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Neutrino Mass and MixingNeutrino Mass and Mixing
Workshop for Underground Experiments
and Astroparticle Physics
Feb. 16-19, 2005 Muju, Korea
Sin Kyu Kang (Seoul National University)
Workshop for Underground Experiments
and Astroparticle Physics
Feb. 16-19, 2005 Muju, Korea
Sin Kyu Kang (Seoul National University)
Contents
Evidence for Neutrino Oscillation• Atmospheric Neutrino• Solar Neutrino• Terrestrial Neutrino Phenomenology of Neutrino Mixing Proposals of Small Neutrino Masses Leptonic CP Violation
Evidence for Neutrino Oscillation• Atmospheric Neutrino• Solar Neutrino• Terrestrial Neutrino Phenomenology of Neutrino Mixing Proposals of Small Neutrino Masses Leptonic CP Violation
Evidence for Neutrino Oscillations
Cosmic Ray
, K
e
e
μ
Neutrinos from the other side of the Earth.
e
Super-Kamiokande (50,000ton water Ch. Detector)
Atmospheric Neutrino Oscillation
• SK observed flux deficit
SK Collab. hep-ex/0404034SK : L/E DependenceSK : L/E Dependence
oscillation
decoherence
decay
• SK observed an apparent oscillation dip. • Rival hypotheses such as neutrino decay and de
coherence disfavored at 3.5
Evidence for muon neutrino oscillation in an accelerator-based experiment (K2K)
(11 November 2004)
Evidence for muon neutrino oscillation in an accelerator-based experiment (K2K)
(11 November 2004)
• beam with mean E=1.3 GeV directed at SK 250 km away
• 107 observed events
• events expected without oscillation
• Best fit :
• beam with mean E=1.3 GeV directed at SK 250 km away
• 107 observed events
• events expected without oscillation
• Best fit :
μν
1210151
2 3 2m 2.8 10 eV 2sin 2 1.0
• neutrino2004
2-flavor oscillations
Oscillation Analysis Results
Kearns, neutrino2004
L / E Oscillation Analysis Result
22 2 atm
atm
mP sin sin
4E
•How the Sun burns
Solar Neutrino Oscillation
solar neutrino
observation via
e d p p e
x xd p n
x xe e
CC
NC
ES
8 B
SNO ExperimentSNO Experiment
• SNO Pure D2O Results (SNO Collab. PRL 89 (2002) )
• (SNO Collab. PRL92 (2004) )
cc(e) = 1.76 (stat.) (syst.) × 106
es(x) = 2.39 (stat.) (syst.) × 106
nc(x) = 5.09 (stat.) (syst.) × 106
+0.06
−0.05
+0.09
−0.09
+0.24
−0.23
+0.12
−0.12
+0.44
−0.43
+0.46
−0.43
cc(e) = 1.70 (stat.) (syst.) × 106
es(x) = 2.13 (stat.) (syst.) × 106
nc(x) = 4.90 (stat.) (syst.) × 106
+0.07
−0.07
+0.09
−0.10+0.29
−0.28
+0.15
−0.08+0.24
−0.24
+0.29
−0.27
Evidence for flux deficit of solar neutrinoThis anomaly can be interpreted by MSW
LMA
8 6 2 1SSM(2004) : ( B) 5.26(1 0.23) 10 cm s
SNO Salt FluxesSNO Salt FluxesSNO Pure D2O Results
SNO Pure D2O Results
• 1st result From Mar. 4 to Oct.6, 2002145.1 live days, 162 ton-year ex.Neutrino disappearence at 99.99%
• 2nd result From Mar.9 (02) to Jan 11 (04)515.1 live days, 766.3 ton-y ex.Neutrino disappearence at 99.99%
Reactor Long Baseline Experiment150 - 210 km ( Epr > 2.6 MeV )
e + p e+ + n
R 0.611 0.085(stat) 0.041(sys)
R 0.686 0.044(stat) 0.045(sys)
Evidence of Spectral Distortion (1 November 2004)
Neutrino Oscillation parameter allowed regions
2 0.6 5 20.5m 8.2 10 eV
2 0.090.07tan 0.40
Best fit
Matter Effect (Mikheyev, Smirnov, Wolfestein)
Elastic forward scattering
e e
W
ee
H0 H = H0 + V
12 1m2m
1m
m
1 e 2m
2
0cc F e e eL 2G n
H common
m2
4E
cos2 sin 2sin 2 cos2
2GFne1 0
0 0
• Distortion of E spectrum :
3 explicit signatures of MSW effect
• Distortion of E spectrum
• Observation of vacuum-dominated mixing at low E
Day/Night Effect Binned (PLB539, 179) Unbinned (PRD 69)
AND = -2.1 % (2.0 %) AND= -1.8% (1.6%)
LMA-IILMA-I
expected
observed(± 1)
LMA-II disfavored
Determination of 13
• intense and nearly pure neutrino flavor composition
( 1km, 3MeV)L E ( )e
CHOOZ CHOOZ experimentexperiment :
e p e n
2sin 2 0.16
2 3 22 10 eV m
for
• Solar and KamLAND provide information on independent of CHOOZ and atmospheric neutrino data
• Global analysis of all available data (Malton et al.) :
6.313 4.44.4 (2 )
13
4.813 7.57.5 (2 )
• Allowed regions at 90%, 95%, 99%, 3 from CHOOZ(lines), CHOOZ+solar+KamLand(colored)
Future experiments for 13
• SNO D2O data+ SK• SNO salt phase Evidence for in • KamLAND Evidence for oscillation in vacuum Confirm LMA solution
• L/E analysis in SK Evidence for oscillation
• For :
SummarySummary
e
8
e
B
Remarkable Progress since 2001
Remarkable Progress since 2001
Solar+KamLAND (Maltoni et al.’04)
Atm+K2K (Maltoni et al. ’04)
13
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
PMNSi
e
U P
e
small
i iU Masseigenstate
Weak eigenstate
m1
m2
m3 3
2
1
Neutrino Mixing
N.H.
