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Neutrinoless Double Beta Decay: Neutrino Physics
Werner Rodejohann
(MPIK, Heidelberg)
Ustron, 15/09/11
1
Outline
(A, Z) → (A, Z + 2) + 2 e− (0νββ) ⇒ Lepton Number Violation
• Standard Interpretation: light Majorana neutrinos
– general properties
– testing the inverted ordering
– distinguishing neutrino models
– light sterile neutrinos
• Non-Standard Interpretations: something else
– heavy Majorana neutrinos
– SUSY
– RH currents
– . . .
review on 0νββ and particle physics: W.R., 1106.1334
2
Why should we probe Lepton Number Violation (LNV)?
• L and B accidentally conserved in SM
• effective theory: L = LSM + 1Λ LLNV + 1
Λ2 LLFV, BNV, LNV + . . .
• baryogenesis: B is violated
• B, L often connected in GUTs
• GUTs have seesaw and Majorana neutrinos
• chiral anomalies: ∂µJµB,L = c Gµν Gµν 6= 0 with JB
µ =∑
qi γµ qi and
JLµ =
∑ℓi γµ ℓi
⇒ Lepton Number Violation as important as Baryon Number Violation
(0νββ is much more than a neutrino mass experiment)
3
Experimental Aspects: existing limits
Isotope T 0ν1/2 [yrs] Experiment
48Ca 5.8 × 1022 CANDLES
76Ge 1.9 × 1025 HDM
1.6 × 1025 IGEX
82Se 3.2 × 1023 NEMO-3
96Zr 9.2 × 1021 NEMO-3
100Mo 1.0 × 1024 NEMO-3
116Cd 1.7 × 1023 SOLOTVINO
130Te 2.8 × 1024 CUORICINO
136Xe 5.0 × 1023 DAMA
150Nd 1.8 × 1022 NEMO-3
4
Experimental Aspects: upcoming experiments
Name Isotope source = detector; calorimetric with source 6= detector
high energy res. low energy res. event topology event topology
CANDLES 48Ca – X – –
COBRA 116Cd (and 130Te) – – X –
CUORE 130Te X – – –
DCBA 82Se or 150Nd – – – X
EXO 136Xe – – X –
GERDA 76Ge X – – –
KamLAND-Zen 136Xe – X – –
LUCIFER 82Se or 100Mo or 116Cd X – – –
MAJORANA 76Ge X – – –
MOON 82Se or 100Mo or 150Nd – – – X
NEXT 136Xe – – X –
SNO+ 150Nd – X – –
SuperNEMO 82Se or 150Nd – – – X
XMASS 136Xe – X – –
next generation: mass from 10 → 100 kg y and background from 0.1 → 0.01
counts/keV/kg/y and lifetime from 1025 → 1026 y
5
Experiment Isotope Mass of Sensitivity Status Start of
Isotope [kg] T0ν1/2
[yrs] data-taking
GERDA 76Ge 18 3 × 1025 running 2011
40 2 × 1026 in progress ∼ 2012
1000 6 × 1027 R&D ∼ 2015
CUORE 130Te 200 6.5 × 1026∗ in progress ∼ 2013
2.1 × 1026∗∗
MAJORANA 76Ge 30-60 (1 − 2) × 1026 in progress ∼ 2013
1000 6 × 1027 R&D ∼ 2015
EXO 136Xe 200 6.4 × 1025 in progress ∼ 2011
1000 8 × 1026 R&D ∼ 2015
SuperNEMO 82Se 100-200 (1 − 2) × 1026 R&D ∼ 2013-2015
KamLAND-Zen 136Xe 400 4 × 1026 in progress ∼ 2011
1000 1027 R&D ∼ 2013-2015
SNO+ 150Nd 56 4.5 × 1024 in progress ∼ 2012
500 3 × 1025 R&D ∼ 2015
6
Experimental Aspects
(T 0ν1/2)
−1 ∝
a M ε t without background
a ε
√
M t
B ∆Ewith background
with
• B is background index in counts/(keV kg yr)
• ∆E is energy resolution
• ǫ is efficiency
• (T 0ν1/2)
−1 ∝ (particle physics)2
Note: factor 2 in particle physics is combined factor of 16 in M × t × B × ∆E
7
Interpretation of Experiments
Master formula:
Γ0ν = Gx(Q, Z) |Mx(A, Z) ηx|2
• Gx(Q, Z): phase space factor
• Mx(A, Z): nuclear physics
• ηx: particle physics
8
Interpretation of Experiments
Master formula:
Γ0ν = Gx(Q, Z) |Mx(A, Z) ηx|2
• Gx(Q, Z): phase space factor; calculable
• Mx(A, Z): nuclear physics; problematic
• ηx: particle physics; interesting
9
Interpretation of Neutrino-less Double Beta Decay
• Standard Interpretation:
Neutrinoless Double Beta Decay is mediated by light and massive Majorana
neutrinos (the ones which oscillate) and all other mechanisms potentially
leading to 0νββ give negligible or no contribution
• Non-Standard Interpretations:
There is at least one other mechanism leading to Neutrinoless Double Beta
Decay and its contribution is at least of the same order as the light neutrino
exchange mechanism
10
Why do we need neutrino mass?
