three neutrino oscillations

Three Neutrino OscillationsThree Neutrino Oscillations

13 13 12 12

23 23 12 12

23 23 13 13

1 0 0 cos 0 sin cos sin 0

0 cos sin 0 1 0 sin cos 0

0 sin cos sin 0 cos 0 0 1

i

MNSi

e

U

e

small

i iU Masseigenstate

Weak eigenstate

m1

m2

m3 3

2

1

Neutrino Mixing

LBL (future)Reactor

SolarKamLAND

AtmosphericLBL

CP phase

factory

P. F. HarrisonD. H. PerkinsW. G. ScottS.Chang,SK.,S.Kim

Utbm = U23(/4)U12

Utbm = U23(/4)U12

- maximal 2-3 mixing- zero 1-3 mixing- no CP-violation

Utbm = 2/3 1/3 0- 1/6 1/3 1/2 1/6 - 1/3 1/2

2is tri-maximally mixed

3 is bi-maximally mixed

L. WolfensteinTri/bimaximal Mixing

Baryogenesis via LeptogenesisBaryogenesis via Leptogenesis

IntroductionIntroduction

• Why do we exist ? matter antimatter asymmetry

• What created this tiny excess matter? Baryogenesis

CMB 10B BB

n n(6.3 0.3) 10

n

B number non-conservation CP violation Non-equilibrium

Models of Baryogenesis

Baryogenesis at the Electroweak Phase Transition: (Kuzmin, Rubakov, Shaposhinikov PLB155(1985))

GUT Baryogenesis through the decay of a heavy particle: (Yoshimura, PRL41 (1978), Dimopoulos, Suskind, PRD18(1978)

Baryogenesis via Leptogenesis (Fukugida, Yanagida, PLB174 (1986) )

• Sakharov’s conditions– B violation EW anomaly– CP violation KM phase– Non-equilibrium 1st order phase trans.

Standard Model may satisfy all 3 conditions!

Electroweak Baryogenesis (Kuzmin, Rubakov, Shaposhnikov)

• Two big problems in the Standard Model– 1st order phase transition requires mH<60GeV– CP violation too small because

J det[Yu†Yu, Yd

†Yd] ~ 10–20 << 10–10

Baryogenesis in Standard ModelBaryogenesis in Standard Model

• GUT necessarily breaks B. • A GUT-scale particle X decays out-of-equilibrium

with direct CP violation

• Now direct CP violation observed: ’ !!!

• But keeps B–L0 “anomaly washout”• Also monopole problem

B(X q) B(X q)

Original GUT Baryogenesis Original GUT Baryogenesis

B(K 0 ) B(K 0 )

One of the most attractive possibilities for baryogenesis Well motivated due to neutrino oscillation Realized in the framework of seesaw mechanism Asymmetry is generated via decay of RH neutrinos

LeptogenesisLeptogenesis

• Seesaw Mechanism

1 01( ) . .

2D LT T

mass L RD R

mL N C c c

m M N

Yanagida,Gell-MannSlansky,Ramond,

2 / ~D R Lm M

~RN M

• You generate Lepton Asymmetry first

from the direct CP violation in NR decay

• L gets converted to B via EW anomaly

More matter than anti-matter We have survived “The Great Annihilation”

(complex matrices mD and M natural CPV source)

Interference between tree level and (vertex+self energy) 1-loop diagrams:

2 22 i i

1 D D i1 V S2 2 2i 2,3D D 11 1 1

M M1Im[(m m ) ] f f

8 v (m m ) M M

1 11

1 1

( ) ( )

( ) ( )

c

c

N L N L

N L N L

CP Asymmetry

Ingredients of LeptogenesisIngredients of Leptogenesis

The efficiency factor (due to washout)

1

*

LL

n

s g

if N1 decay out-of-equilibrium

In equilibrium

1

1

Out-of-equilibrium condition

1 1( )N NH T M

slow lepton number violating processes

Conversion L into B via Sphaleron process

conversion factor : 28

79B L

311.38 10B

processes which can put N1 in thermal eq. : inverse decay process scattering

1,2L

In practice, to calculate the efficiency factor we need to solve Boltzmann eq.

(Bari ‘04)

(Davidson & Ibarra ’02, Buchmuller et al.’02)

1

3 1

2

1 2

3

8atm

N

mM

v m m

for fully herarchical neutrinos 3 2 1

m m m

CMB8 1B

1 10 2atm

0.05eVM 6.4 10 GeV

6 10 m

101M (1.5 10) 10 GeV

Lower Bound on Lightest Heavy Neutrino Mass

Lower Bound on Lightest Heavy Neutrino Mass

Assuming very hierarchical Mi

Assuming very hierarchical Mi

2 22 i i

1 D D i1 V S2 2 2i 2,3D D 11 1 1

M M1Im[(m m ) ] f f

8 v (m m ) M M

1

1

3 1 2,3

22

1 2 2

3

8Natm

NN

MmM d

v m m M

can be large : not small for large not zero for

(ex)

compatible with successful leptogenesis for special configuration of Yukawa matrix

(Hambye et al ‘04, Raidal, Strumia, Turzynski ‘04)

im

1 2 3m m m

3 1

6~ 0.5 eV or ~10 GeVNm M

For hierarchy For hierarchy 2,3 1

10 100N NM M

If , resonant effects can enhance

Resonant condition :

1 2N NM M1

Resonant LeptogenesisResonant Leptogenesis (Pilaftsis)

Quasi-degenerate case : Quasi-degenerate case : 1 2N NM M

• No more lower limit on for successful leptogenesis possible TeV scale leptogenesis

• Much larger upper limit on light neutrino masses (Hambye, Lin, Notari, Papucci, Strumia’ 04.)