LBL (future)Reactor
SolarKamLAND
AtmosphericLBL
CP phase
factory
Bi-large mixing between neighboring families
(1,2) & (2,3)
The ratio
no strong mass hierarchy
Mixing between remote (1,3) families small ??
Absolute mass scale
Type of mass spectrum
Type of mass hierarchy
• What is the origin of neutrino mass ?
• Why are neutrino masses so small?
• Why is the lepton flavor mixing large and so different from quark mixing?
• Does the result of lepton mixing imply GUT ?
• Are neutrinos Dirac or Majorana?• If new light sterile neutrinos exis
t, what is their nature and underlying physics?
• Is leptonic CP violated?• Can neutrinos play a role in gener
ating our Universe?• Non-oscillating phenomena
Known & UnknownKnown & Unknown
2 221 32m / m 0.01 0.15
Theoretical QuestionsTheoretical Questions
(Guzzo, Holanda, Peres ’04 ; Friedland, Lunardini, Pena-Garay ’04) Very small flavor universality violation can lead to
suppression of ve earth regeneration shift of resonance layer in the sun
(Holanda & Smirnov ’03 ; Dev & Kumar ’04)• Upturn of the solar neutrino sepctrum at low energy Homestake lower rate of Ar-production No apparent upturn of boron neutrino spectrum explained if a light sterile neutrino exists cf.) fit to solar data : (Bahcall, Gonzalez-Garcia, Pena-Garay ’04)
Probing subleading effects
2sin 0.09(0.35)
Nonstandard interactions
Sterile neutrino mixing
Pattern of neutrino mixing
exp
0.79 0.86 0.50 0.61 0 0.16
0.24 0.52 0.44 0.69 0.63 0.79
0.26 0.52 0.47 0.71 0.60 0.77
U
2
3 1,eU
cos sin 0
sin cos 1
2 2 2
sin cos 1
2 2 2
s s
s s
s s
U
Why both mixings Large ?
45atm •In the limit•In the limit
Bi-maximal mixing
(1) Deviation from Bi-maximal mixing (Giunti & Tanimoto, ’02 Frampton, Petcov, Rodejohann ’04)
In the case of small using data :
In the case of using data
lep bimaxU U ( )U , 1 1
02 21 1 1
2 2 21 1 1
2 2 2
bimaxU
lepU ( ), ij
lepijsin
ij( 0.35)
2 2sol 12 13
2 2 3atm 23
2e3 12 13
tan 1 2 2( ) ( )
sin 2 1 4 ( )
| U | | ( ) / 2 ( ) |
lep CKMU U ,
e3
2 2sol e3 e3
2 4 4atm e3
| U | 0.162
tan 1 4 | U | 8 | U |
sin 2 1 4 1 16 | U |
23
12
13
0.19
(0.21 0.26)
0.03
2sol
2atm
0.22
tan 0.52
sin 0.96
(2) Quark-Lepton Complementary (Grand Unification) (Ramond et
al.’03, Minakata & Smirnov ’04, Raidal, Frampton & Mohapatra ’04)
Simplest Higgs structure which relates quark & lepton Yukawa matrices:
expC 12.7 exp
sol 32.6 1.6
exp expsol C 45.3 1.6
Td l
u Dirac
M M
M M
: SU(5)
: SO(10)
Dd dL d dRM U M U ,
Du uL u uRM U M U ,
Dl lL l lRM U M U , D
Dirac 0L Dirac 0RM U M U ,
D * D Tseesaw 0L Dirac 0R 0R Dirac 0L
R
1M U M U U M U
M
T0L 0LU CU TC VD V
TMNS lL 0L dR dL CKMQ Lsymmetry
U U U V U U U V
In models where Md is symmetric,
MNS CKMU U V
(3) tri/bi-maximal mixing Harrison, Perkins, Scott ’99,’02 Z.Xing,’02, He, Zee, ’03, Koide ’03 Chang, Kang, Kim ’04, Kang ’04
Origin of tri/bi-maximal mixing S3 permutation family symmetry
MNS
2 10
6 31 1 1
U6 3 2
1 1 1
6 3 2
I
22 2
e2 e3 3U 1 3, U 0, U 1 2
This symmetry supports an inverted mass hierarchy, but rather large mee shows strong violation of this symmetry.