• in all seesaws (type I, II, III): neutrino mass inverse proportional to its origin
• GUTs: normal hierarchy. . .
• IH and QD neutrinos: special flavor symmetries required. . .
• QD: HDM, strong RG effects, leptogenesis,. . .
• mass hierarchy is moderate:
NH :m2
m3≥
√
∆m2⊙
∆m2A
>∼1
5≃
√mµ
mτ≃
√ms
mb≃
√√
mc
mt
⇒ Neutrino masses are strange and can tell us a lot
11
∆L 6= 0: Neutrinoless Double Beta Decay
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
UeiIm
Rem
mm
ee
ee
ee
(1)
(3)
(2)
| |
| || | e
e.
.
eem
2iβ2iα
Amplitude proportional to coherent sum (“effective mass”):
|mee| ≡∣∣∑
U2ei mi
∣∣ =
∣∣|Ue1|2 m1 + |Ue2|2 m2 e2iα + |Ue3|2 m3 e2iβ
∣∣
7 out of 9 parameters of mν !
12
• Standard Interpretation:
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
• Non-Standard Interpretations: e.g.
W
WR
NR
NR
νL
W
dL
dL
uL
e−R
e−L
uL
dR
χ/g
dRχ/g
dc
dc
uL
e−L
e−L
uL
W
W
∆−−
dL
dL
uL
e−L
e−L
uL
√2g2vL hee
uL
uL
χ/g
χ/g
dc
dc
e−L
uL
uL
e−L
W
W
dL
dL
uL
e−L
χ0
χ0
e−L
uL
13
Schechter-Valle theorem: no matter what process, neutrinos are Majorana:
Blackbox diagram is 4 loop:
mν ∼ 1
(16π2)4MeV5
m4W
<∼ 10−23 eV
14
The usual plot
15
Crucial points
• NH: can be zero!
• IH: cannot be zero! |mee|inhmin =
√
∆m2A c2
13 cos 2θ12
• gap between |mee|inhmin and |mee|nor
max
• QD: cannot be zero! |mee|QDmin = m0 c2
13 cos 2θ12
• QD: cannot distinguish between normal and inverted ordering
16
Plot against other observables
0.01 0.1mβ (eV)
10-3
10-2
10-1
100
<m
ee>
(e
V)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.01 0.1
Inverted
CPV(+)(-)
10-3
10-2
10-1
100
<m
ee>
(e
V)
0.1 1
Σ mi (eV)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.1 1
Inverted
CPV(+)(-)
17
Neutrino Mass Matrix
18
Which mass ordering with which life-time?
Σ mβ |mee|NH
√
∆m2A
√
∆m2⊙ + |Ue3|2∆m2
A
∣∣∣
√
∆m2⊙ + |Ue3|2
√
∆m2Ae2i(α−β)
∣∣∣
≃ 0.05 eV ≃ 0.01 eV ∼ 0.003 eV ⇒ T 0ν1/2
>∼ 1028−29 yrs
IH 2√
∆m2A
√
∆m2A
√
∆m2A
√
1 − sin2 2θ12 sin2 α
≃ 0.1 eV ≃ 0.05 eV ∼ 0.03 eV ⇒ T 0ν1/2
>∼ 1026−27 yrs
QD 3m0 m0 m0
√
1 − sin2 2θ12 sin2 α
>∼ 0.1 eV ⇒ T 0ν1/2
>∼ 1025−26 yrs
19
From life-time to particle physics: Nuclear Matrix Elements
20
SM vertex
Nuclear Process Nucl
Σi
νiUei
e
W
νi
e
W
Uei
Nucl
• 2 point-like Fermi vertices; “long-range” neutrino exchange; momentum
exchange q ≃ 1/r ≃ 0.1 GeV
• NME ↔ overlap of decaying nucleons. . .
