Transcript Bridges of Low-E observables with Leptogenesis in mu

Non-zero Ue3, TeV-Leptogenesis in
A4 Symmetry and LHC
Y.H.Ahn (Academia Sinica)
based on the on-going paper with Chian-Shu Chen
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Present Knowledges
Neutrino oscillation
(PRL101,141801)
Bi-Large mixing angles
theta13>0
Nothing is known about all three CP-vilating phases CP , 1 , 2
Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(JCAP10,104)
Starting to disfavor the degenerate spectrum of neutrinos
10
BAU B  6.2 10
About 20% of the Universe is
made up of cold dark matter.
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All data can be explained in terms of oscillation between just 3 known species
: Three possible orderings of neutrino masses
U PMNS
0
1

  0 c23
 0 s
23

0   c13

s23   0
c23    s13eiCP
0 s13e iCP   c12

1
0    s12
0
c13   0
s12
c12
0
0

0  P ;
1 
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1 for Dirac  s
P  
i1
i2
Diag.(e ,1,e ) for Mj. s
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Tri-Bimaximal
The current neutrino oscillation data are well described by so called “Tri-Bimaximal mixing”
matrix
(Harrison, Perkins and Scott;
see also Wolfenstein(1970) and He and Zee)
It is suggestive of a flavor symmetry.
It also suggests that flavor structure for mixing should be divorced from trying
to understand the mass eigenvalues.
Unless flavor symmetries are assumed, particle masses and mixings are generally
undetermined in gauge theory: To understand the present neutrino oscillation data we
consider A4 flavor symmetry.
(E.Ma and G.Rajarasekaran; G.Altarelly and F.Feruglio; X.G.He, Y.Y.Keum and R.Volkas)
For the existence of DM or LHC signal (?)(N.G.Deshpande, E.Ma) and the BAU to be
explained at or around TeV scale in radiative see-saw, we also introduce extra discrete
symmetry Z2 .
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A4
A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation
of four objects: its irreducible representations contain one triplet 3 and three singlets
1,1’,1” with the multiplication rules
3×3=3+3+1+1’+1” and
1’×1’=1”
Let’s denote two A4 triplets
and
where
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Construction of Lagrangian
Under SU(2)×U(1)×A4×Z2×Z4
Hence its Yukawa interaction in the lepton sector
Z2:
forbidden
after EW symmetry breaking
Z4: To prevent direct couplings of the right-handed neutrinos to
and
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and
,
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In the charged lepton sector:
Assumption: the VEVs of A4 triplets can be equally aligned, i.e,
“Tri-maximal”
Charged lepton mass matrix comes from
eigenvalues)
and has the form U(w)×Diag.(arbitrary
In the neutrino sector:
: unit matrix
No Leptogenesis and No CP-violation(
)
In the lagrangian level, assume that above a cutoff-scale Λ there is no CP-violation term in
the neutrino Yuawa interaction, which for scales below Λ is expressed in terms of 5-D
operator.
: off-diagonal matrix
The breaking scale of A4×Z4 is assumed to be lower than the cutoff scale Λ.
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Spontaneous Breaking of A4
Taking the scale of A4×Z4 symmetry breaking to be above EW scale,
And assuming the vacuum alignment,
and ,
Keeping
Right-handed Maj. mass term :
where
It will give rise to “Bi-maximal”
While, Neutrino Yukawa coupling matrices
CP-asymmetry≠0
Theta13 ≠0
where
CP-asymmetry=0
Theta13=0
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In a basis where both charged lepton and heavy Mj. Neutrino mass matrices are diagonal
where
“Bi-maximal”
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The couplings
with leptons and scalars
:
Concerned with CP violation, the CP phases
coming from
from
obviously take part in low-energy CP violation.
Leptogenesis is associated with both
matrix
with
which implies both CP-phases in
as well as the CP phase
itself and the combination of the Yukawa neutrino
and
take part in Leptogenesis.
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Radiative seesaw
Due to Z2 symmetry, we can not get the neutrino Dirac masses, and therefore the usual
seesaw does not operate any more:
The light neutrino mass matrix can be generated
through one-loop diagram with the quartic scalar
interactions
(E.Ma)
After EW symmetry breaking, i.e.
with
where
and
We assume
, so the lightest Z2 odd neutral particle of
candidate of DM or LHC signal:
is stable and can be a
with
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A very attractive feature of Seesaw ?
In addition to the explanation of neutrino masses, seesaw has another appearing feature socalled “Leptogenesis”
 nB
nB nNR  nL


  

 nL
s
s  nNR

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains
unbroken.
Choose at or around TeV scale
Flavor effects:

wash-out factor
3
5 10 y T  H
2
T2
for T  TEQ
M Pl
(PRD49,6394)
with
At TeV scale,
this will make a generated lepton asymmetry be strongly washed out .
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Light neutrino mass matrix
To prevent a produced CP-asymmetry from being strongly washed out at or around TeV scale,
we should consider the case
where
is the lightest of the heavy Mj.neutrinos.
hggkjhkjk
The light neutrino mass matrix can be obtained
where
In the limit of x→0,
this matrix can be diagonalized by TB mixing with the eigenvalues
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Mixing Angles
The mass eigenvalues can be roughly expressed as
The TB mixing angles are corrected by the parameters x and ø
For x=0 agrees with the results of TB
In order for
to be in the experimental bounds, the relation
should be satisfied; for
the size of x should be small.
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Mass orderings of light neutrino
Because of the observed hierarchy
, and the requirements of MSW
resonance for solar neutrinos, there are two possible neutrino mass ordering:
(1) Normal ordering (m1<m2<m3)↔
with
with
Degenerate light neutrino mass spectrum
very small x (or very small
)
(2) Inverted ordering (m3<m1<m2)↔
with
with
Degenerate light neutrino mass spectrum
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Overall scale of neutrino masses
Parameters κ(or a, b), x, φ can be determined by experimental data, whereas is arbitrary:
however, the value of
depends on the magnitude of in the case that
is determined
as
where
the value of
and
are used,
only depends on the size of
denotes
.
:
Dark matter :
The mass splitting
is controlled by
, which is stable against radiative corrections.
Opens the interesting possibility of explaining the DAMA annual modulation data;
is needed to realize DAMA (JHEP0907;090,2009)
could Not give a successful leptogenesis in our scenario.
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Can we extract the signal of η at the LHC ?
Production of scalar
pair at the LHC
In order for LHC signal to be briefly considered, we consider, with Z2×Z4 symmetry the most
general scalar potential of
invariant under SU(2)×U(1):
After EW sym. Breaking, the masses of the resulting scalar particles
where
is the mass of
and
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Scalar interactions: scalar
themselves
and
interact with Higgs boson h of the SM and among
Gauge interactions: Being electroweak doublet, they have gauge int. , but not directly
interact with SM fermions.
Assume
The dominant decay of
where f=SM fermion and
The dominant decay of
is into
through the gauge interaction,
is the missing energy.
is into
and
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through the gauge interaction,
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Leptogenesis
If LHC gives a signal,
then, a successful leptogenesis can be implemented in our scenario:
In the case of
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Conclusions
Hierarchical normal mass spectrum of light neutrino can give a large theta13 within
experimental bounds, on the other hand, degenerate case only gives very small theta13 less
than 2 degree.
Upcoming LBL, Reactor experiments and LHC signal of scalar η will give a test of our model.
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