Anarchy, Neutrinoless double beta decay and Leptogenesis

Xiaochuan Lu and Hitoshi Murayama

NuFact 2013, Aug 22nd

UC Berkeley

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• Anarchy approach applied to neutrino physics

Outline

• What is Anarchy Approach

Neutrinoless double beta decay

Leptogenesis

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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

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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!