Neutrino oscillations and massesNeutrino oscillations and masses

1. Neutrino oscillations

2. Atmospheric neutrinos

3. Solar neutrinos, MSW effect

4. Reactor neutrinos

5. Accelerator neutrinos

6. Neutrino masses, double beta decay

1. Neutrino Oscillations

��e� ����=�

U e1 U e2 U e3

U 1� U 3� U 3�

U 1� U 2� U 3�����1

�2

�3�

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

�e=U e1�1�U e2�2�U e3�3

Constant for massless ν: mixing is question of convention

�� �t � ��=�

i

U i� e�iE

it�� i �0 ��=�

i , �

U i� U i�

*e

�iEit�� � �

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

Massive neutrinos develop differently in time.

��i� t � �=�� i�0 � �e�iE

it=�� i�0 � �e

�i � pi�mi2

2pi

� for masses mi<<Ei:

E i= p2�mi2= p i�

mi2

2pi

Two-Flavor mixing (for simplicity)

�� ����=�cos� sin �

�sin� cos� ����1

� 2�

Time development for an initially pure |να> beam:

���� t � �=cos� e

�iE1t��1��sin� e

�iE2t��2 �

= [cos2� e�iE

1t�sin

2� e

�iE2t ]���� �

� [cos� sin� � e�iE

1t� e

�iE2t� ]��� � �

Mixing probability:

P � �� �

�, t �=���

����� t ���2=2�cos� sin� �2[1�cos2

E2�E1

2t ]

P � �� �

�, t �=sin2 2� sin2 � m� 2

4 EL�=sin2 2� sin2 � 1. 27� m�

2[ eV ]

4 E [GeV ]L [ km ]�

E i= p2�mi2= p�

m i2

2p

E 2�E1=m1

2�m22

2p�m�

2

2 E�assuming p

i is the same �

t=L/ � w/ ��1 :

� E2�E1 � t=m� 2

2EL

Definite momentum p; same for all mass eigenstate components

Search for Neutrino Oscillations (PDG 1996)

• Disappearance: reactor experiments.Nuclear reactors are most intensivesources of νe on Eearth.(I) With known neutrino flux: measure flux at distance L. Only νe flux is measured via

νe + p e+ + n

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

More sensitive to small ∆m2 , as longer L can be used due to high flux

• Appearance: Use neutrino beam of type A (νµ) and

search at distance L for neutrinos of type B (νe).

More sensitive to small sinθ due to appearance

Exclusion plots

More statistics

excluded

Baseline longer

P � �� �

�, t �=sin2 2� sin2 � m�

2

4EL�

–

––

(–)

(–)

Observation of Neutrino Oscillations

Oscillation signal(Super)KamiokandeAtmospheric neutrinos

Oscillation signalLSNDAccelerator

Clear disappearance signalK2K

Clear disappearance signalKamLAND, CHOOZReactor

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

Heavy 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

Clear disappearance signalMINOS

much disputed

KARMEN and MiniBooNE refuted

2 Atmospheric neutrino problem

Cosmic radiation: Air shower

p�N �± , K±

�±, K

± �±��� � �� �

�±e±��e � �e �� � � �� � �

R=��� � �

�e� �e=2

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

Cherenkov Light

Experiments: (Super)-Kamiokande in Kamioka Mining and Smelting Co.'s Mine in Japanese Alpes,

IMB (Irvine-Michigan-Brookhaven) in salt mine on the shore of lake Erie (USA)

Detection of Cherenkov photons: photomultiplier

�x �x

e� e

�

Z

�X X�

e� �e

WCharged current Kinematical limit for νµ: Eν>mµ

Primary goal of both experiments: discover proton decay. KamiokaNDE = Kamioka Nucleon Decay Experiment.

Super-Kamiokande

• Largest artificial water detector (50 kt),41 m height and 39 m diameter

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

• Back in operation since 2003, fully restored 2006

located 1 km underground

Stopped Muon

cos �=1

n�

��=42o � �=1 �

Cherenkov cone:

Experiment can distinguish electron and muon events, and can measure energy

Electrons suffer multiple interactions – fuzzy ring.Muons fly straight through – sharp edge ring.

