Double beta decay and neutrino physics

Osaka University

M. Nomachi

Outline

Weak interaction and neutrino propertyExercise: HelicityExercise: parity violation

Neutrino massExercise: Seesaw mechanism

Neutrino oscillationExercise; Neutrino oscillation

Oscillation experimentsNeutrino mass measurement

Beta decayExercise: Beta ray energy spectrum

Double beat decay

Beta decay

epn p

e

n

In the modern view

u

e

dW

Weak interaction

Neutrino

http://particleadventure.org/particleadventure/index.html

LeptonSpin ½No chargeThree generationsMass ??

Helicity

spin

spin

Helicity = +1

Helicity = -1

spin

Helicity = +1

Helicity is not Lorentz invariant

Free Dirac equation

mpt

i

,3,2,1are 4x4 matrix

Special relativity

32105 i

Pseudo Scalar operator

Chirality operator

Diagonal representation

0̂ˆ

ˆ0̂,

0̂1̂

1̂0̂,

ˆ0̂

0̂ˆ,

1̂0̂

0̂1̂5

In usual representation, βis diagonal

uThe solution of the Dirac equation is

mpE

mpE

p

p

p

p

,

Helicity operator and its eigen states

pE

pEu

pE

pEu

m

pENu

m

pENu

,

,

pE

pEu

pE

pEu ,

pE Is zero for mass-less particle

E

uE

u2

0,

0

2

Helicity eigenstate = chirality eigenstate for mass-less particle

Wrong helicitym

E

m

pE

pEpE

2

22

Chirality

5 +1: Right handed-1: Left handed

Weak interaction

Weak current

uue )1( 5

2

1 5LP

Projection operator of negative (left handed) chirality

In Weak interactionElectron and neutrino are always left handed

WhilePositron and anti-neutrino are always right handed

Parity violation

In Weak interactionElectron and neutrino are always left handed

WhilePositron and anti-neutrino are always right handed

mirror

spin spin

electron electronanti-neutrino anti-neutrino

We can know which is our world!

Beta decay of 60CoZ Z

560 Co 460 Ni

Electron and anti-neutron spin

Z

electron

Electron should be left handedElectron must have

21zs

Angular distribution

Z Z

1

0

22

22

cossin

sincos)(2

1

d

2

2

cos

sin

For angular momentum conservation, spin must be down.Angular distribution will be

cos1cos)( 21

22 W

Rotation of spin 1/2

Dirac particle and Majorana particle

• Dirac particle– Particle and anti-particle can be distinguished

• Majorana particle– Particle and anti-particle can not be

distinguished

Mass

..chmL

..chmmL RLLR

..chmL RC

R

Dirac mass

Majorana mass

CR Charge conjugate

Charged particle cannot have Majorana mass.

Neutrino mass

..2

..

chm

L

chmL

RC

RR

MAJORANA

LRDDIRAC

..),( chmm

mmL C

R

L

RD

DLR

CLmass

Neutrino may have both Dirac mass and Majorana mass.

Dirac mass breaks chiral symmetry.

Mass eigenvalue

RD

D

mm

m00)(det 2

DR

RD

D mmmm

m

R

DR

DRR

DDRR

DRR

m

mm

mmm

mmmm

mmm

2

22

222

22

,)4(2

4,

2

4

2

4

Seesaw mechanism

R

D

m

m Dirac mass will be the same order as the others. (0.1~10 GeV)

