Francis Ngouniba Ki Tezpur University,

India

Quasi-Degenerate Neutrinos and Leptogenesis

Ist IAS-CERN, NTU-SINGAPORE Jan 26, 2012

Specialized Knowledge Promotes Creativity

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Cosmology

Leptogenesis

Through

Through seesaw models

Btransitionsphaleron

L YY

Outline

I. Background +II. QDN III. Particle Cosmology

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I. Background-3 Thought Provoking Statements:

1. Neutrino Physics is all about neutrino mass ???2. Noble Prize in Neutrino Mass ???

3. Ironically, neutrino oscillations is not yet recognized by Noble Prize (evidence follows).

Talk Strategy: -Fast on Accepted Standard Conventions -Slow on Actual Works How Studied?-Lies between Experimental & Hard Core Theory. -Mathematical Manipulations & Assumptions .4

2002 Noble Prize in Physics"for pioneering contributions to

astrophysics, in particular for the detection of cosmic neutrinos" 

Masatoshi Koshiba and  Ray Davis Riccardo Giacconi (Comic X-rays source)

             

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NEUTRINO OSCILLATION ??Simple Pendulum

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Neutrino Oscillation(1957)

BRUNO PONTECORVO (Italy1913- Russia1993)

Half of his ashes is now buried in the Protestant Cemetery in Rome, and another half in Dubna, Russia, according to his will.

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We only know

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Journey of Neutrino1930-Pauli (neutron):[ 1934-Fermi-

neutrino] 58 Years Later1998-Kamioka Japan: Neutrino-Oscillations

Year ???- Noble Prize in Physics (Smile)???:

Absolute Neutrino Mass

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Journey of Neutrino

Neutrinos are Massive

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SINGARA, TAMULNADU, INDIA AIM: To Study Atmospheric Neutrinos and Measure a Precise Neutrino Mixing Parameters.

The absolute scale of masses, consequences:Addresses key issues in particle physics –hierarchical or degenerate neutrino mass spectrum –understanding the scale of new physics beyond SM, or a crucial datum for reconstructing PHYSICS Beyond SM –potential insight into origin of fermion massesImpacts cosmology and astrophysics –early universe, relic neutrinos (HDM), structure formation, anisotropies of CMBR –supernovae, origin of elements –potential influence on UHE cosmic rays. [0vbb Phys. Lett. B 586 (2004) 198]11

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Upper bound on absolute neutrino mass

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Direct measurements of neutrino mass

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WhatWhat

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Type of Neutrino ???

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18

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mass & mixing -oscillation experiments

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II. Quasi-Degenerate Oscillation QDN

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MOTIVATIONS

To study the Compatibility of Theoretical Calculations with Experimental data:

1. Absolute neutrino masses (m1,m2, m3). 2. 0 decay mass parameter mee . 3 3. Cosmological bound / sum ∑(mi )abs i

4. Solar mixing angle θ12 for different CP-phases

5. Leptons Charged Corrections effects on θ13 .

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MAJORANA PHASES IN MASSES

Majorana Phases:

i

i

e

eP

00

00

001

Diagonal mass matrix:

i

idiag

em

em

m

M2

3

22

1

00

00

00

25

NEUTRINO OSCILLATIONS AND MNS MIXING MATRIX:

3

2

1

321

321

321

UUU

UUU

UUU eeee

3,2,1;,,; iefU if

||

;0)(21

23

2231

21

22

2221

mmmm

mmmm

atm

sol

Two neutrino eigenstates: Flavour and mass eigenstates

Which may be greater or less than zero

(Neutrino mixing matrix is known as MNS mixing matrix due to Z. Maki, M. Nakagawa, S. Sakata)

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Types of Quasi-degenerate mass models

),,(:

),,(:

),,(:

321

321

321

mmmmC

mmmmB

mmmmA

i

i

i

We consider 3X3 mass matrices through parameterizations with two parameters in the present analysis.

