IX. Flavor oscillation and CP violation

1. Quark mixing and the CKM matrix

2. Flavor oscillations: Mixing of neutral mesons

3. CP violation

4. Neutrino oscillations

1. CKM Matrix

b

s

d

)-(1 )t,c,u( 5 CKMV

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

b

s

d

)-(1 )t,c,u(J 5

weak eigenstates

mass/ flavor

W

d uudVCharged currents:

weak

mass eigenstates

CKM matrix

1CKMCKMVV

Unitarity

d )-(1J 5u

18 parameter (9 complex elements)

-5 relative quark phases (unobservable)

-9 unitarity conditions

=4 independent parameters: 3 angles + 1 phase

Number of independent parameters:

PDG parametrization

b

s

d

cs

sc

ces

esc

cs

sc

b

s

d

i

i

100

0

0

0

010

0

0

0

001

'

'

'

1212

1212

1313

1313

2323

2323

132313231223121323122312

132313231223121323122312

1313121312

ccescsscesccss

csesssccessccs

escscc

ii

ii

i

ijijijij sc sin,cos where

3 Euler angles

1 Phase

1.1 Parameters of CKM matrix

121323 ,,

Unobservable Phases

Phases of left-handed fields in Jcc are unobservable: possible redefinition

Lui

L ueu )( Lci

L cec )( Lti

L tet )(

Ldi

L ded )( Lsi

L ses )( Lbi

L beb )(

Real numbers

Under phase transformation:

)(

)(

)(

)(

)(

)(

00

00

00

00

00

00

bi

si

di

tbtstd

cbcscd

ubusud

ti

ci

ui

e

e

e

VVV

VVV

VVV

e

e

e

V

jVjijV ))]()((exp[ 5 unobservable phase differences !

b

s

d

VVV

VVV

VVV

tbtstd

cbcscd

ubusud

'

'

'

b

s

dd s b

u

C

t

Magnitude of elements

4

23

22

32

1)1(2

1

)(2

1

O

AiA

A

iA

VCKM

Wolfenstein Parametrization , A, , , = 0.22

itdtd eVV

iubub eVV

Reflects hierarchy of elements in O()

komplex in O(3)

Complex CKM elements and CP violation

Lid L

jujiV Rid R

jujiV

Lju L

idjiV

CP

T

Remark: For 2 quark generations the mixing is described by the real 2x2 Cabbibo matrix no CP violation !!. To explain CPV in the SM Kobayashi and Maskawa have predicted a third quark generation.

CP (T) violation jiji VV

i.e. Complex elements

2. Mixing of neutral mesons

As result of the quark mixing the Standard Model predicts oscillations of neutral mesons:

Neutral mesons:

bsBbdBcuDsdKP

bsBbdBcuDsdKP

sd

sd

00000

00000

:

:

00dd BB

2007 1987 2006discovery of mixing 1960

0dB

d

b

0dB

dtcu ,,

b,,, tcu

0dB

d

b

0dB

d

tcu ,,

btcu ,,W

W

Similar graphs for other neutral mesons:

2.1 Phenomenological description of mixing

Schrödinger equation for unstable meson:

2

imH

dt

di

t

timt

et

eet

2

0

2

2

1

0

)(

)(

2211

2211

2211

CPT mmm

HHH

2112 CP HH

00 PP WH

M and Γ hermitian:

*

1221

*

1221

mm

0

0

22221212

*12

*121111

0

0

0

0

2212

2111

0

0

0

0

22

222 P

Pi

mi

m

im

im

P

Pi

P

P

HH

HH

P

P

P

P

dt

di MH

),(),,(),,(),,(00000000

ss BBBBDDKKFor neutral mesons consider 2 components

HHH

LLL

mPqPpP

mPqPpP

,00

,00

with

with

2112

2112

2112,

2112,

Im4

Re2

Im2

Re

HH

HHmmm

HH

HHmm

LH

LH

LH

LH

2

und ym

x

Mass eigenstates (by diagonalizing matrix)

