anarchy, neutrinoless double beta decay and...

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

A method to study the parameter space

What is Anarchy Approach?

3

the next-layer model ?

explain predict

, , ,,( )ma λ θ α δ=known unknown



4


explain predict


0a a=

0 1a a a= +

0 1 22a a a a= + + +



5


explain predict


0a a=

0 1a a a= +

0 1 22a a a a= + + +

Monarchy



6

( )a daρ• Dimensional analysis • Symmetries • Cuts


explain predict


0a a=

0 1a a a= +

0 1 22a a a a= + + +

Monarchy



7

( )a daρ• Dimensional analysis • Symmetries • Cuts


explain predict


0a a=

0 1a a a= +

0 1 22a a a a= + + +

Monarchy Anarchy

relax

constrain

Anarchy is a kind of Statistics

How to understand anarchy

8 Anarchical model

explain predict

, , ,,( )ma λ θ α δ=

relax

constrain



9 Anarchical model

explain predict

, , ,,( )ma λ θ α δ=check consistency

relax

constrain



10 Anarchical model

explain predict


distribution

relax

constrain



11 Anarchical model

explain predict


distribution

expectation

relax

constrain



12 Anarchical model

explain predict


distribution

correlation

expectation

13

( ) 01 . .2

cDc L

L R TD R R

mh c

m mν

ν νν

⊃ − +

Seesaw Mechanism, 3 generations

Neutrino Anarchy: model

Tm U D Uν ν ν ν=

1 TD R Dm m m mν

−=

14

( ) 01 . .2

cDc L

L R TD R R

mh c

m mν

ν νν

⊃ − +




1 TD R Dm m m mν

−=normal inverted

2 2 221 2 1m m m∆ ≡ −2 2 232 3 2m m m∆ ≡ −Masses

15

( ) 01 . .2

cDc L

L R TD R R

mh c

m mν

ν νν

⊃ − +




1 TD R Dm m m mν

−=normal inverted

2 2 221 2 1m m m∆ ≡ −2 2 232 3 2m m m∆ ≡ −Masses

1

2

3

e

Uνµ

τ

ν νν νν ν

=

Mixings

known

213sin 2 0.095 0.010θ = ±

223sin 2 0.95 (90% C.L.)θ >

212sin 2 0.857 0.024θ ±=

2 5 221 (7.50 0.20) 10m eV−∆ = ± ×

2 0.12 3 232 0.082.32 10m eV+ −

−∆ = ×

unknown

δCP phase

232m∆Sign of (mass hierarchy)

1mNeutrino mass scale

Other physical phases 1χ 2χ,

Neutrinoless double beta decay ffemLeptogenesis 0Bη

Neutrino Anarchy: parameters

16

known

213sin 2 0.095 0.010θ = ±

223sin 2 0.95 (90% C.L.)θ >

212sin 2 0.857 0.024θ ±=

2 5 221 (7.50 0.20) 10m eV−∆ = ± ×

2 0.12 3 232 0.082.32 10m eV+ −

−∆ = ×

unknown

δCP phase

232m∆Sign of (mass hierarchy)

1mNeutrino mass scale

Other physical phases 1χ 2χ,

Neutrinoless double beta decay ffemLeptogenesis 0Bη

Ddmdistribution (measure)

Rdm

Neutrino Anarchy: parameters

17

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗

A tempting choice: Entry Independence

What measure to choose? ,D Rdm dm

Rm∗ ∗ ∗ = ∗ ∗ ∗

generated independently

Each free entry ∗ is

18

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗



Rm∗ ∗ ∗ = ∗ ∗ ∗

A second thought: Basis Independence



19

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗



Rm∗ ∗ ∗ = ∗ ∗ ∗




No distinction among three generations

20

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗



Rm∗ ∗ ∗ = ∗ ∗ ∗




0

0

L L L

R R R

UU

ν νν ν′ =′ =


21

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗



Rm∗ ∗ ∗ = ∗ ∗ ∗




0

0

L L L

R R R

UU

ν νν ν′ =′ =

†0 0D D L D Rm m U m U′→ =

*0R R Rm m U′→ = †

0R Rm U


22

Dm∗ ∗ ∗ = ∗ ∗ ∗ ∗ ∗ ∗



Rm∗ ∗ ∗ = ∗ ∗ ∗




0

0

L L L

R R R

UU

ν νν ν′ =′ =

†0 0D D L D Rm m U m U′→ =

*0R R Rm m U′→ = †

0R Rm UD D

R R

dm dmdm dm

′ =′ = 0 0,L RU U∀


23

Basis Independence

24

1 2 0D

R R R

dm dU dU dDdm dU dD

==

Factorize

1 2, , RdU dU dUHaar measure

RRU UU→invariant RdU

†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization

Basis Independence

Haar measure 1U Haar measure Uν

25

1 2 0D

R R R

dm dU dU dDdm dU dD

==

Factorize



†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization

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 00 0 1 0 00 0 0 0 1

i

i i i ii

i

c s e c sU e e c s s c e

s c s e c

δ

φ λ φ λ χ λ χ λη

δν

−

+ +

= −

− −


26

1 2 0D

R R R

dm dU dU dDdm dU dD

==

Factorize



†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization

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 00 0 1 0 00 0 0 0 1

i

i i i ii

i

c s e c sU e e c s s c e

s c s e c

δ

φ λ φ λ χ λ χ λη

δν

−

+ +

= −

− −


2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d dν δ χ χ η φ φ= ⋅ ⋅ Haar measure