• different approaches (QRPA, NSM, IBM, GCM, pHFB) imply uncertainty
• plus uncertainty due to model details
• plus convention issues
21
48Ca
76Ge
82Se
94Zr
96Zr
98Mo
100Mo
104Ru
110Pd
116Cd
124Sn
128Te
130Te
136Xe
150Nd
154Sm
0
2
4
6
8
M0ν
(R)QRPA (Tü)SMIBM-2PHFBGCM+PNAMP
0
2
4
6
8
10
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
Isotope
NSMQRPA (Tue)
QRPA (Jy)IBMIBM
GCMPHFB
Pseudo-SU(3)
M′0
νFaessler, 1104.3700 Dueck, W.R., Zuber, PRD 83
22
0νββ and Neutrino physics
Isotope T 0ν1/2 [yrs] Experiment |mee|limmin [eV] |mee|limmax [eV]
48Ca 5.8 × 1022 CANDLES 3.55 9.91
76Ge 1.9 × 1025 HDM 0.21 0.53
1.6 × 1025 IGEX 0.25 0.63
82Se 3.2 × 1023 NEMO-3 0.85 2.08
96Zr 9.2 × 1021 NEMO-3 3.97 14.39
100Mo 1.0 × 1024 NEMO-3 0.31 0.79
116Cd 1.7 × 1023 SOLOTVINO 1.22 2.30
130Te 2.8 × 1024 CUORICINO 0.27 0.57
136Xe 5.0 × 1023 DAMA 0.83 2.04
150Nd 1.8 × 1022 NEMO-3 2.35 5.08
23
Best limit on |mee| from best life-time?
0.01
0.1
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
Isotope
T1/2 = 5 x 1025 y
<m>IHmax
<m>IHmin, sin2 θ12 = 0.27
<m>IHmin, sin2 θ12 = 0.38
IH rangeNSMTue
JyIBMIBM
GCMPHFB
Pseudo-SU(3)
〈mν〉[
eV]
0.01
0.1
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
Isotope
T1/2 = 1026 y
<m>IHmax
<m>IHmin, sin2 θ12 = 0.27
<m>IHmin, sin2 θ12 = 0.38
IH rangeNSMTue
JyIBMIBM
GCMPHFB
Pseudo-SU(3)〈m
ν〉[
eV]
24
Inverted Ordering
Nature provides 2 scales:
〈mν〉IHmax ≃ c213
√
∆m2A and 〈mν〉IHmin ≃ c2
13
√
∆m2A cos 2θ12
if we know that ordering is inverted: ruling out Majorana nature
if limit below 〈mν〉IHmin: inverted ordering ruled out (if Majorana is assumed)
25
Ruling out Inverted Hierarchy
|mee|IHmin =(1 − |Ue3|2
)√
|∆m2A|
(1 − 2 sin2 θ12
)=
(0.015 . . . 0.020) eV 1σ
(0.010 . . . 0.024) eV 3σ
• small |Ue3|
• large |∆m2A|
• small sin2 θ12
Current 3σ range of sin2 θ12 gives factor of 2 uncertainty for |mee|IHmin
⇒ combined factor of 16 in M × t × B × ∆E
⇒ need precision determination of θ12
Dueck, W.R., Zuber, PRD 83
26
Ruling out Inverted Hierarchym3 = 0.001 eV
IH, 3σIH, BF
0.01
0.1
0.28 0.3 0.32 0.34 0.36 0.38
0.125
0.25
0.5
1
2
4
8
1
2
4
8
16
32
0.25
0.5
1
2
4
8
16
〈mν〉[
eV]
sin2 θ12
T0ν
1/2
[102
7y]
Dueck, W.R., Zuber, PRD 83
27
Ruling out Inverted Hierarchy
0.1
1
10
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
T1
/2 [
10
27 y
]
Isotope
0.27 < sin2(θ12) < 0.38
spread due to NMEs and due to θ12!!
