Neutrinoless Double Beta Decay and Particle Physics Werner Rodejohann (MPIK, Heidelberg) Teilchentee 8/12/11 1
Neutrinoless Double Beta Decay and Particle Physics
Werner Rodejohann
(MPIK, Heidelberg)
Teilchentee
8/12/11
1
Outline
(A, Z) → (A, Z + 2) + 2 e− (0νββ) ⇒ Lepton Number Violation
• Introduction
• Standard Interpretation (neutrino physics)
• Non-Standard Interpretations (BSM 6= neutrino physics)
review on 0νββ and particle physics:
W.R., Int. J. Mod. Phys. E20, 1833-1930 (2011)
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
What is Neutrinoless Double Beta Decay?
(A, Z) → (A, Z + 2) + 2 e− (0νββ)
• second order in weak interaction: Γ ∝ G4F ⇒ rare!
• not to be confused with (A, Z) → (A, Z + 2) + 2 e− + 2 νe (2νββ)
(which occurs more often but is still rare)
4
Need to forbid single β decay:
•• ⇒ even/even → even/even
• either direct (0νββ) or two simultaneous decays with virtual (energetically
forbidden) intermediate state (2νββ)
5
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Slide by A. Giuliani
6
Upcoming experiments: exciting time!!
current best limit from 2001. . .
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 – –
multi-isotope determination good for 3 reasons
7
Experiment Isotope Mass of Sensitivity Status Start of
Isotope [kg] T 0ν1/2 [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∗∗
hline 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 ∼ 2013-15
KamLAND-Zen 136Xe 400 4 × 1026 in progress ∼ 2011
1000 1027 R&D ∼ 2013-15
SNO+ 150Nd 56 4.5 × 1024 in progress ∼ 2012
500 3 × 1025 R&D ∼ 2015
8
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
9
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
10
3 Reasons for Multi-isotope determination
1.) credibility
2.) test NME calculation
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
3.) test mechanism
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
11
Experimental Aspects
particle theory:
(T 0ν1/2)
−1 ∝ (particle physics)2
experimentally:
(T 0ν1/2)
−1 ∝
a M ε t without background
a ε
√
M t
B ∆Ebackground-dominated
Note: factor 2 in particle physics is combined factor of 16 in M × t × B × ∆E
12
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
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
13
∆L 6= 0: Neutrinoless Double Beta Decay
Im
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
∣∣
actually,
U2ei mi
q2 − m2i
≃ U2ei mi
q2
14
U =
0
BB@
c12 c13 s12 c13 s13 eiδ
−s12 c23 − c12 s23 s13 e−iδ
c12 c23 − s12 s23 s13 e−iδ
s23 c13
s12 s23 − c12 c23 s13 e−iδ
−c12 s23 − s12 c23 s13 e−iδ
c23 c13
1
CCA
=
0
BB@
1 0 0
0 c23 s23
0 −s23 c23
1
CCA
| {z }
0
BB@
c13 0 s13 e−iδ
0 1 0
−s13 eiδ 0 c13
1
CCA
| {z }
0
BB@
c12 s12 0
−s12 c12 0
0 0 1
1
CCA
| {z }
atmospheric and SBL reactor solar and
LBL accelerator LBL reactor
15
U =
0
BB@
c12 c13 s12 c13 s13 eiδ
−s12 c23 − c12 s23 s13 e−iδ
c12 c23 − s12 s23 s13 e−iδ
s23 c13
s12 s23 − c12 c23 s13 e−iδ
−c12 s23 − s12 c23 s13 e−iδ
c23 c13
1
CCA
=
0
BB@
1 0 0
0 c23 s23
0 −s23 c23
1
CCA
| {z }
0
BB@
c13 0 s13 e−iδ
0 1 0
−s13 eiδ 0 c13
1
CCA
| {z }
0
BB@
c12 s12 0
−s12 c12 0
0 0 1
1
CCA
| {z }
atmospheric and SBL reactor solar and
LBL accelerator LBL reactor0
BBB@
1 0 0
0q
1
2−
q1
2
0q
1
2
q1
2
1
CCCA
0
BB@
1 0 0
0 1 0
0 0 1
1
CCA
0
BBB@
q2
3
q1
30
−
q1
3
q2
30
0 0 1
1
CCCA
(sin2θ23 = 1
2) (sin2
θ13 = 0) (sin2θ12 = 1
3)
∆m2
A∆m2
A∆m
2
⊙
16
U =
0
BB@
c12 c13 s12 c13 s13 eiδ
−s12 c23 − c12 s23 s13 e−iδ
c12 c23 − s12 s23 s13 e−iδ
s23 c13
s12 s23 − c12 c23 s13 e−iδ
−c12 s23 − s12 c23 s13 e−iδ
c23 c13
1
CCA
=
0
BB@
1 0 0
0 c23 s23
0 −s23 c23
1
CCA
| {z }
0
BB@
c13 0 s13 e−iδ
0 1 0
−s13 eiδ 0 c13
1
CCA
| {z }
0
BB@
c12 s12 0
−s12 c12 0
0 0 1
1
CCA
| {z }
atmospheric and SBL reactor solar and
LBL accelerator LBL reactor0
BBB@
1 0 0
0q
1
2−
q1
2
0q
1
2
q1
2
1
CCCA
0
BB@
1 0 ǫ
0 1 0
−ǫ 0 1
1
CCA
0
BBB@
q2
3
q1
30
−
q1
3
q2
30
0 0 1
1
CCCA
(sin2θ23 = 1
2) (sin2
θ13 = ǫ2) (sin2
θ12 = 1
3)
∆m2
A∆m2
A∆m
2
⊙
17
Tri-bimaximal Mixing
UTBM =
√23
√13 0
−√
16
√13 −
√12
−√
16
√13
√12
Harrison, Perkins, Scott (2002)
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. . .
18
19
The usual plot
20
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
21
0νββ and Ue3
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
Ème
eÈ@e
VD Dm31
2 < 0
Dm312 > 0
sin2 2Θ13 = 0
Dis
favo
red
by
Co
sm
olo
gy
Disfavored by 0ΝΒΒ
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
Ème
eÈ@e
VD
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
Ème
eÈ@e
VD Dm31
2 < 0
Dm312 > 0
sin2 2Θ13 = 0.10
Dis
favo
red
by
Co
sm
olo
gy
Disfavored by 0ΝΒΒ
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
Ème
eÈ@e
VD
22
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(+)(-)
θ12
10-3
10-2
10-1
100
<m
ee>
(e
V)
0.1 1
Σ mi (eV)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.1 1
Inverted
CPV(+)(-)
Complementarity of |mee| = U2ei mi , mβ =
√
|Uei|2 m2i and Σ =
∑mi
23
Neutrino Mass Matrix
24
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
(for 1026 yrs you need 1026 atoms, which are 103 mols, which are 100 kg)
25
From life-time to particle physics: Nuclear Matrix Elements
26
From life-time to particle physics: Nuclear Matrix Elements
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 (Cowell, PRC 73; Smolnikov, Grabmayr, PRC 81;
Dueck, W.R., Zuber, PRD 83)
27
typical model for NME: set of single particle states with a number of possible
wave function configurations; solve H in a mean background field
• 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) (many single particle states, few configurations) (many single particle
states, few configurations)
• Generating Coordinate Method (GCM) (many single particle states, few configurations)
• projected Hartree-Fock-Bogoliubov model (pHFB)
tends to overestimate NMEs
tends to underestimate NMEs
28
From life-time to particle physics: Nuclear Matrix Elements
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
ν 76 82 96 100 128 130 136 150
A
0
1
2
3
4
5
6
7
8GCM
IBM
ISM
QRPA(J)
QRPA(T)
M0ν
Faessler, 1104.3700 Dueck, W.R., Zuber, PRD 83 Gomez-Cadenas et al., 1109.5515
to better estimate error range: correlations need to be understood
29
Faessler, Fogli et al., PRD 79
ellipse major axis: SRC (blue, red) and gA
ellipse minor axis: gpp
30
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
31
Experiment Isotope Mass of Sensitivity Status Start of Sensitivity
Isotope [kg] T 0ν1/2 [yrs] data-taking 〈mν〉 [eV]
GERDA 76Ge 18 3 × 1025 running ∼ 2011 0.17-0.42
40 2 × 1026 in progress ∼ 2012 0.06-0.16
1000 6 × 1027 R&D ∼ 2015 0.012-0.030
CUORE 130Te 200 6.5 × 1026∗ in progress ∼ 2013 0.018-0.037
2.1 × 1026∗∗ 0.03-0.066
MAJORANA 76Ge 30-60 (1 − 2) × 1026 in progress ∼ 2013 0.06-0.16
1000 6 × 1027 R&D ∼ 2015 0.012-0.030
EXO 136Xe 200 6.4 × 1025 in progress ∼ 2011 0.073-0.18
1000 8 × 1026 R&D ∼ 2015 0.02-0.05
SuperNEMO 82Se 100-200 (1 − 2) × 1026 R&D ∼ 2013-15 0.04-0.096
KamLAND-Zen 136Xe 400 4 × 1026 in progress ∼ 2011 0.03-0.07
1000 1027 R&D ∼ 2013-15 0.02-0.046
SNO+ 150Nd 56 4.5 × 1024 in progress ∼ 2012 0.15-0.32
500 3 × 1025 R&D ∼ 2015 0.06-0.12
Note: with same lifetime: 150Nd and 100Mo do best. . .
32
Inverted Ordering
Nature provides 2 scales:
〈mν〉IHmax ≃ c213
√
∆m2A and 〈mν〉IHmin ≃ c2
13
√
∆m2A cos 2θ12
requires O(1026 . . . 1027) yrs
33
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
34
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
35
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!!
Note: 100Mo and 150Nd do best. . .
36
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!!
Note: 100Mo and 150Nd do best. . .
37
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)
38
What’s more to do with 0νββ?
• neutrino mass scale m0:
|mee|QD= m0
∣∣c2
12 c213 + s2
12 c213 e2iα + s2
13 e2iβ∣∣
⇒ m0 ≤ |mee|expmin
1 + tan2 θ12
1 − tan2 θ12 − 2 |Ue3|2≤
1.6 eV (1σ)
2.4 eV (3σ)
• CP phase
|mee| = m0
∣∣c2
12 + s212 e2iα
∣∣
• distinguish neutrino models
39
Flavor Symmetry Models
suppose your model predicts TBM:
(mν)TBM =
x y y
· z + x y − z
· · z + x
m1 = x − y , m2 = x + 2y , m3 = x − y + 2z
if z = y + x/2:
m1 = x − y , m2 = x + 2y , m3 = 2x + y
and one has a neutrino mass sum-rule
m1 + m2 = m3
40
The Zoo (of A4 models)
Barry, W.R., PRD 81, updated regularly on
http://www.mpi-hd.mpg.de/personalhomes/jamesb/Table_A4.pdf
41
Sum-rules in Models and 0νββ
constrains masses and Majorana phases
Barry, W.R., NPB 842
42
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
43
Sterile Neutrinos??
• LSND/MiniBooNE
• cosmology
• BBN
• r-process nucleosynthesis in Supernovae
• 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
44
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
45
Which one is sterile?
46
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
︸ ︷︷ ︸
mactee
+ |Ue4|2m4 e2iΦ1
︸ ︷︷ ︸
mstee
|
• ∆m2st ≃ 1 eV2 and |Ue4| ≃ 0.15
• sterile contribution to 0νββ:
|mee|st ≃√
∆m2st |Ue4|2 ≃ 0.02 eV
≫ |mee|actNH
≃ |mee|actIH
• ⇒ |mee|NH cannot vanish and |mee|IH can vanish!