Heavy and light mass eigenstate:

complex coefficients

Parameters of the mass states

)(2

1

)(2

1

0

0

HL

HL

PPq

P

PPp

P

Flavor eigenstates

21 and PPPP HL )(Moriond07 64.009.0/

)%90(07.0/

2006) (CDF ps1.08.17

(PDG) ps007.0502.0

1

1

ss

s

d

CL

m

m

Neutral B mesons

MeV10)033.0337.3( 10

MeV10118 10

00

00

0000

)()()(

)()(

)()(2

1

2

,,)(

0

0

Btfq

pBtft

Btfp

qBtf

BqBptbBqBptbpp

tBtBt

B

HLHL

B

timtLHLHLHLH

LHLH eetbBtbtB ,, 2,,,, )( mit )(,

2/2/

2

1)(

ttimttim LLHH eeeetf

2

200

200

)(,

)(,

tfp

qtBBP

tftBBP

2

200

200

)(,

)(,

tfq

ptBBP

tftBBP

0

B0

B

Time evolution “Generic particle” ( PH,L )

)(2

10HL BB

pB

Time evolution of neutral meson states

mteeeBBPBBPttt HLHL

cos24

1)()(

2/0000

mteee

q

pBBP

mteeep

qBBP

ttt

ttt

HLHL

HLHL

cos24

1)(

cos24

1)(

2/2

00

2/2

00

CPT

No mixing part:

With mixing:

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10

)cos1(2

1)(

00mteBBP

t

mteBBPt

cos12

1)(

00

-1,5

-1

-0,5

0

0,5

1

1,5

0 1 2 3 4 5 6 7 8 9 10

B

t

)()(

)()(0000

0000

BBPBBP

BBPBBP

For very small: H L (e.g. B0)

CP, T- violation in mixing: 1)()(0000

p

qBBPBBP

Two mixing mechanisms:

• Mixing through decays

• Mixing through oscillation )1(

)1(2

Om

x

Oy

),(),,(

),,(),,(0000

0000

ss BBBB

DDKK

show different oscillation behavior

In general:

0K 0K

0K

d

W

s

0Kd

tcu ,,s

„long distant, on-shell states“„short distant, virtual states“

For K0 important, for B0 negligible

m

Mixing mechanisms: e.g. K0

2.2 Neutral kaonsObservation of two neutral kaons KL (long) and KS (short) with different lifetimes:

1CP 1CP

2 3

ns 001.0089.0)( ns 4.07.51)(00

00

SL

SL

KK

KK

-0.9966 2

007.0942.0x

y

m

19

12

110

s10182.11

MeV 10006.049.3

s100009.05303.0

m

Large differences between lifetimes

1100

1

2200

2

CP2

1""

CP2

1""

KKKKKK

KKKKKK

S

L

KL and KS can be identified with the mass eigenstates (ignoring CP violation)

Phase convention:

00

00

KKCP

KKCP

Neutral kaon system

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

0 5 10 15 20

)()(

)()(0000

0000

KKPKKP

KKPKKP

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10

)( 00 KKP

S

t

)( 00 KKP

CPLEAR

ee eKeK and 00

Initially pure K0 beam

mte t cos~

Expectation

Measurement

After the lifetime of the Ks the K0 consists entirely out of Kl’s, which are essentially an equal mixture of K0 and K0.

self-tagging

K0 - K0 (strangeness) oscillation in the SM

0Kd

W

W

s

0Kd

tcu ,,s 0K 0K

Short range effects Long range effects: difficult to calculate

Oscillation frequency m:

2222

2

,,

222

44~ cdcscKK

Fqdqs

tcuqqKK

F VVmfmG

VVmfmG

m

c quark contribution dominant: although mt2 is very large,

the factor |VtsVtd|2 ~ 5 is very small !

2.3 Neutral B Meson

Mixing mechanisms:

• Mixing through decay: many possible hadronic decays is large

decay via mixing expect tdon' B for )1.0(

B for 0 small is

2 0s

0d

O

y

0dB

d

b

0dB

dt

bt

0sB

s

b

0sB

st

bt

Significant contribution only from top loop

)(~~ 6222 OmVVmm ttdtbt )(~~ 4222 OmVVmm ttstbt

Large ms,d: ms~1/2 md Bs osc. is about 35 times faster than Bd osc.