IH will begin to be tested within this decade
28
Ruling out Inverted Hierarchy
0.1
1
10
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
T1/2
[10
27 y
]
Isotope
sin2(θ12) = 0.27NSMTue
JyIBM
GCMPHFB
Pseudo-SU(3)
0.1
1
10
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
T1/2
[10
27 y
]
Isotope
sin2(θ12) = 0.38
NSMTue
JyIBM
GCMPHFB
Pseudo-SU(3)
sin2 θ12 = 0.27 sin2 θ12 = 0.38
spread due to NMEs and due to θ12!!
IH will begin to be tested within this decade
29
Testing Inverted Hierarchy
lifetime to enter the IH regime
0.01
0.1
1
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
T1
/2 [
10
27 y
]
Isotope
mihmaxNSMTue
JyIBM
GCMPHFB
Pseudo-SU(3)
30
Testing neutrino models
UTBM =
√23
√13 0
−√
16
√13 −
√12
−√
16
√13
√12
with mass matrix
(mν)TBM = U∗TBM mdiag
ν U †TBM =
A B B
· 12 (A + B + D) 1
2 (A + B − D)
· · 12 (A + B + D)
A =1
3
(2 m1 + m2 e−2iα
), B =
1
3
(m2 e−2iα − m1
), D = m3 e−2iβ
⇒ Flavor symmetries. . .
Recent reviews: Altarelli, Feruglio 1002.0211; Ishimori; Kobayashi; Ohki;
Okada; Shimizu; Tanimoto, 1003.3552
31
The Zoo
Barry, W.R., PRD 81, updated regularly on
http://www.mpi-hd.mpg.de/personalhomes/jamesb/Table_A4.pdf
32
How to distinguish?
• LFV
• low scale scalars: Higgs, LFV
• compatible with GUTs?
• leptogenesis possible?
• neutrino mass observables
33
correlation with observables
12
PRD78:093007 (2008)
PRL 99 (2007) 151802
PRD72, 091301 (2005)
A4
0-nu DBD & FLAVOR0-nu DBD & FLAVOR
1/
Slide by J. Valle
34
Sum-rules in Models and 0νββ
constrains masses and Majorana phases
Barry, W.R., NPB 842
35
10-3
10-2
10-1
<m
ee>
(eV
)
0.01 0.1
mβ (eV)
10-3
10-2
10-1
0.01 0.1
3σ 30% error3σ exactTBM exact
2m2 +
m3 =
m1
m1 +
m2 =
m3
InvertedNormal
10-3
10-2
10-1
<m
ee>
(eV
)
0.01 0.1
mβ (eV)
10-3
10-2
10-1
0.01 0.1
3σ 30% error3σ exactTBM exact
Normal Inverted2/m
2 + 1/m
3 = 1/m
11/m
1 + 1/m
2 = 1/m
3
m1 + m2 − m3 = ǫ mmax
stable: new solutions not before ǫ ≃ 0.2
36
Sterile Neutrinos??
• LSND/MiniBooNE
• cosmology
• BBN
• reactor anomaly (Mention et al., PRD 83)
∆m241[eV
2] |Ue4| |Uµ4| ∆m251[eV
2] |Ue5| |Uµ5|3+2/2+3 0.47 0.128 0.165 0.87 0.138 0.148
1+3+1 0.47 0.129 0.154 0.87 0.142 0.163
or ∆m241 = 1.78 eV2 and |Ue4|2 = 0.151
Kopp, Maltoni, Schwetz, 1103.4570
37
Mass Orderings
ν4
m2
ν1,2,3
∆m241
m2
ν4
ν1,2,3
∆m241
ν4
ν5
∆m241
∆m251
m2
ν1,2,3
ν4
m2
ν5
ν1,2,3
∆m241
∆m251
νk
∆m2
k1
m2
νj
ν1,2,3
∆m2j1
3 active neutrinos can be normally or inversely ordered
1+3+1 scenarios first noticed in Goswami, W.R., JHEP 0710
38
Which one is sterile?