Barry, W.R., Zhang, JHEP 1107
47
Non-Standard Interpretations:
There is at least one other mechanism leading to Neutrinoless DoubleBeta Decay and its contribution is at least of the same order as the
light neutrino exchange mechanism
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
48
Schechter-Valle theorem: no matter what process, neutrinos are Majorana:
νe
W
e−
d u u
e−
d
νe
W
Blackbox diagram is 4 loop:
mν ∼ 1
(16π2)4MeV5
m4W
<∼ 10−23 eV
explicit calculation: Duerr, Lindner, Merle, 1105.0901
49
mechanism physics parameter current limit test
light neutrino exchange˛
˛
˛U2ei
mi
˛
˛
˛ 0.5 eV
oscillations,
cosmology,
neutrino mass
heavy neutrino exchange
˛
˛
˛
˛
˛
S2ei
Mi
˛
˛
˛
˛
˛
2 × 10−8 GeV−1 LFV,
collider
heavy neutrino and RHC
˛
˛
˛
˛
˛
˛
V2ei
Mi M4WR
˛
˛
˛
˛
˛
˛
4 × 10−16 GeV−5 flavor,
collider
Higgs triplet and RHC
˛
˛
˛
˛
˛
˛
(MR)ee
m2∆R
M4WR
˛
˛
˛
˛
˛
˛
10−15 GeV−1
flavor,
collider
e− distribution
λ-mechanism with RHC
˛
˛
˛
˛
˛
˛
Uei SeiM2
WR
˛
˛
˛
˛
˛
˛
1.4 × 10−10 GeV−2
flavor,
collider,
e− distribution
η-mechanism with RHC tan ζ˛
˛
˛Uei Sei
˛
˛
˛ 6 × 10−9
flavor,
collider,
e− distribution
short-range /R
˛
˛
˛λ′2111
˛
˛
˛
Λ5SUSY
ΛSUSY = f(mg, muL, m
dR, mχi
)
7 × 10−18 GeV−5 collider,
flavor
long-range /R
˛
˛
˛
˛
˛
˛
˛
sin 2θb λ′131 λ′
113
0
B
@
1
m2b1
− 1
m2b2
1
C
A
˛
˛
˛
˛
˛
˛
˛
∼GFq
mb
˛
˛
˛λ′131 λ′
113
˛
˛
˛
Λ3SUSY
2 × 10−13 GeV−2
1 × 10−14 GeV−3
flavor,
collider
Majorons |〈gχ〉| or |〈gχ〉|2 10−4 . . . 1spectrum,
cosmology
50
Distinguishing Mechanisms
The inverse problem of 0νββ
1.) Other observables (LHC, LFV, KATRIN, cosmology,. . .)
2.) Decay products (individual e− energies, angular correlations, spectrum,. . .)
3.) Nuclear physics (multi-isotope, 0νECEC, 0νβ+β+,. . .)
51
1.) Distinguishing via 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(+)(-)
θ12
10-3
10-2
10-1
100
<m
ee>
(e
V)
0.1 1
Σ mi (eV)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.1 1
Inverted
CPV(+)(-)
standard mechanism: KATRIN, cosmology
52
Energy Scale:
Note: standard amplitude for light Majorana neutrino exchange:
Al ≃ G2F
|mee|q2
≃ 7 × 10−18
( |mee|0.5 eV
)
GeV−5 ≃ 2.7 TeV−5
⇒ for 0νββ holds:
1 eV = 1 TeV
⇒ Phenomenology in colliders, LFV
53
Examples
• Fermions and no RHC:
A ∝ m
q2 − m2→
m for q2 ≫ m2
1
mfor q2 ≪ m2 µ 1�m²
µ m²
m»q
mass
rate
Note: maximum A corresponds to m ≃ 〈q〉: limits on O(mK) Majorana neutrinos from
K+ → π−µ+e+
• heavy scalar:
A ∝ 1
q2 − m2→ 1
m2
54
Heavy neutrinos
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
same diagram with U → S
Ah = G2F
S2ei
Mi≡ G2
F 〈 1m 〉 ⇒ 〈 1
m 〉 ≤ 5 × 10−8 GeV−1
literature value: 2 × 10−8 GeV−1 . . .
⇒ comparison on amplitude level is fine
55
Hea
vyneu
trin
os
Mitra,
Senjanovic,
Vissani,
1108.0004
56
An exact See-Saw Relation
Full mass matrix:
M =
0 mD
mTD MR
= U
mdiag
ν 0
0 MdiagR
UT with U =
N S
T V
• N is the PMNS matrix: non-unitary
• S = m†D (M∗
R)−1 describes mixing of heavy neutrinos with SM leptons
The upper left 0 in M gives exact see-saw relation Uαi (mν)i Uiβ = 0, or:
|N2ei mi| = |S2
ei Mi| <∼ 0.5 eV
Xing, PLB 679; W.R., PLB 684
compare withS2
ei
Mi< 2 × 10−8 GeV−1 and |Sei|2 ≤ 0.0052
57
exact see-saw relation gives stronger constraints!
1 1000 1e+06 1e+09 1e+12 1e+15 1e+18
Mi [GeV]
1e-28
1e-26
1e-24
1e-22
1e-20
1e-18
1e-16
1e-14
1e-12
1e-10
1e-08
1e-06
0,0001
0,01
|Se
i|2
|Sei|2 M_i
|Sei|2 /M_i
W.R., PLB 684
⇒ cancellations required to make heavy neutrinos contribute significantly to
0νββ
(other possibility: seesaw extensions)
58
TeV scale seesaw with sizable mixing
naively: mν = m2D/MR = (102)2/1015 GeV = 0.01 eV, mixing
S = mD/MR = mν/MR ≪≪ 1 and heavy neutrino contribution is negligible:
S2/MR = m2D/M3
R
MD = m
fǫ2 0 0
0 gǫ 0
0 0 1
M−1R = M−1
a b k
b c dǫ
k dǫ eǫ2
M/GeV m/MeV ǫ a k b c d e f g
5.00 0.935 0.02 1.00 1.35 0.90 1.4576 0.7942 0.2898 0.0948 0.485
gives successful mν and
∣∣∣∣
Al
Ah
∣∣∣∣=
G2F
q2 |mee|G2
F 〈 1m〉
≃ 10−2
59
Did that look natural to you?
60
Supersymmetry: short range
eL
χ
eL
χ
dc
dc
uL
e−L
e−L
uL
eL
χ
uL
χ
dc
dc
uL
e−L
uL
e−L
uL
uL
χ/g
χ/g
dc
dc
e−L
uL
uL
e−L
dR
χ
χ
eL
dc
dc
uL
e−L
e−L
uL
dR
χ/g
χ/g
uL
dc
dc
uL
e−L
uL
e−L
dR
χ/g
dRχ/g
dc
dc
uL
e−L
e−L
uL
A/R1≃ λ′2
111
Λ5SUSY
61
Supersymmetry: short range
interplay with LHC:
eL
χ
uL
χ
dc
dc
uL
e−L
uL
e−L
eL uL
u
dc
e−L u
dc
e−L
χ
“resonant selectron production”
σ ∝ λ′2111
s
Allanach, Kom, Paes, 0903.0347
62
tanβ = 10, A0 = 0, 10 fb−1
M0/GeV
M1/2/G
eV
T 0νββ1/2 (Ge) < 1.9 × 1025
yrs
100 > T 0νββ1/2 (Ge)/1025
yrs > 1.9
T 0νββ1/2 (Ge) > 1 × 1027
yrs
→ observation in white region in conflict with 0νββ
→ if 0νββ observed: dark yellow region tests R/ SUSY mechanism
→ light yellow region: no significant R/ contribution to 0νββ
63
Supersymmetry: long range
b
νe
bc
W
dc
dL
uL
e−L
e−L
uL
νe
d
bc
b
dc
Ab/R2
≃ GF1
qUei mb
λ′131 λ′
113
Λ3SUSY
λ′131 λ′
113
Λ2SUSY
0νββ B0-B0 mixing
64
“Inverse 0νββ”
this is not
76Se++ + e− + e− → 76Ge
but rather
e− + e− → W− + W−
Rizzo; Heusch, Minkowski; Gluza, Zralek; Cuypers, Raidal;. . .
65
Inverse Neutrinoless Double Beta Decay
1 10 100 1000 10000 1e+05 1e+06 1e+07 1e+08
Mi [GeV]
1e-14
1e-12
1e-10
1e-08
1e-06
0,0001
0,01
1
100
10000
1e+06
1e+08
σ [
fb]
e- e
- ---> W
- W
- , s = 16 TeV
2
|Sei|2 = 1.0
|Sei|2 = 0.0052
|Sei|2 = 5.0 10
-8 (M
i /GeV)
W.R., PRD 81
dσ
d cos θ=
G2F
32 π
{∑
(mν)i U2ei
(t
t − (mν)i+
u
u − (mν)i
)}2
66
Inverse Neutrinoless Double Beta Decay
Extreme limits:
• light neutrinos:
σ(e−e− → W−W−) =G2
F
4 π|mee|2 ≤ 4.2 · 10−18
( |mee|1 eV
)2
fb
⇒ way too small
• heavy neutrinos:
σ(e−e− → W−W−) = 2.6 · 10−3
( √s
TeV
)4 (S2
ei/Mi
5 · 10−8 GeV−1
)2
fb
⇒ too small
• √s → ∞:
σ(e−e− → W−W−) =G2
F
4π
(∑
U2ei (mν)i
)2
⇒ amplitude grows with√
s? Unitarity??