• Mixing through oscillation

0dB

0dB

b

b

e

e )4( s

00

00

00

BB

BB

BB

00)4(

:GeV58.10 at

BBSee

s

ARGUS 1987

Mixed: *0 DBSD 0

K

*0 DB0D

K

Discovery of B0 mixing

First e+e- B factory at DESY:

nb1)( BB

Unmixed:

Same charge

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6 8 10

)cos1(2

1)(

00mteBBP

t

mteBBPt

cos12

1)(

00

-1,5

-1

-0,5

0

0,5

1

1,5

0 1 2 3 4 5 6 7 8 9 10

B

t

)()(

)()(0000

0000

BBPBBP

BBPBBP

Mixing of neutral B mesons

mixedunmixed

mixedunmixedA

dm

-1ps004.0006.0506.0 dm

B

0.774

26

ps)syst.(07.0)stat.(10.077.17 1- sm

Observation:

Spring 2006

]ps[t

5 Messung

(CDF Collaboration, September 2006) 35 times faster than B0

3. CP violation in the K0 and B0 system

P

P

C C

forbidden

forbidden

• C and P violated in weak decays

• CP conserved in weak interaction ? No !

allowed

1100

1

2200

2

CP2

1""

CP2

1""

KKKKKK

KKKKKK

S

L

Phase convention:

00

00

KKCP

KKCP

Reminder:

3.1 Observation of CP violation (CPV) in KL decays

If no CPV:

1CP2

1 00 KKKL

3102~

1CP

BR

KL

should always decay into 3:

CP(|3>)= -1

and never into 2 CP(|2>)= +1

Christenson, Cronin, Fitch, Turlay, 1964

Explanation:

1221

1KKKL

1CP 1CP

Not a CP eigenstate: CP violation !

If no CPV:

3

3

10)26.067.1()Re(

10)014.0284.2(

)K(/ st

1999 0KKpp

After 35 years of kaon physics:

1221

1KKKL

(mixing)

(Direct CPV)

Interpretation of CPV measured in the kaon system is difficult. Much easier to understand and to predict in the SM is the B meson system: CPV in the B0 system was observed in 2000.

3.2 CP Violation in the Standard Modell

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

'

'

'

Quarks:

Antiquarks:

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

***

***

***

'

'

'

Phase angle0: complex CKM matrix

Different mixing for quarks and anti-quarks

Origin of CP Violation (CPV)

iubub eVV

itdtd eVV

see Wolfenstein parametrization

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

V

Unitary CKM matrix: VV† = 1

0

tbtdcbcdubud VVVVVV

0

ubtbustsudtd VVVVVV

*tbtdVV

*cbcdVV

*

ubudVVarea = J/2

Important for Bd and Bs decays

6 “triangle” relations in complex plane:

0

tbtdcbcdubud VVVVVV

**Im kjilklij VVVVJ Strength of CPV: Characterized by Jarlskog invariant

51026210~)(21]Im[

OAVVVVJ csubcbusIn SM:

Re

Im

Rescaled unitarity condition

*

*

cbcd

ubud

VV

VV *

*

cbcd

tbtd

VV

VV

0 1

Im

Re

*

*

argcbcd

ubud

VV

VV

*

*

argtbtd

cbcd

VV

VV

*

*

argubud

tbtd

VV

VV

0

tbtdcbcdubud VVVVVV

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

i

i

e

e

3.3 Observation of CP Violation

1AfB

ii eeA CP2

fB

)cos(2 21

22

21

2

CPAA

AAA

CP

1AfB

ii eeA CP2

fB

)cos(2 21

22

21

2

CPAA

AAAWeak and CP invariant phase difference

Need two phase differences between A1 and A2: Weak difference which changes sign under CP and another phase difference (strong) which is unchanged.

Phase measurement Interference experiment

“3 Ways” of CP violation in meson decays

p/q

0B 0B

q/p

0B0B

f f

)()( 0000 BBPBBP

)()( fBPfBP

1f

f

A

A

B f

weak strong

ii eeAfBA )(

2 2

0Bf f

0B

fAfA

1p

q

a) Direct CP violation

b) CP violation in mixing

c) CP violation through interference of mixed and unmixed amplitudes

f0B

0B

))(())(( 00

00 tfBtfB tt

Asymmetrie modulated by mtsin~

Combinations of the 3 ways are possible!