39
Sterile Neutrinos and 0νββ
• recall |mee|actNH can vanish and ||mee|actIH | ∼ 0.02 eV cannot vanish
• |mee| = | |Ue1|2m1 + |Ue2|2m2 e2iα + |U2e3|m3 e2iβ
︸ ︷︷ ︸
|mee|act+ |Ue4|2m4 e2iΦ1
︸ ︷︷ ︸
|mee|st|
• ∆m2st ≃ 1 eV2 and |Ue4| ≃ 0.15
• sterile contribution to 0νββ:
||mee|st| ≃√
∆m2st |Ue4|2 ≃ 0.02 eV
≫ |mee|NH
≃ |mee|IH
• ⇒ |mee|NH cannot vanish and |mee|IH can vanish!
Barry, W.R., Zhang, JHEP 1107
40
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
1+3, Normal, SN 1+3, Inverted, SI
3 ν (best-fit)3 ν (2σ)1+3 ν (best-fit)1+3 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)1+3 ν (best-fit)1+3 ν (2σ)
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
2+3, Normal, SSN 2+3, Inverted, SSI
3 ν (best-fit)3 ν (2σ)2+3 ν (best-fit)2+3 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)2+3 ν (best-fit)2+3 ν (2σ)
41
An exotic modifications of the neutrino picture
one neutrino could be (Pseudo-)Dirac, the other Majorana!
“Schizophrenic neutrinos”
For instance: inverted hierarchy, m2 Dirac:
|mee| = c212 c2
13
√
∆m2A
factor 2 larger than lower limit
Mohapatra et al., PLB 695
42
10-3
10-2
10-1
100
10-3
10-2
10-1
100
<m
ee>
(eV
)
10-3
10-2
10-1
100
0.1 1
Σ mν (eV)0.1 1
Normal Inverted
ν1
ν2
ν3
10-3
10-2
10-1
100
10-3
10-2
10-1
100
<m
ee>
(eV
)10
-3
10-2
10-1
100
0.1 1
Σ mν (eV)0.1 1
Normal Inverted
ν2 & ν
3
ν1 & ν
3
ν1 & ν
2
Barry, Mohapatra, W.R., PRD 83
43
Summary
• Standard Interpretation
– probes 1/Λseesaw
– neutrino parameters: m0, phase, mass ordering
– inverted hierarchy and θ12 !
– testing models!
– sterile neutrinos mix things up!
Note: 0νββ is a broad particle physics (not only neutrino!) experiment
44
W.R., 1106.1334
45
Summary
46
Neutrinoless Double Beta Decay Goldhaber-Grodzins-Sunyar Celebration
Sensitivity and backgrounds
T"0" = ln(2)N$t/UL(%)1-tonne 76Ge Example
slide by J.F. Wilkerson
47
M0ν =( gA
1.25
)2(
M0νGT − g2
V
g2A
M0νF
)
with
M0νGT = 〈f |∑
lk
σl σk τ−l τ−
k HGT(rlk, Ea)|i〉
M0νF = 〈f |∑
lk
τ−l τ−
k HF(rlk, Ea)|i〉
• rlk ≃ 1/p ≃ 1/(0.1 GeV) distance between the two decaying neutrons
• Ea average energy
• sum over all multipolarities!
• ’neutrino potential’ HGT,F(rlk, Ea) integrates over the virtual neutrino
momenta
• (if heavy particles exchanged: nucleon structure: gA = gA(0)/(1 − q2/M2A)2)
48
The 2νββ matrix elements can be written as
M2νGT =
∑
n
〈f |P
aσa τ−
a |n〉〈n|P
b
σb τ−b |i〉
En−(Mi−Mf )/2
M2νF =
∑
n
〈f |P
aτ−
a |n〉〈n|P
b
τ−b |i〉
En−(Mi−Mf )/2
• no direct connection to 0νββ. . .
• sum over 1+ states (low momentum transfer)
• adjust some parameters to reproduce 2νββ-rates
• 2νββ observed in 48Ca, 76Ge, 82Se, 96Zr, 100Mo (plus exc. state), 116Cd,128Te, 130Te, 150Nd (plus exc. state) with half-lives from 1018 to 1024 yrs
• can partly be tested with forward angle (= low momentum transfer) (p, n)
charge exchange reactions
49
A typical spectrum will look like. . .