By taking particular choice of phases:

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28

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Present status of neutrino mass, mixing and oscillation

←CHOOZ

Table-5:Best-fit values and allows nσ ranges for the global three flavor neutrino oscillation parameters, from Ref. [21].

parameters

∆m221

(10-5 eV2)

∆m223

(10-3 eV2)

tan2 θ12 Sin2 θ13

Sin2 θ23

Σ|mi| eV

|mee |

eV

Best-fit

7.67 2.39 0.312 0.016 0.466 ≤ 0.28

≤

0.27 1 σ2 σ3 σ

7.48-7.837.31-8.017.14-8.19

2.31-2.502.19-2.662.06-2.81

0.294-0.3310.278-0.3520.263-0.375

0.006-0.026<0.036<0.046

0.408-0.5390.366-0.6020.331-0.644

≤ 0.28≤ 0.28≤ 0.28

≤ 0.27

≤ 0.27≤ 0.27

{[21] G.L.Fogli et al, Phys Rev.D 78, 033010 (2008) [arXiv: 0805.2517 [hep-ph]}.

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νμ

Accelerator Detectorl = 730 km (MINOS) & 250 km (K2K)

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Recently the last one has gone down to 0.28 eV (PRL 105, 031301 (2010))34

To compute various parameters

To calculate m1 and m2

NH: α = , β = ,

Where = 7.60 x 10-3 eV2 and =2.40 x 10-5 eV2 [39].

m1 = m0 ; m2 = m0 ; = m0.

IH: α = - , β =+ ,where = 7.60 x 10-3 eV2 and = 2.40 x

10-5 eV2. m1 = m0 ; m2 = m0 ; =

m0.

{[39] T.Schwetz, M.Tortola.J.W.F.Valle, hep-hp/08082016;

M. C. Gonzales-et al, arXiv: 0812.3161.

G.L.Fogli et al, Phys Rev.D 78, 033010 (2008) }.

 

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Table1. The absolute neutrino masses in eV estimated from oscillation data [8](Using calculated value of β = 0.03166).

TABLE-1

II. For Calculation of ε and η the following Expressions were used.

For Type-IA (NH or IH):

m1 = (2ε - 2η) m0, m2 = (- ε -2η) m0, m3 = m0.

For Type – IB/IC (NH or IH):

m1 = (1-2ε -2η) m0, m2 = (1+ ε – 2η) m0, m3 = m0.

Where m1 and m2 are directly substituted from Tables A & B

corresponding to each case. Calculations is easy so we simply give the final calculations of ε and η in Tables 1 to 4.

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Parameters QD-NHType-IA Type-IB

QD-IHType-IA Type-IB

cdm3 (eV)

εη

1.01.00.100.579720.14602

1.01.00.100.00150.0649

1.00.100.080.780040.19628

1.00.100.080.00169-0.0855

m1 (eV)

m2 (eV)

m3 (eV)

Σ|mi| eV

0.08674-0.08720.100.273

0.086720.087170.100.273

0.09340-0.09380.080.267

0.093400.093800.080.267

Δm221 eV2

|Δm223 |eV2

tan2θ12

|mee| eV

7.6x10-5

2.4x10-3

0.500.0869

7.6x10-5

2.4x10-3

0.500.0869

7.6x10-5

2.4x10-3

0.500.0869

7.6x10-5

2.4x10-3

0.500.0869

Table-2: Predictions for tan2θ12 = 0.50 & other parameters consistent with observations.

Table-3: Predictions for tan2θ12 = 0.45 and other

parameters consistent with observational data.Parameters QD-NH

Type-IA Type-IB QD-IHType-IA Type-IB

cdm3 (eV)

εη

0.861.0250.100.66160.1655

0.9450.9980.100.001450.06483

0.8681.00.080.887620.22317

0.961.0020.080.00169-0.0855

m1 (eV)

m2 (eV)

m3 (eV)

Σ|mi| eV

0.08754-0.08790.09960.275

0.086760.087170.100020.274

0.09392-0.09430.080.268

0.093410.093810.080010.267

Δm221 eV2

|Δm223 |eV2

tan2θ12

|mee| eV

7.7x10-5

2.2 x10-3

0.450.0877

7.3x 10-5

2.4x 10-3

0.450.0869

7.6 x10-5

2.4x 10-3

0.450.0936

7.4x 10-5

2.4 x10-3

0.450.0935

CHARGED LEPTONS CORRECTIONSCHARGED LEPTONS CORRECTIONS

  =   Where =

[Ref [25]-Mohapatra et al Phys Lett B636 114 (2006)]

is same as in the case of mass matrix diagonalization without Charged Leptons Corrections.