Ad a) Direct CP violation (B system)

B0

gB0

1AK0B

ii eeA CP2

Strong phase difference

sinsin4 2122

AAAA CP Asymmetrie

0

0

BB K

K

BB Mio227

]GeV/c[m 2Kπ

511606)/( 00 KBBN

)()(

)()(00

00

KBNKBN

KBNKBNACP

4.2009.0030.0133.0 CPA

PRL93(2004) 131801.

1p

q

b) CP (T) violation in mixing

)()( 0000 BBPBBP

1

1

p

qm 122

1

1KKK K

K

L

Reminder:

Re41

Re4

1

1

))(())((

))(())(()(

24

4

0000

0000

pq

pq

tBBPtBBP

tBBPtBBPtA

T violation

Measured using semileptonic decays

))(())((

))(())(()(

00

00

00

00

tXBtXB

tXBtXBtA

tt

ttSL

XB0

XB 00B 0B

Skippe

d.

CPLEAR

3107.12.6)Re(4 K

K0K0 System: B0B0 System:

0017.00007.0Re4

0034.00013.1

0067.00026.0

B

SL

p

q

A

HFAG 2004

0K

)()() (

)() ()(

00

00

00

00

teKeK

eKeKtA

etet

etetSL

24

21 4 sin 5 10c

t

mq

p m

Standard model prediction for B Skippe

d.

c) CP violation in interference between mixing and decay

sKJB /0 CP

CP=-1

sKJB /0

A

A

222 ~ iii eeep

q

sKJ /0B

0B

A

A

222 ~ iii eeeq

p

sKJ /0B

0B

A

A

p

qCP

)()(/0 tftfAKJB CPs

)(

1)(/0 tftfAKJB

CPs

SM prediction of CP for B0→J/Ks

i

cdcb

cdcb

tdtb

tdtb

cdcs

cdcs

cscb

cscb

tdtb

tdtb eVV

VV

VV

VV

VV

VV

VV

VV

VV

VV

A

A

p

q 2*

*

*

*

*

*

*

*

*

*

CP

b

d b

dB0 mixing

pq /

b

d

ccsd

W+

B0 decay

*cscbVVA

K0 mixings

d s

d

KK pq /

iep

q 2~

β)sin(2)Im(

1

CP

CP

i

tdtd eVV no direct CPV, no CPV in mixing

1CP

Sam

e fo

r al

l ccK

0

chan

nels

Beside Vtd all other CKM elements are real

Calculation of the time-dependent CP asymmetry

tmtme

tfB

tmtme

tfB

dCP

dCPCP

CP

t

CP

dCP

dCPCP

CP

t

CP

B

B

cos2

1sinIm

2

1

1))((

cos2

1sinIm

2

1

1))((

22

2

/

0

22

2

/

0

0

0

tmCtmSftBftB

ftBftBtA dfdf

CPCP

CPCPCP

cossin

))(())((

))(())(()(

00

00

Time resolved

Interference= sin2 for B0J/KS

indicates direct CP violation if |q/p|1

2

2

21

1

1

Im2

CP

CPf

CP

CPf CS

negligible

To measure CP violation in Bd system:

• Need many B (several 100 109)

• Need to know the flavor of the B at t=0

• Need to reconstruct the decay length to measure t

3.4 Measurement of sin2: Asymmetric e+ e- B factory

GeV3.5e e B mesons decay at rest decay length z0

GeV9e e

GeV3.5

GeV1.3

Boost = 0.56 tcz

GeV58.10ECMS 50% / 50%

Symmetric:

Asymmetric:

decay length z250m

21 vt

11 vt /J

sK

2vt

0CP

0tag B)0(B BB t

0CP

0tag B)0(B BB t

tagBCPB

)sin( β2sin)( mttACP

(4s)

Ere

igni

sse

Measurement of sin2: Coherent oszillation

B0 D*+ -fast

D0+

soft

K-+

(2S) Ks

+- +-

B0(t)CPB

tagB

PRL 94, 161803. BB Mio227

023.0040.0722.02sin

sKB 0

)sin( β2sin)( mttACP

Measurement of sin2: Golden decay channel

3.5 Experimental status of the Unitarity Triangle

A triple triumph

Standard Model CKM mechanism confirmed

1. Large CP Violation in B decays

2. Large direct CP violation observed

3. CPV parameter related to magnitude of non-CP observables

• Baryon number violation

• C and CP Violation

• Departure from thermal equilibrium

Does the Standard Model explain the baryon symmetry in universe?

No

No

• CP violation in quark sector is a factor ~1010 to small.

• for MHiggs> 114 GeV: Symmetry breaking = 2nd order phase transition

Attractive: Super-symmetric extensions of Standard Model

• Additional CP violation through supersymmetric particles

• Extended Higgs-sector strong phase transition

Alternative: Lepto-genesis

Andrei D. Sakharov, 1967

3.6 Baryon asymmetry in the universe

3.7 Flavor and CP Physics as probe for New Physics

Aim: Search for New Physics in loop-processes

WNew

PhysicsW

New Physics

Box-Diagramms (oscillation) Penguin amplitudes

Deviation from the Standard Model Absolute rates und phase dependent CP asymmetries

Complementary to the direct searches for NP by ATLAS/CMS

Historical examples: GIM Mechanism, B Oscillation

Future searches for New Physics

W

b

s

s

u

u

d

gtcu ,,

Bs

T. Hurth

CP Violation in penguin decays:

sKBB )( 00

)( 00ss BB

Bs mixing (new phases):

/)( 00 JBB ss

Rare deacys:

)(0 KB

0)(sB

s

s

s

910~ BR

610~ BR (visible)

5103~ BR (visible)

610~ BR

6102~ BR (visible)

Precision meas. of CKM Phase :

Tree Zerfälle: 0,00, KDBLoop Zerfälle: KKKDB ss ,

610~ BR

LHCb – B Physics at the LHC

B Meson Production at the LHC

LHC

• pp Kollisionen bei s = 14 TeV

• Korrelierte Vorwärtsproduktion der bb

• für L ~ 2 x 1032 cm-2s-1 (defokussierte Strahlen am LHCb IP):

n = 0.5 IA / BX (ATLAS 5…25)

~1012 bb Ereignisse/Jahr

LHCb

• Ein-Arm Vorwärtsspektrometer 12 mrad < < 300 mrad(1.8<<4.9)

inel ~ 80 mb

bb ~ 500 b

bb Produktion

b b

pp

b

b

1x 2x

Gluon-Gluon-Fusion:

Typisches B Ereignis in LHCb

• Zerfallslänge L typisch ~ 7 mm • Zerfallsprodukte p ~ 1–100 GeV

• Trigger auf “low pt” Teilchen (wie Untergrund)

• Physik verlangt Rekonstruktion des Zerfalls

alle 25 ns

Simuliertes Ereignis

4. Neutrino Oscillations

3

2

1

321

331

321

UUU

UUU

UUU eeee

For massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states:

332211 eeee UUU

Constant for massless : mixing is question of convention

tiE

ii

iitiE

ii

ii eUUeUt *

,

)0()(

there will be a mixing of the flavor states with time.

Massive neutrinos develop differently in time.

)2

(2

)0()0()( i

ii

i pm

pi

itiE

ii eet

for masses mi<<Ei:

i

iiii p

mpmpE

2

222

4.1 Two-Flavor mixing (for simplicity)

2

1

cossin

sincos

Time development for an initially pure |> beam:

)(sincos

sincos

sincos)(

21

21

21

22

21

tiEtiE

tiEtiE

tiEtiE

ee

ee

eet

Mixing probability:

t

EEttP

2cos1)sin(cos2)(),( 1222

2

][

][4

][27.1sin2sin

4sin2sin),(

222

222 kmL

GeVE

eVmL

E

mtP

LE

mtEE

E

m

p

mmEE

p

mpmpE i

ii

2

:1w/L/t

same) the is p (assuming

22

2

2

12

i

222

21

12

222

Definite momentum p; same for all mass eigenstate components

Search for Neutrino Oscillations (PDG 1996)

• Disappearance: (I) With known neutrino flux: Measurement of flux at distance L: reactor experiments,

(II) Measure neutrino flux at position 1 and verify flux after distance L.

• Appearance: Use neutrino beam of type A and search at distance L for neutrinos of type B.

