K. Zuber, University of Sussex

Neutrinoless double beta decay

SUSSP 61, St. Andrews, 9-23 Aug. 2006

References

• F. Boehm, P. Vogel, Physics of massive neutrinos, Cambridge Univ. Press 1992

• K. Zuber, Neutrino Physics, IOP, 2004• M. Doi, T. Kotani, E. Takasugi, Prog. Theo. Phys. 69, 602 (1983),

Prog. Theo. Phys. Suppl. 83,1 (1985)• W. Haxton, G. Stephenson, Prog. Nucl. Part. Phys. 12, 409 (1984)• J. Suhonen, O. Civitarese, Phys. Rep. 300, 123 (1998)• A. Faessler, F. Simkovic, J. Phys. G 24,2139 (1998)• H. Ejiri, Phys. Rep. 338, 265 (2000)• S. Elliott, P. Vogel, Ann. Rev. Nucl. Part. Sci. 52, 115 (2002)• S, Elliott, J. Engel, J. Phys. G 30, R183 (2004)• K. Zuber, Contemp. Physics 45, 491 (2005) • Several more....

Contents

Lecture 1

• General introduction

• What is measured in DBD ?

• Neutrino oscillations and DBD

• Other BSM physics and DBD

• Nuclear matrix elements

Lecture 2

• Experimental considerations

• Current status of experiments

• Future activities

• Outlook and summary

• (A,Z) (A,Z+1) + e- + e -decay

• (A,Z) (A,Z+2) + 2 e- 0

-

Beta and double beta decay

• (A,Z) (A,Z+2) +2 e- + 2e 2

• n p + e- + e-

-Double beta decay

Beta decay

changing Z by two units while leaving A constant

Requirements - I

2.) Single beta decay must be forbidden (m (A,Z) < m (A,Z+1))or at least strongly suppressed (large change in angular momentum)

1.) m(A,Z) > m(A,Z+2)

Requirements- II

Weizsäcker formula for A=const near minimum well approximated by

€

m(Z, A) = const + 2bS

(A /2 − Z)2

A2+ bC

Z 2

A1/ 3+ meZ + δ

Pairing energy leads to splitting: = 0 for even-odd, odd-even = - 12 MeV/A1/2 for even-even = + 12 MeV/A1/2 for odd-odd

O-OE-E A Even

Z

m

Zo

There are 35 -- isotopes in nature

Example - Ge76

History

1934: E. Fermi theory of weak interaction

1935: M. Goeppert-Mayer discussed 2

1937: E. Majorana two component neutrino

1937,39: G. Racah, W.H. Furry discussed 0

1949: First half-life limits (Fireman, Fremlin,...)

1967: First geochemical evidence for 2

1987: First laboratory evidence for 2

2002: First laboratory evidence for 0???

2All even-even ground state transitions are 0+ 0+

€

dλ = 2πδ(E0 − E f

f

∑ )< f Hβ m >< m H β i >

E i − Em − pν − Eem,β

∑2

2:Fermi‘sGolden rule

Only Gamow-Teller transitions

No unknowns from particle physics

2

€

dN

dE≈ E(Q − E)5(1+ 2E +

4E 2

3+

E 3

3+

E 4

30)Sum energy spectrum:

S. Elliott et al., 198782Se, 35 events

Measured for about 10 isotopes

Important for nuclear matrix elements

0Any ∆L=2 process can contribute to 0

Rp violating SUSY V+A interactionsLeptoquarksDouble charged Higgs bosonsCompositenessHeavy Majorana neutrino exchangeLight Majorana neutrino exchange...

1 / T1/2 = PS * NME2 *2

Schechter-Valle theorem

The standard lore

Measured quantity

Phase space integralcalculable

Nuclear transitionmatrix element

Quantity of interestEffective Majorana neutrino mass

1 / T1/2 = PS * NME2 * (<m> / me)2

Light Majorana neutrino exchange

(A,Z) (A,Z+2) + 2 e-

0

New situation for nuclear matrix elements, higher multipoles contribute

Contents

Lecture 1

• General introduction

• What is measured in DBD ?

• Neutrino oscillations and DBD

• Other BSM physics and DBD

• Nuclear matrix elements

Lecture 2

• Experimental considerations

• Current status of experiments

• Future activities

• Outlook and summary

Oscillation evidences

LSND

Atmospheric

Solar + reactors

sin2 2 = 10-1-10-3 , m2 = 0.1-6 eV2

sin2 2 = 1.00 , m2 = 2.5 10-3 eV2

sin2 2 = 0.81 , m2 = 8.0 10-5 eV2

If all three are correct... we need more (sterile ones)

€

m2 = m22 − m1

2depends on No absolute mass measurement

3 Flavour oscillations (PMNS)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⇒⇒⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