Discrete symmetries : A4, S3, Zn, D4
U(1) : Froggatt-Nielsen Non-abelian symmetries : SU(2), SO(3), SU(3)
Dirac type : demands RH components (EW singlet), but their masses are unportected by symmetry
Majorana type : due to neutrality
Flavor Symmetry & neutrino masses
Flavor Symmetry & neutrino masses
eL L L
Do the patterns of neutrino masses and mixing reflect certain symmetry?
Generation of neutrino mass :
How small Neutrino Mass ?
• Cosmological Mass Limit :
2 0.007692.5
mh
eV
0.23(eV)m
WMAP
(1) Simplest possibility : (Yanagida, Gell-mann,Ramond, Slansky,Mohapatra, Senjanivic,’80)
cf) type II seesaw : introducing SU(2) triplet Higgs (Mohapatra & Senjanovic, ’81, Wetterich ’81)
Neutrino Majorana : can lead to and other processes
Scale of M : roughly speaking could be indication of grand unification
Why ?Why ?u,d,em m
..0
)(2
1cc
Mm
mL
R
L
D
DRLmass
Mass eigenvalues ~
0
L 2 14 1510 10 GeV
2Dm
;MM
Seesaw mechanism
Implications of Seesaw
Directly : to observe heavy RH neutrinos difficult! Indirectly : (1) and other processes
(2) RH neutrinos generate renormalization effect between M and GUT scale which modifies masses and mixing of light neutrinos
(3) If SUSY is realized, Yukawa couplings via RG give contributions to slepton mass matrix which in turn produces a number of observable effects via LFV
(4) Leptogenesis : probing Dirac Yukawa structure. it leads to bounds on lightest M
0 L 2
How to Probe seesaw ?
(2) Radiative mechanism : Zee model : excluded in its minimal version
no RH beutrino, new scalar (Frampton etal.’02, X. He ’04)
Two loop generations : (Babu ’88, Chang & Zee ’00)
no RH neutrino, new singlet scalar
SUSY with trilinear R-parity violating couplings (Hall & Suzuki, Dree et al.)c c
ijk i j k ijk i j kL L E L Q D
l
l~
q
q~
)/ln(16
)/ln(16
2~
22
*2~
22
*
bbblll mmmmmmm
,
2,H
(3) Interesting attempts in extra dimensions large EXD (ADD) :Dirac mass suppressed by the large
volume of EXD (Dienes et al ’98, ADD’02)
warped EXD (RS) : RH neutrinos can be zero modes localized on the hidden brane leading to small Dirac mass (Grossman & Neubert ’00)
(4) Combination of Seesaw & radiative generations : (Hall & Suzuki, Hempfuling,Joshipura & Novakowski, Chun et al, Chun & Kang, Jung et al.,
Kong, Hirsch et al. Valle, Grossman & Haber, Losada & Davidson)
in SUSY with tri/bi-linear R-parity violating terms tree neutrino mass generated from the seesaw
due to mixing of neutrinos with neutralinos 1-loop mass via tri-linear couplings
Probing in Future Collider Experiments
SUSY without R-parity as a theory of massive neutrinos can be testable in collider ! (Chun et al, ’99,’02,’04, Bartl et al.’03, Hirsch et al., ’01,’02,’03)
Key idea : Probing of decays of LSP (lightest SUSY particle)
Decay amplitude 0
2 3 F iG M
( )
ij i j
i i
m c
Dirac CP violation : CKM-like phase in UPMNS
measurable in neutrino oscillation if using the hierarchy
for the golden channel
and should be large should not be too small CPV phase should be large the baseline should be long enough (typically 3000 or 7000km)
Leptonic CP violation Leptonic CP violation
P( ) P( )
2 221 32m m ,
222 3121
CP
13 23 13 12
m Lm LA [P( ) P( )] 8J sin ,
2E 2E
1J cos sin 2 sin 2 sin 2 sin
8
e
221m
1213
Dirac CP violation
Conditions for observing CPV effects
I
• In matter : matter effect violates CP & CPT ( & ) in matter with costant density :
How to measure ? Reactor Experiments Super Beam :
JHF & SK ~300km neutrino factories ~3000, 7000km NuMI ~ 800km
P P P P P P P P
CP
mattCPA J
13
213sin
JHFJHF
~1GeV beamKamiokaJAERI
(Tokaimura)
0.77MW 50 GeV PS
( conventional beam)
Super-K: 22.5 kt
4MW 50 GeV PS
Hyper-K: 1000 kt
Phase-I (0.77MW + Super-Kamiokande)Phase-II (4MW+Hyper-K) ~ Phase-I 200
Plan to start in 2007
• The present neutrino experiments indicate the strong evidence for massive neutrinos
new physics beyond SM
• Small but finite neutrino masses need drastic idea to understand it
• Neutrino era is just beginning and we have long way to go…..