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Cal VALUES CHARGED LEPTONS CORRECTIONS

Parameters

Normal Ordering

Inverted Ordering

NH-IA**

NH-IB**Type-

IAType-IB Type-IA Type-IB

cd

m3 (=mo ) eV

0.08631.00.080.887620.22317

0.9450.9980.100.00150.0648

0.8631.00.080.887620.22317

0.961.0020.080.0016917-0.085456

0.8631.00.400.66160.1655

1.01.00.10.00150.0649

tan2θ12

tan2θ23

Sinθ13

0.500.940.026

0.500.940.026

0.500.940.026

0.500.940.026

0.55**0.940.026

0.55**0.9450.0256

m1 (eV)m2 (eV)m3 (eV)Σ|mi| (eV)

∆m221 (10-5 eV2)

∆m223 (10-3 eV2)

0.0934533-0.09385810.080.07959

7.72.25

0.08675510.08718790.1000130.2739

7.32.39

0.0934533-0.09385810.080.267

7.62.39

0.09341390.0938140.08001370.2672

7.42.39

0.348958-0.3491180.401.098

7.62.39

0.086720.087170.100.27389

7.62.39

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Parameters

Without Charged Lepton Corrections. NH-IA

NH-IB IH-IA IH-IB NH-IA

tan2θ12

tan2θ23

Sinθ13

0.451.00.00

0.451.00.00

0.451.00.00

0.451.00.00

0.50*1.00.00

With Charged Lepton Corrections. tan2θ12

tan2θ23

Sinθ13

0.500.940.026

0.500.940.026

0.500.940.026

0.500.940.026

0.55*0.9450.026

Comparison

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III. Particle Cosmology

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The Early Universe Condition

Big Bang now

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The universe's timeline, from inflation to the WMAP.

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NOW

Neutrino Masses in Cosmology

Primordial Neutrino as Hot Dark Matter

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1. Thermal leptogenesis• See saw Mechanism• Majorana decays into two modes

• CP asymmetry is caused by interference of tree level and one loop correction for decays

of

TLRRRLRu mMmm

RN

LR lN Ll

)( 1 LlN )( 1 LlN

RN

Interference of Tree level and one loop correction

Lepton asymmetry for non-susy

2

2

2

22

3,2

)(Im1

8

1

i

j

i

jij

jiji M

Mg

M

Mfhh

hh

3

1

11

212

2

1

11

212

)(

)(Im

)(

)(Im

16

3

M

M

hh

hh

M

M

hh

hhi

1111

11 )Im(

)(16

3 hmhhh

MLL

…Eq(2)

..Eq(1)

R

hh

hh

11

212

1 )(

)(Im

8

1

21

22

222

21

21

22

22

)(

)(

MMM

MMMR

8

)( 2222

Mhh

For SUSY• For susy case

xxxf

11ln)(

1

2)(

x

xxg

xxgxf

3)()( When x is large

Btransitionsphaleron

L YY

LLBB

B CYCYS

Y

HF

HF

NN

NNC

1322

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nS 04.7

3

1i i

iiLLL gS

nnY

B-L Conserved and B+L violated

Baryon and Photon densities• Baryon number density over photon number

density corresponds to BAU by11

dn

nBB

1

211

1

)(~M

vhhm

GeVv 174

eVmeV 31

2 10~10 6.0

31

1

3

11 10

~log~

103.0)~(

m

mm

TABLE-4

TABLE-5

Table 5: Thermal Leptogenesis for all neutrino mass models with tan2 θ12 = 0.45.

2.Flavoured thermal leptogenesis• Flavoured effects in thermal Leptogenesis,

lepton asymmetry is

3,211

3,21

11 1

1)(Im)()(Im

)(

1

8

1

j jjjj

jjij x

hhhhxghhhhhh

j

jx

xg1

2

3)(

2

2

i

jj M

Mx

m

m eVM

Hvm 3

21

2

101.1~8

2

1

11 vM

hhm

Efficiency factor for the out-of-equilibrium

This leads to the Baryon Asymmetry of the Universe-BAU

• This leads to the BAU

m

mn

nBBB ~10~10 22

)()(Im)(8

1

8

1 2

111 jij xghh

hh

11212

1 10~10

m

mB

For single flavoured case

Leading to BAU

TABLE-6

3.Non-thermal Leptogenesis(NTL)

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Neutrino Mass Models validity

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TABLE-7

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Conclusion

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Future Challenge

1. Neutrino Physics: To Find a General Model or Method without parameterizations.

2. Particle Cosmology: CP violation in the leptogenesis/BAU.

In this direction we are working out earnestly.

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IAS, NTUSingapore

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