27

1 2 0D

R R R

dm dU dU dDdm dU dD

==

Factorize



†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization

28

23θ

12θ13θ

completely consistent

{ }212 23 13sin 2 , , ,x θ θ θ θ θ= ∈

1( )2 1

xx

ρ =−

Distribution of mixing angles

2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d dν δ χ χ η φ φ= ⋅ ⋅

siny δ=

2

1( )1

yyπ

ρ =−

29

Distribution of phases

2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d dν δ χ χ η φ φ= ⋅ ⋅ uniform distribution

siny δ=

2

1( )1

yyπ

ρ =−

30

Distribution of phases

2 4 223 13 12 1 2 1 2dU ds dc ds d d d d d dν δ χ χ η φ φ= ⋅ ⋅ uniform distribution

2 2213 2312

12 12 23 132

23 1316 s sin sin sin4 4 4

ine em L m Lm LP P c

E Es

Es c s cµ µ δ ∆ ∆∆

− = −

31

Entry Independence

†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization

Basis Independence 01 2, , , ,R RU U D U D independent

Haar measure 1 2, , RdU dU dU

32

Entry Independence

†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization



Entry Independence

33

Entry Independence

†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization



Entry Independence

34

Entry Independence

†1 0 2unitD

unitMD

TR R R R

m U D Um U D U

= ⋅

= ⋅

Parameterization



Entry Independence Each free entry Gaussian measure

35

Mass splits and mass hierarchy

exp130

R ≈


2

2s

l

R mm

∆≡∆

36


The Cuts 5

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

θ

θ

θ

−

−

×∈ × ±

×=

=

=

exp130

R ≈


2

2s

l

R mm

∆≡∆

37


The Cuts 5

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

θ

θ

θ

−

−

×∈ × ±

×=

=

=

Normal Hierarchy Scenario without cut 95.9%

with cut 99.9%

exp130

R ≈


2

2s

l

R mm

∆≡∆


lepton number violation 2L∆ =

imiν

iν

,eiUν

,eiUν

light-neutrino mass matrix is Majorana mν

1 TD R Dm m m mν

−=Anarchy prediction:

38



imiν

iν

,eiUν

,eiUν


1 TD R Dm m m mν


39



imiν

iν

,eiUν

,eiUν


1 TD R Dm m m mν


2eff

20 eff ,, ei i

im U mmνβ νβ =Γ ∝ ∑

40

41


2 3 232

unitD 30

unitM 2.5 10

GeV

m eV−

=

→ ∆ = ×

42


2 3 232

unitD 30

unitM 2.5 10

GeV

m eV−

=

→ ∆ = ×

43

experimentally challenging

without cuts eff 0.05m eVwith cuts eff 0.01m eV


2 3 232

unitD 30

unitM 2.5 10

GeV

m eV−

=

→ ∆ = ×

44

Leptogenesis

Baryon asymmetry today 100

0 6 10BB

nnγ

η −= ×

CP violation ,R Dm m complex

0L ≠

0B L− ≠

0.35( )B B L= −

1 1N l N lφ φ≠→ →

45

Leptogenesis

Baryon asymmetry today 100

0 6 10BB

nnγ

η −= ×

CP violation ,R Dm m complex

0L ≠

0B L− ≠

0.35( )B B L= −

1 1N l N lφ φ≠→ →

46

light-neutrino masses and mixings favor leptogenesis

Apply the Cuts

Correlations

100 6 10Bη

−×

,D Rm m

light-neutrino parameters

0Bηleptogenesis

47


Apply the Cuts

Correlations

100 6 10Bη

−×

,D Rm m

light-neutrino parameters

0Bηleptogenesis

48

Correlation?


Apply the Cuts

Correlations

100 6 10Bη

−×

49

Correlations

has no correlation with light-neutrino mixings 0Bη Uν

has no correlations with 13 23 112 2, , , ,θ θ θ χ χ or δ0Bη

could have correlations with and thus eff,R m0Bη Dν

50

scatter plots:

Correlations

51

scatter plots:

Correlations

52

scatter plots:

Correlations

53

scatter plots:

Correlations

has a weak negative correlation with and 0Bη R effm

Summary

54

213sin 2 0.095 0.010θ = ±

223sin 2 0.95 (90% C.L.)θ >

212sin 2 0.857 0.024θ ±=

2 5 221 (7.50 0.20) 10m eV−∆ = ± ×2 0.12 3 232 0.082.32 10m eV+ −

−∆ = ×

Completely Consistent

Summary

55

δCP phase and 1χ 2χ, uniform, maximal CP violation 232m∆Sign of 99.9% normal hierarchy

213sin 2 0.095 0.010θ = ±

223sin 2 0.95 (90% C.L.)θ >

212sin 2 0.857 0.024θ ±=

2 5 221 (7.50 0.20) 10m eV−∆ = ± ×2 0.12 3 232 0.082.32 10m eV+ −

−∆ = ×


Summary

56

δCP phase and 1χ 2χ, uniform, maximal CP violation 232m∆Sign of 99.9% normal hierarchy

213sin 2 0.095 0.010θ = ±

223sin 2 0.95 (90% C.L.)θ >

212sin 2 0.857 0.024θ ±=

2 5 221 (7.50 0.20) 10m eV−∆ = ± ×2 0.12 3 232 0.082.32 10m eV+ −

−∆ = ×


Summary

0Bη

very challenging to experimental sensitivity effm

on the correct order of magnitude

weak negative correlations with and effmRno correlations with 13 23 112 2, , , ,θ θ θ χ χ or δ

57

58

Thank you!

anarchy, neutrinoless double beta decay and...

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