anarchy, neutrinoless double beta decay and leptogenesis xiaochuan lu and hitoshi murayama nufact...
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Anarchy, Neutrinoless double beta decay and Leptogenesis
Xiaochuan Lu and Hitoshi Murayama
NuFact 2013, Aug 22nd
UC Berkeley
2
• Anarchy approach applied to neutrino physics
Outline
• What is Anarchy Approach
Neutrinoless double beta decay
Leptogenesis
3
A method to study the parameter space
What is Anarchy Approach?
( )a da• Dimensional analysis• Symmetries• Cuts
the next-layer model ?
explain predict
, , ,,( )ma known unknown
0a a
0 1a a a ò
0 1 22a a a a ò ò
Monarchy Anarchy
4
relax
constrain
Anarchy is a kind of Statistics
How to understand anarchy
Anarchical model
explain predict
, , ,,( )ma check consistency
distribution
correlation
expectation
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01. .
2
cDc L
L R TD R R
mh c
m m
L
Seesaw Mechanism, 3 generations
Neutrino Anarchy: model
Tm U DU
1 TD R Dm m m m
normal inverted
2 2 221 2 1m m m 2 2 232 3 2m m m Masses
1
2
3
e
U
Mixings
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known
213sin 2 0.095 0.010
223sin 2 0.95 (90% C.L.)
212sin 2 0.857 0.024
2 5 221 (7.50 0.20) 10m eV
2 0.12 3 232 0.082.32 10m eV
unknown
CP phase
232mSign of (mass hierarchy)
1mNeutrino mass scale
Other physical phases 1 2,
Neutrinoless double beta decay ffem
Leptogenesis 0B
Ddmdistribution (measure)
Rdm
Neutrino Anarchy: parameters
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Dm
A tempting choice: Entry Independence
What measure to choose?,D Rdm dm
Rm
A second thought: Basis Independence
generated independently
Each free entry is
0
0
L L L
R R R
U
U
†0 0D D L D Rm m U m U
*0R R Rm m U †
0R Rm UD D
R R
dm dm
dm dm
0 0,L RU U
No distinction among three generations
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Basis Independence
1 3 2 8 1 3 2 8
13 13 12 12
23 23 12 12
23 23 13 13
1 0 0 0 0
0 0 1 0 0
0 0 0 0 1
i
i i i ii
i
c s e c s
U e e c s s c e
s c s e c
Haar measure1U Haar measureU
2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d d Haar measure
1 2 0D
R R R
dm dU dU dD
dm dU dD
Factorize
1 2, , RdU dU dUHaar measure
RRU UUinvariantRdU
†1 0 2unitD
unitM
D
TR R R R
m U DU
m U D U
Parameterization
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23
1213
completelyconsistent
212 23 13sin 2 , , ,x
1( )
2 1x
x
Distribution of mixing angles
2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d d
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siny
2
1( )
1y
y
Distribution of phases
2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d d uniform distribution
2 2213 2312
12 12 23 132
23 1316 s sin sin sin4 4 4
ine e
m L m Lm LP P c
E Es
Es c s c
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Entry Independence
†1 0 2unitD
unitM
D
TR R R R
m U DU
m U D U
Parameterization
Basis Independence01 2, , , ,R RU U D U D independent
Haar measure1 2, , RdU dU dU
Entry Independence Each free entry Gaussian measure
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Mass splits and mass hierarchy
The Cuts5
3
223
212
213
7.59 10(1 0.05)
2.32 10
sin 2 1.0
sin 2 0.861
sin 2 0.092
R
Normal Hierarchy Scenariowithout cut 95.9%
with cut 99.9%
exp
1
30R
completelyconsistent
2
2s
l
Rm
m
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Neutrinoless double beta decay
lepton number violation2L
imi
i
,eiU
,eiU
light-neutrino mass matrix is Majoranam
1 TD R Dm m m m
Anarchy prediction:
2eff
20 eff ,, ei i
i
m U mm
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experimentally challenging
without cutseff 0.05m eV
with cutseff 0.01m eV
Neutrinoless double beta decay
2 3 232
unitD 30
unitM 2.5 10
GeV
m eV
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Leptogenesis
Baryon asymmetry today100
0 6 10BB
n
n
CP violation,R Dm m complex
0L
0B L
0.35( )B B L
1 1N l N l
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,D Rm m
light-neutrino parameters
0Bleptogenesis
Correlation?
light-neutrino masses and mixings favor leptogenesis
Apply the Cuts
Correlations
100 6 10B
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Correlations
has no correlation with light-neutrino mixings0B U
has no correlations with 13 23 112 2, , , , or 0B
could have correlations with and thus eff,R m0B D
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scatter plots:
Correlations
has a weak negative correlation with and0B R effm
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CP phase and 1 2, uniform, maximal CP violation
232mSign of 99.9% normal hierarchy
213sin 2 0.095 0.010
223sin 2 0.95 (90% C.L.)
212sin 2 0.857 0.024
2 5 221 (7.50 0.20) 10m eV 2 0.12 3 232 0.082.32 10m eV
Completely Consistent
Summary
0B
very challenging to experimental sensitivity effm
on the correct order of magnitude
weak negative correlations with and effmR
no correlations with 13 23 112 2, , , , or
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Thank you!