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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

Cosmological limit (including WMAP 3-years result) upper bound on neutrino masses (JCAP10,104) Starting to disfavor the degenerate spectrum of neutrinos

BAU

About 20% of the Universe is made up of cold dark matter.

1 2, , CP

106.2 10B

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All data can be explained in terms of oscillation between just 3 known species : Three possible orderings of neutrino masses

1 2

13 13 12 12

23 23 12 12

23 23 13 13

1 0 0 0 01 for Dirac s

0 0 1 0 0 ; Diag.( ,1, ) for Mj. s

0 0 0 0 1

CP

CP

i

PMNS i ii

c s e c sU c s s c P P

e es c s e c

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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

6

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 , 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 and has the form U(w)×Diag.(arbitrary eigenvalues)

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 as well as the CP phase from obviously take part in low-energy CP violation.

Leptogenesis is associated with both itself and the combination of the Yukawa neutrino matrix

with which implies both CP-phases in 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 generatedthrough one-loop diagram with the quartic scalarinteractions (E.Ma)

After EW symmetry breaking, i.e.

with

where and

We assume , so the lightest Z2 odd neutral particle of is stable and can be a candidate of DM or LHC signal:

with

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A very attractive feature of Seesaw ? In addition to the explanation of neutrino masses, seesaw has another appearing feature so-

called “Leptogenesis”

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: (PRD49,6394)

wash-out factor with

At TeV scale, this will make a generated lepton asymmetry be strongly washed out .

R

R

NB L B

N L

nn n ns s n n

23 2

EQPl

5 10 for Ty T H T TM

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Light neutrino mass matrixTo 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.

hggkjhkjkThe 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 and are used, denotes . the value of only depends on the size of :

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 and interact with Higgs boson h of the SM and among

themselves

Gauge interactions: Being electroweak doublet, they have gauge int. , but not directly interact with SM fermions.

Assume The dominant decay of is into through the gauge interaction,

where f=SM fermion and is the missing energy.

The dominant decay of is into and 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.