Ratio of muon to electron neutrinos

• Too few muon neutrinos observed

• Can be explained by oscillations

Prediction with oscillation

Oscillation pattern of atmospheric neutrinos

P � �� �� �=1�sin2 2� sin2 � 1.27 m�2

(eV)2

E (GeV)L (km)�Survival probability:

Oscillation pattern of atmospheric neutrinos

νµ ↔ ντ mixing of atmos. neutrinos

m�2=�2 .4±0 . 4 �×10

�3eV

sin22��0.92 @ 90% CL

allowed

3 Solar neutrino problemNeutrino production

Neutrino energy spectrum

2-body decays

Cl2 detectors νe + 37Cl → 37Ar + e, 37Ar → 37Cl (EC) Eν>0.8 MeVGa detectors νe + 71Ga → 71Ge + e Eν>0.2 MeVH2O detectors Elastic scattering: νe + e → νe + e Eν>5 MeV (detection)

Scintillator (Borexino started 2007, SNO+ under construction) Eν > 0.25 MeV

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

• Count radioactive 37Ar decays

Homestake Cl2 experiment(Homestake gold mine, South Dakota)

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"

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?

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 improve detection of neutrons (salt phase)

• Surrounded by normal water (H20)shielding external radiation

in Vale Inco's Creighton Mine in Sudbury, Ontario, Canada, located 2 km underground

Neutrino detection with SNO

0 .154� ��e �=

����= � �

��

Charged current

�x

�x

e� e

�

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

35Cl � n , �36

Cl

��=�

�e

��=�

�e��� �

����

��/6

��=�

�e���

����

�

Eν < mµ,τ

2H �n , � 3

H orγ−ray 6.25 MeV or 8.5 MeV

measure Eν

Eν = Ee + 1.442 MeV

lower rate, strong forward peak

Signals are determined not event-by-event but on statistical basis

Energy

resembles8B ν spectrum

γ-ray in NC makesCompton scatteringor e+e- pair andCerenkov light isobserved. 6.25 MeVline within resolution

softer than CC

RAV = acrylic vessel radius

CC only ondeuteronswithin heavywater vessel

NC only ondeuteronsin heavy waterdecreases dueto long thermaldiffusion of n.In normal waterEγ = 2.2 MeV – below analysisthreshold

also inwater

strong forward peakdirection from the Sun

no correlation

SNO Evidence for Neutrino Oscillation

Electron neutrino flux is too low:

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

P e e� �=�35±2�%

But in case of simple “vacuum oscillation”: P e e� � �1�1

2sin

22�=50%?

Neutrino oscillations in matter: MSW-effect

Neutrino oscillation in vacuum:

Mikheyev, Smirnov (1986), Wolfenstein (1976)

time development of mass eigenstates

id

dt ��1

�2�= 1

2p �m12 0

0 m22 ���1

� 2�

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

U �=�cos� sin��sin � cos� �

id

dt ��e���=1

2pUMU T ��e�

��

=M 2

2p ��e���

UMU T=m�

2

2 ��cos2� sin 2�sin 2� cos 2� �

M

Neutrinos in matter:

�x �x

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:

m2=E

2� p2� E�V e �2� p2�m2�2EV e

m� M2 =22 G F N eE

�e e

e� �e

W

Ne = electron densityV e=G F2 N e

a=22 EGF N e / m�2

Neutrino oscillation in matter:

M2M M

2=

m� 2

2 ��cos2� sin 2�

sin 2� cos 2� ��� m� M2 0

0 � m� M2 �

Define the matter mass eigenstates which one obtains by diagonalizing M M

��1m

�2m�=U �

m

T ��e�x �

Go the opposite direction…

U�m

TM

2U �

m=

1

2�m1

2�m1

2����m 0

0 �m ��m= m� 2�a�cos2� �2�sin2 2�

m� M2=22 G F N eE

a=22 EGF N e / m�2

sin22�=4�10

�2

sin22�=1�10

�2

sin22�=4�10

�3

U�m=�cos�m sin�m

�sin�m cos �m � with

sin22�m=sin

22�

�cos 2��a �2�sin22�

Matter mixing angle can go through a resonance:

cos 2��a=0 i .e . N e= m�2 cos2�

22EGF

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

P e e� �=�35±2�%Explains observed with SNO