K. Zuber, University of Susse Neutrinoless double beta decay SUSSP 61, St. Andrews, 9-23 Aug.
Dec 18, 2015
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: