Advanced Particle Physics: IX. Flavor Oscillation and CP ...uwer/lectures/... · →there will be a...

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation 1 U. Uwer 4. Neutrino Oscillations = 3 2 1 3 2 1 3 3 1 3 2 1 ν ν ν ν ν ν τ τ τ µ µ µ τ µ U U U U U U U U U e e e e For massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states: 3 3 2 2 1 1 ν ν ν ν e e e e U U U + + = Constant for massless ν: mixing is question of convention β β β α α α ν ν ν t iE i i i i t iE i i i i e U U e U t = = * , ) 0 ( ) ( there will be a mixing of the flavor states with time. Massive neutrinos develop differently in time. ) 2 ( 2 ) 0 ( ) 0 ( ) ( i i i i p m p i i t iE i i e e t + = = ν ν ν for masses m i <<E i : i i i i i p m p m p E 2 2 2 2 + = + = 4.1 Two-Flavor mixing (for simplicity) = 2 1 cos sin sin cos ν ν θ θ θ θ ν ν β α Time development for an initially pure |ν α > beam: [ ] [ ] β α α ν θ θ ν θ θ ν θ ν θ ν + + = + = ) ( sin cos sin cos sin cos ) ( 2 1 2 1 2 1 2 2 2 1 t iE t iE t iE t iE t iE t iE e e e e e e t Mixing probability: = = t E E t t P 2 cos 1 ) sin (cos 2 ) ( ) , ( 1 2 2 2 2 θ θ ν ν ν ν α β β α = ⎛∆ = ] [ ] [ 4 ] [ 27 . 1 sin 2 sin 4 sin 2 sin ) , ( 2 2 2 2 2 2 km L GeV E eV m L E m t P θ θ ν ν β α ( ) L E m t E E E m p m m E E p m p m p E i i i 2 : 1 w/ L/ t same) the is p (assuming 2 2 2 2 1 2 i 2 2 2 2 1 1 2 2 2 2 = = = + = + = β β Definite momentum p; same for all mass eigenstate components

Transcript of Advanced Particle Physics: IX. Flavor Oscillation and CP ...uwer/lectures/... · →there will be a...

Page 1: Advanced Particle Physics: IX. Flavor Oscillation and CP ...uwer/lectures/... · →there will be a mixing of the flavor states with time. Massive neutrinos develop differently in

Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

1U. Uwer

4. Neutrino Oscillations

⎟⎟⎟

⎜⎜⎜

⎛⋅⎟⎟⎟

⎜⎜⎜

⎛=

⎟⎟⎟

⎜⎜⎜

3

2

1

321

331

321

ννν

ννν

τττ

µµµ

τ

µ

UUUUUUUUU 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 νννν eeee UUU ++=

Constant for massless ν: mixing is question of convention

βββ

αααννν 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 pmpi

itiE

ii eet+−

− == νννfor masses mi<<Ei:

i

iiii p

mpmpE2

222 +=+=

4.1 Two-Flavor mixing (for simplicity)

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

2

1

cossinsincos

νν

θθθθ

νν

β

α

Time development for an initially pure |να> beam:

[ ][ ] β

α

α

νθθ

νθθ

νθνθν

⋅−+

⋅+=

+=

−−

−−

−−

)(sincos

sincos

sincos)(

21

21

21

22

21

tiEtiE

tiEtiE

tiEtiE

ee

ee

eet

Mixing probability:

⎥⎦⎤

⎢⎣⎡ −−==→ tEEttP

2cos1)sin(cos2)(),( 12222

θθνννν αββα

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆⋅=⎟⎟

⎞⎜⎜⎝

⎛ ∆=→ ][

][4][27.1sin2sin

4sin2sin),(

222

222 kmL

GeVEeVmL

EmtP θθνν βα

( ) LEmtEE

Em

pmmEE

pmpmpE i

ii

2

:1w/L/tsame) the is p (assuming

22

2

2

12

i

222

21

12

222

∆=−

≈=

∆≈

−=−

+=+=

ββ

Definite momentum p; same for all mass eigenstate components

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

2U. Uwer

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

EmtP

4sin2sin),(

222 θνν βα

Observation of Neutrino Oscillations

Oscillation signal(Super)KamiokandeAtmospheric neutrinosMuch disputed signalLSDNAcceleratorClear disappearance signal