For bound on

A degeneracy allows already successful Leptogenesis with

2 1 1

2( ) / 4 10N N NM M M

31eVm

iNM

3m

I IILL LLm m m 2 1I T

LL Rm v Y M Y where

1

* *1 1

,1 2 2

1

Im[( ) ( ) ( ) ]3

16 | ( ) |

I IIf g LL LL fg

N f g

gh

Y Y m mM

v Y

1

1 max2

3| |

16NM

mv

Bound on asymmetry and M

1

2

2max

/16

3 0.97 10B

N

n svM

m

(Antusch, King,E.J.Chun et al. )

Type II leptogenesisType II leptogenesis

Pastor (Moriond05)

Is the mechanism directly testable ? may be impossible if M is very large

Can we probe any effects of leptogenesis at low energy experiments?

Connection between Leptogenesis and Low E CP violation

QuestionsQuestions

• Neutrino Mixing parametrized by UMNS

UPMNS Dirac Phase

Majorana phases

source of CPV : complex Yukawa couplings concerned with both phases

Leptogenesis

Dirac Phase : CP violationmeasurable in neutrino oscillations

13 13 12 12

23 23 12 12

23 23 13 13

1 0 0 cos 0 sin cos sin 0

0 cos sin 0 1 0 sin cos 0

0 sin cos sin 0 cos 0 0 1

i

MNSi

e

U P

e

Majorana Phase :Neutrinoless double beta decay

CP violation in neutrino sectors

CP violation in neutrino sectors

4 ( ) ( ) ( )J P P

• Minimal seesaw model : contains two generations of RH neutrino (Frampton, Glashow, Yanagida, ‘02 : Endoh, Kang, Kaneko, Morozumi, Tanimoto, ‘02)

Observable in low energy phenomenology? May be, in some models

CP violation in Early Universe :

CP violation in Early Universe :

• In minimal seesaw with 2 heavy Majorana neutrinos

mD contains 3 phases

1( )

1,2

( 1 3; )2

cLi Dij Rj Rj j RjL m N N M N

ji

4 ( , ) ( ) ( ) J P P

21 12 11Im[( ) ] /( )D D D Dm m m m

Existence of a correlationbetween

1J &

(Endo,Kaneko,Kang,Morozumi,Tanimoto) PRL89(2002)

Connection between low energy CP violation and leptogenesis

Connection between low energy CP violation and leptogenesis

(Grimus and Lavoura ‘04, Mohapatra, Nasri, Yu ’05, Ahn, Kang, Kim, Lee.)

• Maximal atmospheric neutrino mixing• Vanishing 13

can be realized in some models with discrete neutrino flavor symmetry

Warrant Search for models with these features enforced by symmetry

13 459,45,13 atmsol

Models of maximal atmospheric mixing and leptogenesis

Models of maximal atmospheric mixing and leptogenesis

Angles :

Phases: no CKM phase 2 Majorana phases

23

13

12

45

0

(arbitrary)

1 2 1 3( ),( )

non-physical

mu-tau symmetryZ2 , D4 symmetry

leptogenesis

2 2 21 2sin[2( )](| | | | )Bn

b as

(Grimus and Lavoura ’04)

Soft breaking of the discrete symmetries

generating non-vanishing deviation of from maximal mixing

1323

a b b a b b

M b c d or b c d

b d c b d c

13 | | | |b b or c c

(Mohapatra, Nasri, Yu ’05)

*

*

a b b

M b c d

b d c

*13 1, Im( )b

Alternatively,

( Ahn, Kang, Kim, Lee )

Leptogenesis in SUSY• Gravitino problem BBN constraints on the abundance of gravitino for 0.1 ~ 1 TeV yield the bound (Kawasaki et al.’04)

incompatible with bound from leptogenesis !!

• To avoid gravitino problem: Non-thermal leptogenesis

(Giudice et al. Asaka , Kawasaki et al.)

Heavy gravitino scenarioanomaly mediation (Ibe et al.’04)

Gravitino LSP scenario

• Alternatives to avoid :• Soft Leptogenesis : using soft breaking terms as source

of L-violations which do not lead to seesaw neutrino masses

(Grossman et al., D’ambrosio et al., Boubekeur et al., Allahverdi et al., E.J.Chun)

• Resonant Leptogenesis (Pilaftsis)

L-asymmetry is resonantly enhanced through the mixing of nearly degenerate heavy Majorana neutrinos (~TeV)

• Various models for Low Scale Leptogenesis

6 9RT (10 10 )GeV

Massive neutrinos may be responsible for our existence Leptogenesis

We have studied some neutrino mass constraints arisen from leptogenesis.

There may exist some correlation between leptogenesis and low energy neutrino observables.