Right handed Majorana mass will be at GUT scale 1015 GeV

Rm

R

D

m

m 2

Mixing and oscillation

Time evolution

Eti

et

tEtt

i

)0()(

)()(

2

1

cossin

sincos

b

a

Mixing

Mixing and oscillation

21 sincos)0( aAssuming

Probability to be at t is

tE

itE

ieet

21

21 sincos)(

a

2

22

2

2121

2

21

21

sincos

)sin)(cossin(cos)(

tEi

tEi

tEi

tEi

a

ee

eet

tEE

tEE

ee

ee

eeeet

tEE

itEE

i

tEE

itEE

i

tEi

tEi

tEi

tEi

a

1222

12222

22222

4224

22222

cos2sin1

sin1sincos21

21sincos2)sin(cos

sinsincoscos

sincossincos)(

1212

1212

2121

For small mass particle

p

mpE

2

2

For non relativistic limit

m

pmE

2

2

22 mpE

Lcp

mm

ctcp

mm

tEE

ta

2cos2sin1

2cos2sin1

cos2sin1)(

21

2222

21

2222

12222

Mixing angle⊿m2

c

Lcp

m

Lcp

mta

22

2cos2sin1)(

2

2222

0.2 GeV fm or 0.2x10-6 eVm

6

692

1012

102.010103

cpL

m

The value you have to remember

Atmospheric Neutrinos

Figures from Prof. Y. Suzuki at TAUP 2005

Super Kamiokande DATA

μ neutrino disappearance

Solar neutrino

Nuclear fusion reaction in the sun is WEAK interaction.

Electron neutrino disappearance

MNS matrix

By Minakata

Δm2 (atmospheric)

Mass hierarchy

Δm2 (solar) m=0

Normal hierarchyInverted hierarchy

Mass hierarchy is not derived from the oscillation measurements.

Beta ray spectrum

The transition rate isffi nHR

22

the matrix elementthe density of final states

rdHGH eNiNNfWfi

3***

rkil e

V

1

rdeHV

GH rkki

NiNNfW

fie

3)(*

Assuming plane wave

dEdEEEQEnEnMV

GdR eeeefi

W )()()(2 2

2

2

Phase space volume

L

nkp x

xx

The number of state in momentum p in the volume V

nd

Vnd

Lpd 3

33

33 2

8

pdpdEEQ

VM

V

GdR eefi

W

336

22

2

2

)()2(

2

dpdpEEQppMG

dR eeefiW )(

)2(

)4(2 222

6

22

The transition rate will be

42222 cmcPE dppcEdE 222 gives

22

222

6

22

)()2(

)4(2

cp

dEE

cp

dEEEEQppM

GdR

e

eeeefi

W

The transition rate will be

dEdEEEQpEpEMc

GdR eeeefi

W )(2

2

473

2

eeeefiW dEEQcpEM

c

GdR 22

673

2

)(2

Assuming neutrino mass is zero,

Because of the coulomb potential, the electron wave function is not plane wave. It causes the modification of the result

eeeeefiW dEEQcpEEZFM

c

GdR 22

673

2

)(),1(2

Fermi-function

21

2),(

eEZF e

Z

c

Ze 1

4 0

2

pc

EZZEZF e

2

12),(

eeefiW dEEQEM

c

ZGdR 222

672

2

)( consequently

Neutrino mass in beta decay

dEEEQpE e )( 2

2 1)(

e

e EQ

mEQ

The end point of beta-ray depends on neutrino mass.

Beta decay experiments

KATRIN experiment

http://www-ik.fzk.de/~katrin/

3H beta decay, end point energy

Figure from http://www-ik.fzk.de/~katrin/overview/index.html

FINAL RESULTS FROM PHASE II OF THE MAINZ NEUTRINO MASS SEARCH IN TRITIUM BETA DECAY.Ch. Kraus et al.. Dec 2004. 22pp. Published in Eur.Phys.J.C40:447-468,2005 e-Print Archive: hep-ex/0412056

Double beta decay

2) 0 neutrino double beta decay

Neutrino has mass

Neutrino is Majorana particle

1) 2 neutrino double beta decay.

d(n)

d(n) u(p)

u(p)

W

W

e

eν

ν

T1/2 (): ~ 1.15 x 1019year

d(n)

d(n) u(p)

u(p)W

We

eνν

T1/2 (): > 1023year

Double beta decay

20

21

mT

Lepton number non-conservation

d(n)

d(n) u(p)

u(p)

W

W

e

eν

ν

T1/2 (): ~ 1.15 x 1019year

d(n)

d(n) u(p)

u(p)W

We

eνν

T1/2 (): > 1023year

Lepton number2 electron +22 anti neutrino -2

= Lepton number is conserved.

(Baryon number is conserved.)

Lepton number2 electron +2

= Lepton number is NOT conserved.

(Baryon number is conserved)

Mass measurement

electron electron

eiU eiU

i iW W

Mass term

Probability of helicity flip (wrong helicity) is proportional to m.