Exclusion plots

More statistics

excluded

Baseline longer

L

E

mtP

4sin2sin),(

222

Observation of Neutrino Oscillations

Neutrino source Experiment CommentsSolar neutrinos Radio-chemical exp.:

Homestake Cl exp., GALLEX, SAGE,

First observation of “neutrino disappearance” dates more than 20 years ago: “Solar neutrino problem”

Water experiments:

(Super)Kamiokande, IMB

Confirm disappearance of solar neutrinos

Water++: SNO Ultimate “solar neutrino experiment”: proves the oscillation of solar

Atmospheric neutrinos (Super)Kamiokande Oscillation signal

Accelerator LSDN Much disputed signal

K2K Clear disappearance signal

Reactor KamLAND, CHOOZ Clear disappearance signal

Not confirmed

4.2 Atmospheric neutrino problem

Cosmic radiation: Air shower

)()(

)(,

,

eee

K

KNp

2

ee

R

Exact calculation: R=2.1 (E<1GeV)

(For larger energies R>2.1)

Neutrino detection with water detectors [E~O(GeV)]

Water = “active target”

Elastic scattering

Cherenkov Light

Experiments: (Super)-Kamiokande

IMB

Soudan-2

Detection of Cherenkov photons: Photo multiplier

x x

ee

Z

X X

e e

WCharged current Kinematical limit for : E>m

Super-Kamiokande

• Largest artificial water detector (50 kt)

• Until the 2001 accident: 11000 PMTs (50 cm tubes!): 40% of surface covered with photo-cathode

• Back in operation since 2003

Stopped Muon

)1(42

1cos

o

n

Cherenkov cone:

Experiment can distinguish electron and muon events, can measure energy

Ratio of muon to electron neutrinos

• Too few muon neutrinos observed

• Can be explained by oscillation.

Prediction with oscillation

Zenith angle dependence of the neutrino fluxe

L~15 km

L~13000 km

w/o oscillation

w/ oscillation

Theoretical predicton

deficit depends on angle

e flux okay

Oscillation:

Oscillation pattern of atmospheric neutrinos

mixing of atmos. neutrinos

..%90@92.02sin

eV10)4.04.2(2

32

LC

m

allowed

Neutrino 2004

4.3 Solar neutrino problem

Neutrino production

Neutrino energy spectrum

2-body decays

Cl2 detectors e + 37Cl 37Ar + e, 37Ar 37Cl (EC) E>0.8 MeV

Ga detectors e + 71Ga 71Ge + e E>0.2 MeV

H2O detectors Elastic scattering: e + e e +e E>5 MeV (detection)

Neutrino experiments:

HomestakeSage, Gallex

Radio-chemical experiments: Homestake, SAGE, GALLEX

SSM prediction

• Homestake mine, 1400 m underground

• 615 t of C2Cl4 (perchloroethilene) = 2.2x1030 atoms of 37Cl

• Use 36Ar and 38Ar to carry-out the few atoms of 37Ar (~ 1 atom/day)

• Count radioactive 37Ar decays

Homestake Cl2 experiment

Solar Neutrino Problem: Experimental summary

E>0.8 MeV

E>0.2 MeVE> 5 MeV E> 5 MeV

CC CCES ES

Neutrino disappearance

Can one measure the oscillated neutrinos ??

The Nobel Prize in Physics 2002

Raymond Davis Jr. Masatoshi Koshiba Riccardo Giaconi

"for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos"

"for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources"

Sudbury Neutrino Observatory

• 6 m radius transparent acrylic vessel

• 1000 t of heavy water (D2O)

• 9456 inward looking photo multipliers

• Add 2 t of NaCl to detect neutrons

Neutrino detection with SNO

)()(

)(154.0

e

Charged current

x x

ee

Z

e e

e e

W

e e

pn

W

x x

nn

Z

Elastic scattering

Neutral current

Cherenkov Light

Cherenkov Light

Neutron)()()( e

0)()(

Cl),(Cl 3635 n

e

6/)(

e

e

SNO Evidence for Neutrino Oscillation

Electron neutrino flux is too low:

Total flux of neutrinos is correct. Interpreted as e or oscillation

)%235( eeP

But in case of simple “vacuum oszillation”: %502sin2

11 2 eeP ?