⇒ first reason for multi-isotope determination
50
Testing NMEs
1
T 0ν1/2(A, Z)
= G(Q, Z) |M(A, Z) η|2
if you measured two isotopes:
T 0ν1/2(A1, Z1)
T 0ν1/2(A2, Z2)
=G(Q2, Z2) |M(A2, Z2)|2G(Q1, Z1) |M(A1, Z1)|2
systematic errors drop out, ratio sensitive to NME model
⇒ second reason for multi-isotope determination
51
plus uncertainty due to model details:
• Short range correlations:
– Jastrow function
– Unitary Correlation Operator method
– Coupled Cluster method
• model parameters
– correlated: e.g., gA, gpp, SRC
– uncorrelated: e.g., model space of single particle states
– some include errors, some don’t. . .
52
Convention issues
Through convention:
G0ν ∝ g4A
R2A
with RA = r0A1/3
• careful when comparing NMEs with different gA
• r0 = 1.1 fm or r0 = 1.2 fm
• different G0ν values are out there
Smolnikov, Grabmayr, PRC 81; Cowell, PRC 73;
Dueck, W.R., Zuber, PRD 83
53
Faessler, Fogli et al., PRD 79
ellipse major axis: SRC (blue, red) and gA
ellipse minor axis: gpp
54
Testing Mechanisms
1
T 0ν1/2(A, Z)
= G(Q, Z) |M(A, Z) η|2
if you measured two isotopes:
T 0ν1/2(A1, Z1)
T 0ν1/2(A2, Z2)
=Gx(Q2, Z2) |Mx(A2, Z2)|2Gx(Q1, Z1) |Mx(A1, Z1)|2
particle physics drops out, ratio of NMEs sensitive to mechanism
⇒ third reason for multi-isotope determination
55
Faessler, Fogli et al., PRD 79
ellipse major axis: SRC (blue, red) and gA
ellipse minor axis: gpp
56
Experimental Aspects
Number of events (measuring time t ≪ T 0ν1/2 life-time):
N = ln 2 a M t NA (T 0ν1/2)
−1
suppose there is no background:
• if you want 1026 yrs you need 1026 atoms
• 1026 atoms are 103 mols
• 103 mols are 100 kg
From now on you can only loose: efficiency, background, natural abundance,. . .
57
Need to forbid single β decay:
•• ⇒ even/even → even/even
• either direct (0νββ) or two simultaneous decays with virtual (energetically
forbidden) intermediate state (2νββ)
58
• 35 candidate isotopes
• 9 are interesting: 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 130Te, 136Xe, 150Nd
• Q-value vs. natural abundance vs. reasonably priced enrichment
vs. association with a well controlled experimental technique vs.. . .
⇒ no superisotope
0
5
10
15
20
25
30
35
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
Natu
ral abundance [%
]
Isotope
Natural abundance of different 0νββ candidate Isotopes
0
2
4
6
8
10
12
14
16
18
20
48Ca 76Ge 82Se 96Zr 100Mo 110Pd 116Cd 124Sn 130Te 136Xe 150Nd
G0
ν [10
-14 y
rs-1
]
Isotope
G0ν for 0νββ-decay of different Isotopes
T 0ν1/2 ∝ 1/a T 0ν
1/2 ∝ Q−5
59
typical model for NME: set of single particle states with a number of possible
wave function configurations; solve H in a mean background field
Approaches:
• Quasi-particle Random Phase Approximation (QRPA) (many single particle states, few
configurations)
• Nuclear Shell Model (NSM) (many configurations, few single particle states)
• Interacting Boson Model (IBM)
• Generating Coordinate Method (GCM)
• projected Hartree-Fock-Bogoliubov model (pHFB)
gives uncertainty due to different approach. . .
. . . plus uncertainty due to model details . . .
. . .plus convention issues
60
Statistical Analysis
consider scenario with “true values”:
Scenario m3 [eV] |mee| [eV] mβ [eV] Σ [eV]
QD 0.3 0.11 − 0.30 0.30 0.91
Combine measurements of 2, or all 3, mass approaches
Maneschg, Merle, W.R., EPL 85
61
QD with |mee|exp = 0.20 eV
• if ζ = 0: σ(m3) ≃ 15% at 3σ
• if ζ = 0.25: σ(m3) ≃ 25%
• if Σ wrong: reconstruction of m3 wrong by one order of magnitude
• leave Σ out: σ(m3) ≃ 50%
62
Recommended