SummarySummary
• From CMB acoustic peaks(WMAP)+Large Scale Structure
• A Baryon Asymmetry can be generated in an expanding unive
rse if ( Sakharov) the particle interactions violate B, C & CP the evolution of the universe out of equilibrium
• Those conditions fullfiled in the CP violating, out of equilibrium decays of Ni
generating L asymmetry• L asymmetry B asymmetry
Baryon Asymmetry via LeptogenesisBaryon Asymmetry via Leptogenesis
CMB 10B BB
n n(6.3 0.3) 10
n
iNl( l )
( ) sphaleron
Leptogenesis (Fukugita & Yanagida ’86)
(Buchmuller et al.,Bari)
interference between tree level and (vertex+self energy) 1-loop diagrams:
barring RH neutrino degeneracy & strong phase cancellations:
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
max 21 1 1 1 1 j1(M ) (m m , ), D D 211
1 j j11
m mm m
M
2 2j j1
j2 21 1 j1 max 1 1 j1
atm 1
m Im
(m ,m , ) (m ,m , ) 1m m
max 61 atm 11 1 2 10
M m M3(M ) 10
16 v 10 GeV
CP asymmetry
(Davidson & Ibarra ’02, Buchmuller et al.)• The evolution of particle number densities in the early universe determined by solving Boltzmann equation• The final B asymmetry :
• From the condition :
• For
sph fB B L
aN
f 2B L 1 1 1
3N (z) (z;m ,M ,m )
4
2 2B 1 1 110 (m ,M ,m )
max CMBB B
CMB8 1B
1 10atm
0.05eVM 6.4 10 GeV
6 10 m
sol 1 atmm m m
101M (1.5 10) 10 GeV 9 10
iT (4 10 2 10 )GeV
Lower bound on lightest heavy neutrino mass
• Requirement ,
the domain for shirnks to zero yields upper limits on mi
•Contours of constant for the indicated values of in the plane (for NH) (Buchmuller et al. ’02)
maxB
m1 1(m ,M )
Upper bound on light neutrino masses :
2 2 2 21 2 3m m m m
max CMBB B
m 0.2eV
1 2
3
m ,m 0.11eV
m 0.12eV
2 2 2atm 3 2
2 2 2sol 2 1
m m m
m m m
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
Connection bewteen low energy CP violation and leptogenesis
• In minimal seesaw with two heavy Majorana neutrinos
(Glashow, Frampton, Yanagida)
mD contains 3 phases
1( ) ( 1 3; )
21,2 c
Li Dij Rj Rj j RjL m N N M jN i
4 ( , ) ( ) ( ) J P P 2
1 12 11Im[( ) ] /( ) D D D Dm m m m
Existence of a correlationbetween
1J &
(Endo,Kaneko,Kang,Morozumi,Tanimoto) PRL89(2002)
• Solar + KamLAND
• (K. Inoue, NOW04)
2 0.6 5 20.5m 8.2 10 eV
2 0.09
0.07tan 0.40
Absolute Scale of Mass
Absolute Scale of Mass
From the oscillation result
From
WMAP
2h 31m m 0.04eV
0
2ee ek k
k
m U m
0m 0.23eV
• pe+0, K+, etc– Atmospheric
neutrino main background
• Cosmic rays isotropic– Atmospheric
neutrino up-down symmetric
Neutrino mass & flavor spectra
normal inverted
Neutrino Mixing
• U : Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix
Mass Spectrum & MixingMass Spectrum & Mixing
For unitary matrix Mixing angles : n 2, 3, 4
CP Phases : n 2, 3, 4 Dirac : 0 1 3
Majorana :
e
1
1
2
2
3
3
0.79 0.86 0.50 0.61 0.0 0.16
0.24 0.52 0.44 0.69 0.63 0.79
0.26 0.52 0.47 0.71 0.60 0.77
i iU nn
1n(n 1)
2 1 63
1(n 1)(n 2)
2
1n(n 1)
2 1 3 6
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