Neutrino oscillations in matter: MSW-effect

Neutrino oscillation in vacuum:

Mikhaev, Smirnov (1986), Wolfenstein (1976)

time development of mass eigenstates

2

122

21

2

1

0

0

2

1

m

m

pdt

di

With unitary transformation U one obtains for the flavor oscillation in vaccum:

cossin

sincosU

e

ee

p

pdt

di

2

2

1

2

T

M

UMU

2cos2sin

2sin2cos

2

2mTUMU

M

Neutrinos in matter:

x x

ee

Z

Electron neutrinos suffer an additional potential Ve affecting the forward scattering amplitude which leads to change in the effective mass for e:

ENGm

EVmpVEpEm

eFM

ee

22

2)(2

222222

e e

e e

W

Ne=electron densityeFe NGV 2

222 mNEGa eF

Neutrino oscillation in matter:

2

22

0

0

2cos2sin

2sin2cos

2 M

M

m

mm

2

M2 MM

one define the matter mass eigenstates which one obtains by diagonalizing MM

e

m

m Tθm

U2

1

Go the opposite direction…

m

mmm0

0)(

2

1 21

21mm θ

2Tθ UMU

2sin)2cos( 222 amm

ENGm eFM 222

2/22 mNEGa eF

22 1042sin 22 1012sin 32 1042sin

mm

mmm

cossin

sincosU with

2sin)2(cos

2sin2sin

22

22

am

Matter mixing angle can go through a resonance:

Fe

EGmNa

22

2cos i.e.02cos 2

As in the core of the sun, Ne is larger than the critical density the resonance condition will always be fulfilled: oscillation largely modified by matter.

)%235( eeP Explains observed with SNO

Status of oscillation measurements

Atmosx

Solar+KamLAND ex

LMA = large mixing angle: MSW effect

necessary

..%90@92.02sin

eV10)4.04.2(2

32

LC

m

83.02sin

eV10)6.02.8(2

52

m

Long baseline “many” reactors experiment

Different oscillation pattern for different neutrinos – what can we learn about the masses ??

allowed

allowed

excluded

4.4 Neutrino masses

25eV102.8~

23eV104.2~

25eV102.8~

23eV104.2~

Absolute neutrino masses are not known !

132313231223121323122312

132313231223121323122312

1313121312

ccscsscsccss

cssssccssccs

scscc

Uijijijij sc sin,cos where

sol 12 atm 23 013

Neutrino masses in the Standard Model

L

• Neutrino Mass term: the same as for charged leptons:

R

Higgsh0 Masses of neutrinos through Yukawa coupling to Higgs:

2

m

From the vacuum expectation value of the Higgs, 246 GeV, follows that the Yukawa coupling must be extremely small (<10-11) to generate the small neutrino masses.

• Lepton numbers: Le L and L are not conserved. L is conserved !!

• But why are the neutrino masses so small ?

• Dirac mass terms imply existence of right (left) -handed (anti) neutrinos.

Minimal extension of the Standard Model:

Introduce singlets of right (left)-handed (anti)neutrinos which do not couple to charged and neutral currents.

Dirac mass term

LRm ~

unnatural)( LRRLmm D

Majorana Neutrinos

• Unlike the charged leptons, neutrinos could be their own anti-particles:

RR

LL

Majorana Neutrinos

L R

Higgsh0

Majorana mass term

Mass term violates Lepton flavor conservation: L = ± 2

• Majorana character can be checked in neutrinoless double beta decay (02):

• Majorana-mass terms in addition to Dirac mass terms possible:

• Can we prove that neutrino is a Dirac particle

..0

0,

,

, ccR

R

m

mLLm

RM

LM

Search for 02 Germanium decay (example)

2 energy spectrum

02

?Klapdor-Kleingrothaus

2004

Seesaw mechanism to generate light neutrinos

• If neutrinos are Majorana particles:

Introduce in addition to the Dirac mass term also a Majorana mass term for the right-handed neutrino singlet:

Seesaw Model: Assume Majorana mass MR of the right-handed neutrino very heavy, Majorana mass ML of left handed neutrino =0.

Solving the mass matrix one obtains a small mass m for LH neutrinos

R

D

M

mm

2

L R

0h 0hR

0h 0h

xRM

1

L R L

Seesaw mass term for light neutrino

• Small neutrino masses can be explained … but how large is MR (1010…1015 GeV) ?

..,,

, ccR

R

mm

mmLLm

RMD

DLM

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