• - Number of free parameters is significantly
  reduced
• - Very rich neutrino physics and phenomenology in
  exotic quark sectors
• - There is lepton family number violation
• - There is lepton number violation

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Fermion Masses
The fermions gain masses via Yukawa interactions
P.V. Dong, D. T.Huong H. N. L. PRD
74,053003 (2006)

• The VEV \omega gives mass for exotic quarks U,
  D_2 and D_3
• The VEV u gives mass for u, s and b quarks
• The VEV v gives mass for d, c and t quarks and
  all ordinary leptons
• The VEVs have to be satisfied by the constraints

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Leptons get masses as in the SM
Neutrino Dirac mass matrix is antisymmetric gt
one massless and two degenerate
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1. Up-quark masses
One quark is massless
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2. Down-quark masses
Two quarks are massless
Radiative correction is needed
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One-loop correction to up-quark mass matrix
This diagram gives contribution
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where

Diagonalization yields
and leads to the numerical evaluation
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One-loop radiative corrections to down-quark mass
matrix
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where
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Numerical evaluation gives
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Conclusion In the economical model, all fermions
get correct masses, while significant number of
free parameters is reduced.
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Neutrino mass in the economical version
(hep-ph/0610381)
At the tree level
where
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and
where
Mass eigenvalues
There are three operators
Note that in the version with RH neutrinos, there
are 3 (Chang Long 2006)
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• Quantum corrections will have a form

Diagrams for one-loop correction to
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Matrix elements are given
We suppose that Yukawa coupling h_ab is flavor
diagonal
where
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• In the effective limit

We have
This means that
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• Hence we get

For right-handed part
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We see that
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• Finally we get

where
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• Taking

we get
Remark
due to

• LH RH neutrinos in the same lepton triplets
• VEV u and \omega are in one triplet \chi. This
  does not happen in RH version.

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• This implies that

Note that maximal mixing requires M_D gtgt M_L,M_R
or
Since
has one vanishing eigenvalue. Hence
Does not posses the pseudo-Dirac property in all
three generations.
This matrix contains combined seesaw and
pseudo-Dirac scenario!
Suppose that
Is real. Hence
We diagonalize M_D by biunitary transformation
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• where

is diagonalized by unitary
Hence, in the case M_LM_R0,
transformation
Neutrino mass matrix becomes
In new basis
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see Kobayashi Lim (2001)
where
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• Change position

where
then
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Remarks - off-diagonal elements are much smaller
than
-degenerate values 0, -m_d, m_d (twice) are now
splitting to six ones
The above matrix is effectively decomposed into a
pair of light neutrinos \nu_s and two pairs of
heavy pseudo-Dirac \nu_P.
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which diagonalizes
Here
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• and

The above matrices have exact solutions
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• Mixing matrix

Evaluation
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• We see that above mass matrix is not realistic

This calls for radiative correction of
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or
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• In effective limit, we get

or
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• If we take

Then, there are two cases
-
This case as before
-
Interesting one!
In this case we have
This matrix is nonantisymmetric in a and b
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• All three eigenvalues are nonzero!

Taking
we get
and
This means that
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• Remaining questions

Answer is new physics
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• where

This corresponds to
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• Let us take

then
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• Conclusions
• The economical 3-3-1 model has the following
  advantages
• igt Significant number of free parameters reduced
• iigtModel gives all fermions correct masses
• iiigtVery rich neutrino physics

Model deserves further study.
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Thank you for your attention
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Masses of particles
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