67
Unitarity
high energy limit√
s → ∞:
σ(e−e− → W−W−) =G2
F
4π
(∑
U2ei (mν)i
)2
↔ amplitude grows with√
s?
Answer: exact see-saw relation U2ei (mν)i = 0
M =
0 mD
mTD MR
= U
mdiag
ν 0
0 MdiagR
UT
if Higgs triplet is present: unitarity also conserved
σ(e−e− → W−W−) =G2
F
4π
((U2
ei (mν)i − (mL)ee
)2= 0
W.R., PRD 81
68
Inverse 0νββ and RPV SUSY
W = λ′111L1Q1D
c1 ⇒ e−e− → 4 jets
χ0
uLdc
eL
eL
λ′∗
111
uLdc
eL
eL
λ′∗
111
χ0
uL
dc
eL
eLλ′
111
uL
dceL
eLλ′
111
0νββ resonant selectron production
via gauge interactions
69
Cross section
σ(e−Le−L → e−L e−L ) =πα2|gL|4
s
2m2χ0
s + 2m2χ0 − 2m2
eL
[
L +2λ
(s + 2m2χ0 − 2m2
eL)2 − λ2
]
where
L = lns + 2m2
χ0 − 2m2eL
+ λ
s + 2m2χ0 − 2m2
eL− λ
λ = λ(s, m2eL
, m2eL
) =√
s2 − 4sm2eL
Keung, Littenberg, 1983
adjustable parameters
mχ0 , mg , meL , muL , mdR, λ′
111
squarks and gluinos decoupled;
competing decays eL → e χ0 and eL → jj
70
competing decays eL → e χ0 and eL → jj:
• 0νββ-limit goes with Λ5SUSY ⇒ λ′
111 can be O(1) and thus BR(eL → jj) >
BR(eL → e χ0)
• even for low masses, large BR(eL → jj) possible for narrow band around
meL − mχ0 ≪ meL
reconstruction:
• mass and width of eL: dijet invariant mass distribution
• BR(eL → jj) and thus λ′111: eL decays
• mass of χ0: rate of e−Le−L → e−L e−L
71
100 125 150 175 200 225 250 275
m∼χ0 [GeV]
100
125
150
175
200
225
250
275
m∼ e L
[G
eV
]
-6
-4
-2
0
2
BR
E(beam)
√s=500GeV
log10(σ/fb)
100 125 150 175 200 225 250 275
m∼χ0 [GeV]
100
125
150
175
200
225
250
275
m∼ e L
[G
eV
]
-6
-4
-2
0
2
BR
E(beam)
√s=500GeV
log10(σ/fb)
1.9 × 1025yrs 1.0 × 1027yrs
Kom, W.R., 1110.3220
72
2.) Distinguishing via decay products
SuperNEMO
0
2000
4000
6000
8000
10000
12000
0 0.5 1 1.5 2 2.5 3
E2e (MeV)
Nu
mb
er
of
ev
en
ts/0
.05
Me
V
(a)
100Mo7.369 kg.y
219,000bbevents
S/B = 40
NEMO 3 (Phase I)
0
2000
4000
6000
8000
10000
12000
-1 -0.5 0 0.5 1
cos(Θ)
Nu
mb
er
of
ev
en
ts
(b)
100Mo7.369 kg.y
219,000bbevents
S/B = 40
NEMO 3 (Phase I)
• source foils in between plastic scintillators
• individual electron energy, and their relative angle!
73
Distinguishing via decay products
Consider standard plus λ-mechanism
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
WR
NR
NR
νL
W
dR
dL
uR
e−R
e−L
uL
dΓdE1 dE2 d cos θ ∝ (1 − β1 β2 cos θ) dΓ
dE1 dE2 d cos θ ∝ (E1 − E2)2 (1 + β1 β2 cos θ)
Arnold et al., 1005.1241
74
Distinguishing via decay products
Defining asymmetries
Aθ = (N+ − N−)/(N+ + N−) and AE = (N> − N<)/(N> + N<)
-4 -2 0 2 40
50
100
150
200
250
300
Λ @10-7D
XmΝ\@m
eVD
-4 -2 0 2 40
50
100
150
200
250
300
Λ @10-7D
XmΝ\@m
eVD
75
3.) Distinguishing via nuclear physics
Gehman, Elliott, hep-ph/0701099
3 to 4 isotopes necessary to disentangle mechanism
76
Summary
77