K2K

Clear disappearance signal

KamLAND, CHOOZReactor

Ultimate “solar neutrino experiment”: proves the oscillation of solar ν

Water++: SNO

Confirm disappearance of solar neutrinos

Water experiments:(Super)Kamiokande, IMB

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

Radio-chemical exp.: Homestake Cl exp., GALLEX, SAGE,

Solar neutrinos

CommentsExperimentNeutrino source

Not confirmed

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

3U. Uwer

4.2 Atmospheric neutrino problem

Cosmic radiation: Air shower

)()(

)(,,

µµ

µµ

ννννµ

ννµππ

++→

+→

→+

±±

±±±

±±

eee

KKNp

2=++

=ee

Rνννν µµ

Exact calculation: R=2.1 (Eν<1GeV)

(For larger energies R>2.1)

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

Water = “active target”

Elastic scattering

CherenkovLight

Experiments: (Super)-Kamiokande

IMB

Soudan-2

Detection of Cherenkov photons: Photo multiplier

xν xν

−e −e

Z

Xν −X

−e eν

WCharged current Kinematical limit for νµ: Eν>mµ

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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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

==⇔

=

βθ

βθ

o

n

Cherenkov cone:

Experiment can distinguish electron and muon events, can measure energy

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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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 µ

L~15 km

L~13000 km

w/o oscillationw/ oscillation

Theoretical predicton

νµ deficit depends on angle

νe flux okay

Oscillation: νµ↔ ντ

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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Oscillation pattern of atmospheric neutrinos

νµ↔ ντ mixing of atmos. neutrinos

..%[email protected])4.04.2(

2

32

LCm

>

×±=∆ −

θ

allowed

Neutrino 2004

4.3 Solar neutrino problemNeutrino production

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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Neutrino energy spectrum

2-body decays

Cl2 detectors νe + 37Cl → 37Ar + e, 37Ar → 37Cl (EC) Eν>0.8 MeV

Ga detectors νe + 71Ga → 71Ge + e Eν>0.2 MeV

H2O detectors Elastic scattering: νe + e → νe +e Eν>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

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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Solar Neutrino Problem: Experimental summary

Eν>0.8 MeV

Eν>0.2 MeVEν> 5 MeV Eν> 5 MeV

CC CCES ES

Neutrino disappearance

Can one measure the oscillated neutrinos ??

The Nobel Prize in Physics 2002

Riccardo GiaconiMasatoshi KoshibaRaymond Davis Jr.

"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"

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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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

τµ νσνσνσ=

=⋅ e

Charged current

xν xν

−e −e

Z

eν e

−e eν

W

eν −e

pn

W

eν eν

nn

Z

Elastic scattering

Neutral current

CherenkovLight

CherenkovLight

Neutron)()()( τµ νσνσνσ ==e

0)()( == τµ νσνσ

Cl),(Cl 3635 γn

eνν φφ =

6/)(τµ νννν φφφφ ++=

e

τµ νννν φφφφ ++=e

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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SNO Evidence for Neutrino Oscillation

Electron neutrino flux is too low:

Total flux of neutrinos is correct. Interpreted as νe ↔ νµ or ντ oscillation

)%235( ±=eeP νν

But in case of simple “vacuum oszillation”: %502sin211 2 =−≥ θνν 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

00

21

νν

νν

mm

pdtdi

With unitary transformation U one obtains for the flavor oscillationin vaccum:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=θθθθ