Beta decay observable

Double beta decay observable

It should be larger than that of double beta decay measurements.

It depends on the phase. Could be zero.

From NOON2004 summary by A. Yu. Smirnov

νe

νe

5meV

50meV

Next generation experiments are aiming to explore 50meV region

Mass hierarchy

0.1 eV

10 meV

Double beta decay

S.Elliott, Annu.Rev.Nucl.Part.Sci. 52, 115(2002)

yT 260 102.12

1

2 )05.0(0 eVm

yT 192 108.02

1

100Mo

BackgroundNatural radio activitiesCosmogenic background2 neutrino double beta decay

NEMO3

Drift distance

100Mo foil100Mo foil

Transverse view Longitudinal view

Run Number: 2040Event Number: 9732Date: 2003-03-20

Geiger plasmalongitudinalpropagation

Scintillator + PMT

Deposited energy: E1+E2= 2088 keVInternal hypothesis: (t)mes –(t)theo = 0.22 nsCommon vertex: (vertex) = 2.1 mm

Vertexemission

(vertex)// = 5.7 mm

Vertexemission

Transverse view Longitudinal view

Run Number: 2040Event Number: 9732Date: 2003-03-20

Criteria to select events:• 2 tracks with charge < 0• 2 PMT, each > 200 keV• PMT-Track association • Common vertex

• Internal hypothesis (external event rejection)• No other isolated PMT ( rejection)• No delayed track (214Bi rejection)

events selection in NEMO-3

Typical 2 event observed from 100Mo

Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka 12-14 July 2004

Trigger: 1 PMT > 150 keV

3 Geiger hits (2 neighbour layers + 1)

Trigger rate = 7 Hz events: 1 event every 1.5 minutes

(Data 14 Feb. 2003 – 22 Mar. 2004)

T1/2 = 7.72 0.02 (stat) 0.54 (syst) 1018 y

100Mo 22 preliminary results

4.57 kg.y

Cos()

Angular Distribution

Background subtracted

22 Monte Carlo

• Data

145 245 events6914 g

241.5 daysS/B = 45.8

NEMO-3

100Mo

E1 + E2 (keV)

Sum Energy Spectrum

145 245 events6914 g

241.5 daysS/B = 45.8

NEMO-3

100Mo

• Data

Background subtracted

22 Monte Carlo

Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Paris 12-14 July 2004

Analysis with 100Mo

V-A: T1/2() > 3 1023 y V+A: T1/2 > 1.8 1023 y with E1- E2> 800 keV

Majoron: T1/2 > 1.4 1022 y with Esingle > 700 keVHideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka 12-14 July 2004

100Mo

8

7.0 1.7

5.6 1.7

1.4 0.2

55.8 7.0TOTAL Monte-Carlo

2.6<E1+E2<3.2

50DATA

23.5 6.7Radon M-C

32.3 1.9100Mo 22M-C

100Mo

6914 g265 days

DataMonte-CarloRadonMonte-Carlo

E1+E2 (MeV)

arbitrary unit

PRELIMINARY

2.8<E1+E2<3.2

Cu + natTe + 130Te

265 days

RadonMonte-Carlo

Data

E1+E2 (MeV)

Cu + natTe + 130Te

8

11.4 3.4

11.4 3.4

____

2.6 0.7

2

2.6 0.7

____

2.6<E1+E2<3.2 2.8<E1+E2<3.2

MOON Osaka U. , U. of Washington etc.

100Mo + Plastic scintillator

CANDLES Osaka U.

48Ca + CaF scintillator

Majorana Detector

• GOAL: Sensitive to effective Majorana mass near 50 meV

• 0 decay of 76Ge potentially measured at 2039 keV

• Based on well known 76Ge detector technology plus:– Pulse-shape analysis– Detector segmentation

• Requires:– Deep underground location– 500 kg enriched 86% 76Ge– many crystals, segmentation– Pulse shape discrimination– Time/Spatial Correlation– Special low-background materials

n

n

p+ p+

e-

e-

e

Reference ConfigurationReference Configuration

Homework

Probability to have wrong helicity

Beta ray angular distribution

Seesaw mechanism

Neutrino oscillation

Beta ray energy spectrum