three neutrino oscillations
DESCRIPTION
Three Neutrino Oscillations. Neutrino Mixing. Weak eigenstate. Mass eigenstate. small. m 3. n 3. m 2. n 2. CP phase. m 1. n 1. Solar KamLAND. Atmospheric LBL. LBL (future) Reactor. factory. L. Wolfenstein. Tri/bimaximal Mixing. P. F. Harrison D. H. Perkins W. G. Scott - PowerPoint PPT PresentationTRANSCRIPT
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.