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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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2
Cosmology
Leptogenesis
Through
Through seesaw models
Btransitionsphaleron
L YY
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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
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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.
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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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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
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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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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
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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
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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.
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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
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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
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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
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Interference of Tree level and one loop correction
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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)
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R
hh
hh
11
212
1 )(
)(Im
8
1
21
22
222
21
21
22
22
)(
)(
MMM
MMMR
8
)( 2222
Mhh
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For SUSY• For susy case
xxxf
11ln)(
1
2)(
x
xxg
xxgxf
3)()( When x is large
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Btransitionsphaleron
L YY
LLBB
B CYCYS
Y
HF
HF
NN
NNC
1322
48
nS 04.7
3
1i i
iiLLL gS
nnY
B-L Conserved and B+L violated
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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
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TABLE-4
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TABLE-5
Table 5: Thermal Leptogenesis for all neutrino mass models with tan2 θ12 = 0.45.
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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
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• 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
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TABLE-6
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3.Non-thermal Leptogenesis(NTL)
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60
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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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