θ cossinsincos

U

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

µ

µµ

νν

νν

νν

e

ee

p

dtdi

2

2

T

M

UMU ⎟⎟⎠

⎞⎜⎜⎝

⎛−∆=

θθθθ

2cos2sin2sin2cos

4

2

pmTUMU

p2

2M

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Neutrinos in matter:

xν xν

−e −e

Z

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

ENGm

EVmpVEpEm

eFM

ee

22

2)(2

222222

=∆

+≈−+→−=

eν e

−e eν

W

Ne=electron densityeFe NGV 2=

222 mNEGa eF ∆=

Neutrino oscillation in matter:

⎟⎟⎠

⎞⎜⎜⎝

∆−∆

+⎟⎟⎠

⎞⎜⎜⎝

⎛−∆=→ 2

22

00

2cos2sin2sin2cos

2 M

M

mmm

θθθθ2

M2 MM

one define the matter mass eigenstates which one obtains by diagonalizing 2MM

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

ανν

νν e

m

m Tθm

U2

1

Go the opposite direction…

⎟⎟⎠

⎞⎜⎜⎝

⎛∆

∆−+=

m

mmm0

0)(

21 2

121mm θ

2Tθ UMU

θθ 2sin)2cos( 222 +−∆=∆ amm

ENGm eFM 222 =∆

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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2/22 mNEGa eF ∆=

22 1042sin −⋅=θ22 1012sin −⋅=θ32 1042sin −⋅=θ

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=mm

mmm θθ

θθθ cossin

sincosU with

θθθθ

2sin)2(cos2sin2sin 22

22

+−=

am

Matter mixing angle can go through a resonance:

Fe EG

mNa22

2cos i.e.02cos 2 θθ ∆==−

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 ννExplains observed with SNO

Status of oscillation measurements

Atmosνµ→νx

Solar+KamLANDνe→νx

LMA = large mixing angle: MSW effect

necessary

..%[email protected])4.04.2(

2

32

LCm

>

×±=∆ −

θ

83.02sineV10)6.02.8(

2

52

×±=∆ −

θ

m

Long baseline “many”reactors experiment

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

allowed

allowed

excluded

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

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4.4 Neutrino masses

25eV102.8~ −⋅

23eV104.2~ −⋅

25eV102.8~ −⋅

23eV104.2~ −⋅

Absolute neutrino masses are not known !

⎟⎟⎟

⎜⎜⎜

−−−−−−=

132313231223121323122312

132313231223121323122312

1313121312

ccscsscsccsscssssccssccs

scsccU

ijijijij sc θθ sin,cos where ==

solθθ ≡12 atmθθ ≡23 013 ≈θ

Neutrino masses in the Standard Model

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

Higgsh0 Masses of neutrinos through Yukawacoupling to Higgs:

2υλν

ν =m

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

• Lepton numbers: Le Lµ and Lτ 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 ψψ~

→ unnatural)( νννν LRRLmm D +=

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

14U. Uwer

Majorana Neutrinos• Unlike the charged leptons, neutrinos

could be their own anti-particles: ⎩⎨⎧

==

=RR

LL

νννν

νν

Majorana Neutrinos

Lν Rν

Higgsh0

Majorana mass term

Mass term violates Lepton flavor conservation: ∆L = ± 2

• Majorana character can be checked in neutrinoless double beta decay (0ν2β):

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

• Can we prove that neutrino is a Dirac particle

( ) ..0

0,

,

, ccRR

mm

LLmRM

LM +⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

ν

ννν

Search for 0ν2βGermanium decay (example)

2β energy spectrum

0ν2β

?Klapdor-Kleingrothaus

2004

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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

15U. Uwer

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 mν for LH neutrinos

R

D

Mmm

2

=νLν Rν

0h 0h=Rν

0h 0hx

RM1

Lν Rν Lν

Seesaw mass term for light neutrino

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

( ) ..,,

, ccRR

mmmm

LLmRMD

DLM +⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

ν

ννν

The End