τ

μ

τττ

μμμ

τ

μ

e2i

3

2

1

321

321

3e2e1ee

E2

m

UUU

UUU

UUU

solar If sin 13 0 CP-violation atmospheric

U= UPMNS diag(1,e i1 ,e i2 )Majorana:€

U =

cosθ12 sinθ12 0

−sinθ12 cosθ12 0

0 0 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

cosθ13 0 sinθ13e−iδ

0 1 0

−sinθ13eiδ 0 cosθ13

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

1 0 0

0 cosθ23 sinθ23

0 −sinθ23 cosθ23

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

1 0 0

0 e iα 1 0

0 0 e iα 2

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Neutrino mass schemes

normal inverted

• almost degenerate neutrinos m1≈ m2≈ m3

• hierarchical neutrino mass schemes

Physical quantities

Experimental observable: Half-life

Double beta decay: Effective Majorana neutrino mass

Beta decay

m = |Uek|2 mk

€

mν = Uei2 mi∑ = m1 Ue1

2+ m2 Ue 2

2e iα 1 + m3 Ue 3

2e iα 2

€

mν = Uei2 mi∑ = m1 Ue1

2± m2 Ue 2

2± m3 Ue 3

2CP-invariance:

Measurements are complementary

Contents

Lecture 1

• General introduction

• What is measured in DBD ?

• Neutrino oscillations and DBD

• Other BSM physics and DBD

• Nuclear matrix elements

Lecture 2

• Experimental considerations

• Current status of experiments

• Future activities

• Outlook and summary

Oscillations and 0

General:

Rough estimate:

0 - Normal hierarchy

Neutrino mass schemes and 0 M. HirschNeutrino 2006

Best fit values

Neutrino mass schemes and 0

Adding errors

Effect of 13 in normal hierarchy

0-Inverted mass scheme

0 - Inverted hierarchy

Normal + inverted scheme

Comments

• Uncertainties in nuclear matrix elements not included• Difference between normal and inverted tiny, might be swamped by NME• Benchmark number of 50 meV neutrino mass, in case of inverted hierarchy should lead to an observation• Eff. Majorana mass should be plotted against other observables (beta, decay, cosmology)

Claimed evidence

Contents

Lecture 1

• General introduction

• What is measured in DBD ?

• Neutrino oscillations and DBD

• Other BSM physics and DBD

• Nuclear matrix elements

Lecture 2

• Experimental considerations

• Current status of experiments

• Future activities

• Outlook and summary

Right handed weak currentsAdd a (V+A) weak interaction (left-right symmetric theories)

Neutrino mass vs. right handed currents

€

λ,η <<1

<m> (eV)

<λ>

Possible evidence

M. Hirsch et al., Z. Phys. A 347,151 (1994)

EC/ß+

€

T1/ 20ν

( )−1

= Cmm

mν

me

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+ Cηη η2

+ Cλλ λ2

+ Cmλ λmν

me

⎛

⎝ ⎜

⎞

⎠ ⎟+ Cmη η

mν

me

⎛

⎝ ⎜

⎞

⎠ ⎟+ Cηλ η λ

++ - modes

• (A,Z) (A,Z-2) + 2 e+ (+2e) ++ • e- + (A,Z) (A,Z-2) + e+ (+2e ) +/EC

• 2 e- + (A,Z) (A,Z-2) (+2e) EC/EC

Important to reveal mechanism if 0 is discoveredEnhanced sensitivity to right handed weak currents

(V+A)

n

n

p

pe

eIn general:

Q-4mec2

Q-2mec2

Q

Double charged higgs bosons,R-parity violating SUSY couplings,leptoquarks...

More on V+A interactions

Transitions to excited 2+ statesdominated by V+A

0+1+

0+

(A,Z)(A,Z+1)

(A,Z+2)

2+

Nice signal: Coincidence of electron and gamma

Angular correlationcoefficient

Single electron spectra

SupersymmetryEach known particle gets a supersymmetric partner

MSSM: Conserves R-parity = (-1)3B+L+2S

Rp violating SUSY

Double beta probes

€

′ λ 111

L=2 Processes

3.5 10-10 1.7 (8.2) 10-2 8.4 103

500 8.7 103

2.0 104

CPkk

kkkk

kkk mUUmUUm η ∑∑ ==In general 9 mass terms

limits on <m> (in GeV)

W. Rodejohann, K. Zuber,Phys. Rev. D 62, 094017 (2000)

• μe-conversion on nuclei

XN ++−→ μμμ μ

++−+ → μμπK

Xvpe e )()( +++++ → τμτμ

•

•

•

M. Flanz, W. Rodejohann, K. Zuber, Eur. Phys. J. C 16, 453 (2001)

K. Zuber, Phys. Lett. B 479,33 (2000)

M. Flanz, W. Rodejohann, K. Zuber,Phys. Lett. B 473, 324 (2000)

W. Rodejohann, K. Zuber,Phys. Rev. D 63, 054031 (2001)

Candidate events

NOMAD trimuon eventH1 charged current event

XN ++−→ μμμ μXvpe e )()( +++++ → τμτμ

Majoron modes

€

dN

dE≈ E(Q − E)n (1+ 2E +

4E 2

3+

E 3

3+

E 4

30)

Majoron = Goldstone boson of spontaneously broken global (B-L) symmetry

n=1,3,7 (depending on transformation under weak isospin)Triplet and pure doublet ruled out by Z-width

€

gνχ = gνχ∑ UeiUej Current bounds around 10-4

Sum energy spectrum of electrons

Observable: