Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Neutrinoless Double Beta Decay and Particle Physics
Werner Rodejohann
(MPIK, Heidelberg)
01/10/2012
1
2
Outline
(A,Z) → (A,Z + 2) + 2 e− (0νββ) ⇒ Lepton Number Violation
• 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
reviews on 0νββ:
Int. J. Mod. Phys. E20, 1833 (2011); Focus issue J. Phys. G [1206.2560]
3
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
4
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
5
Upcoming/running experiments: exciting time!!
best limit was from 2001. . .
Name Isotope source = detector; calorimetric with source 6= detector
high energy res. low energy res. event topology event topology
AMoRE 100Mo X – – –
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
6
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
7
Experimental Aspects
particle physics:
(T 0ν1/2)−1 ∝ (particle physics)2
experimentally:
(T 0ν1/2)−1 ∝
aM 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
8
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
9
∆L 6= 0: Neutrinoless Double Beta DecayIm
Rem
mm
ee
ee
ee
(1)
(3)
(2)
| |
| || | e
e.
.
eem
2iβ2iα
Amplitude proportional to coherent sum (“effective mass”):
|mee| ≡∣∣∑
U2eimi∣∣ =
∣∣|Ue1|2 m1 + |Ue2|2 m2 e2iα + |Ue3|2 m3 e2iβ
∣∣
7 out of 9 parameters of mν !
10
The usual plot
11
The usual plot
0.001 0.01 0.1m
light (eV)
10-4
10-3
10-2
10-1
100<
mee
> (
eV)
Normal
= 0.4 eV
mβ =
0.2
eV
Σ =
1 e
V
Σ =
0.2
eV
Σ =
0.1
eV
Σ =
0.5
eV
mβ =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
0.001 0.01 0.1
Inverted
= 0.4 eV
Σ =
0.2
eV
Σ =
0.1
eV
Σ =
0.5
eV
Σ =
1 e
V
mβ =
0.2
eV
mβ =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
12
Plot against other observables
0.01 0.1mβ (eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
Normal
= 0.4 eV
Σ =
0.1
eV
Σ =
0.2
eV
Σ =
0.5
eV
Σ =
1 e
V
mβ =
0.2
eV
Σ =
1 e
Vm
β =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
0.01 0.1
Inverted
= 0.4 eV
Σ =
0.1
eV
Σ =
0.2
eV
Σ =
0.5
eV
Σ =
1 e
V
mβ =
0.2
eV
mβ =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
Complementarity of |mee| = U2ei mi and mβ =√
|Uei|2m2i and Σ =∑
mi
13
Plot against other observables
10-3
10-2
10-1
100
<m
ee>
(eV
)
0.1 1
Σ mi (eV)
Normal
= 0.4 eV
Σ =
0.1
eV
Σ =
0.2
eV
Σ =
0.5
eV
Σ =
1 e
V
mβ =
0.2
eV
mβ =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
0.1 1
Inverted
= 0.4 eV
Σ =
0.1
eV
Σ =
0.2
eV
Σ =
0.5
eV
Σ =
1 e
V
mβ =
0.2
eV
mβ =
0.3
5 e
V
CPV(+,+)(+,-)(-,+)(-,-)
Complementarity of |mee| = U2ei mi and mβ =√
|Uei|2m2i and Σ =∑
mi
14
Neutrino Mass Matrix
15
0νββ and Ue3
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
ÈmeeÈ@eVD Dm31
2 < 0
Dm312 > 0
sin2 2Θ13 = 0
Dis
fav
ore
db
yC
osm
olo
gy
Disfavored by 0ΝΒΒ
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
ÈmeeÈ@eVD
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
ÈmeeÈ@eVD Dm31
2 < 0
Dm312 > 0
sin2 2Θ13 = 0.10
Dis
fav
ore
db
yC
osm
olo
gy
Disfavored by 0ΝΒΒ
0.0001 0.001 0.01 0.1 1m @eVD
0.0001
0.001
0.01
0.1
1
ÈmeeÈ@eVD
Lindner, Merle, W.R., hep-ph/0512143
16
Vanishing effective mass. . .
conspiracy of 7 parameters?
(L1, L2) L3 (νR1 , νR2) eR µR τR (φ1, φ2) χ
S3 2∗ 1S 2 1S 1S 1S 2 1S
Z3 ω ω ω ω 1 ω2 ω ω
leads to |mee| = 0 and
tan2 θ13 =
√
∆m2⊙∆m2A
sin2 θ12
W.R., Tanimoto, Watanabe, 1201.4936
17
From life-time to particle physics: Nuclear Matrix Elements
SM vertex
Nuclear Process Nucl
Σi
νiUei
e
W
νi
e
W
Uei
Nucl
18
From life-time to particle physics: Nuclear Matrix Elements
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′0ν
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
0
1
2
3
4
5
6
7
8
M0ν
76Ge
82Se
96Zr 100Mo
130Te 136Xe
150Nd
RQRPANSMIBM-2PHFBEDF
Dueck, W.R., Zuber, PRD 83 Gomez-Cadenas et al., 1109.5515 Vogel, 1208.1992
(current) uncertainty of factor 2 to 3, directly translates into uncertainty on
particle physics parameter
19
Isotope T 0ν1/2 [yrs] Experiment |mee|limmin [eV] |mee|
limmax [eV]
48Ca 5.8× 1022 CANDLES 3.55 9.91 ×0.9876Ge 1.9× 1025 HDM 0.21 0.53 ×1.04
1.6× 1025 IGEX 0.25 0.63 ×1.0482Se 3.2× 1023 NEMO-3 0.85 2.08 ×1.0496Zr 9.2× 1021 NEMO-3 3.97 14.39 ×1.06
100Mo 1.0× 1024 NEMO-3 0.31 0.79 ×1.06116Cd 1.7× 1023 SOLOTVINO 1.22 2.30 ×1.06130Te 2.8× 1024 CUORICINO 0.27 0.57 ×1.09136Xe 1.6× 1025 EXO-200 0.15 0.36 ×1.10150Nd 1.8× 1022 NEMO-3 2.35 5.08 ×1.12
(recent reevaluation of phase space factors by Iachello+Kotila)
HDM limit reached/improved by EXO-200 !
20
EXO-200 vs. Klapdor
T−1Ge = GGe |MGe|2 |mee|2 =
(2× 1025 yrs
)−1
T−1Xe = GXe |MXe|2 |mee|2 ≤
(1.6× 1025 yrs
)−1
Ge-claim is ruled out when
TXe ≥ 2.9× 1024∣∣∣∣
MGeMXe
∣∣∣∣
2
yrs
With compilation from Vogel, 1208.1992:
∣∣∣∣
MGeMXe
∣∣∣∣
2
≃
4.0 (RQRPA) ⇒ TXe ≥ 1.2× 1025 yrs4.2 (NSM) ⇒ TXe ≥ 1.2× 1025 yrs2.5 (IBM-2) ⇒ TXe ≥ 7.3× 1024 yrs1.2 (EDF) ⇒ TXe ≥ 3.5× 1024 yrs
21
Xe (yr)136 1/2T
2410 2510 26102410
2510
2610
68%
CL
EXO
-200
(thi
s wo
rk)
90%
CL
Kam
LAND
-ZEN
90%
CL
RQRP
A-1
QRPA
-2
IBM-
2
GCM
NSM
KK&K 68% CL
Heidelberg-Moscow90% CL
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.2
0.3
0.4
0.5
0.6
0.7
0.2
0.3
0.4
0.5
0.3
0.4
0.5
0.6
0.7
0.80.9
1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
Ge
(yr)
76 1/
2T
2410
2510
2610
EXO, 1205.5608
22
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 running ∼ 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 running ∼ 2011 0.03-0.07
1000 1027 R&D ∼ 2013-15 0.02-0.046
SNO+ 150Nd 132 1.8 × 1025 in progress ∼ 2014 0.09-0.18
(with same lifetime: 150Nd and 100Mo do best. . .)
23
With 0νββ one can
• test Majorana nature of neutrinos
• probe neutrino mass scale
• test inverted ordering
• extract Majorana phase
• test flavor symmetry models: neutrino mass “sum-rules”
24
Inverted Ordering
Nature provides 2 scales:
〈mν〉IHmax ≃ c213√
∆m2A and 〈mν〉IHmin ≃ c213√
∆m2A cos 2θ12
requires O(1026 . . . 1027) yrs
25
Ruling out Inverted Hierarchy
|mee|IHmin =(1− |Ue3|2
)√
|∆m2A|(1− 2 sin2 θ12
)=
(0.016 . . . 0.020) eV 1σ
(0.013 . . . 0.024) eV 3σ
• small |Ue3|
• large |∆m2A|
• small sin2 θ12Current 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
Sterile Neutrinos and 0νββ
• recall: |mee|actNH can vanish and |mee|actIH ∼ 0.03 eV cannot vanish
• |mee| = | |Ue1|2 m1 + |Ue2|2 m2 e2iα + |U2e3|m3 e2iβ︸ ︷︷ ︸
mactee
+ |Ue4|2 m4 e2iΦ1︸ ︷︷ ︸
mstee
|
• ∆m2st ≃ 1.8 eV2 and |Ue4| ≃ 0.13
• sterile contribution to 0νββ (assuming 1+3):
|mee|st ≃√
∆m2st |Ue4|2 ≃ 0.03 eV
≫ |mee|actNH≃ |mee|actIH
• ⇒ |mee|NH cannot vanish and |mee|IH can vanish!
usual phenomenology gets completely turned around!
27
Usual plot gets completely turned around!
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
Normal Inverted
3 ν (best-fit)1+3 ν (best-fit)
0.001 0.01 0.1
3 ν (best-fit)1+3 ν (best-fit)
[10
28
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
∆m2k1
m2
νj
ν1,2,3
∆m2j1
3 active neutrinos can be normally or inversely ordered
29
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
)
3+1, Normal, NS 3+1, Inverted, IS
3 ν (best-fit)3 ν (2σ)3+1 ν (best-fit)3+1 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)3+1 ν (best-fit)3+1 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)
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
3+2, Normal, NSS 3+2, Inverted, ISS
3 ν (best-fit)3 ν (2σ)3+2 ν (best-fit)3+2 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)3+2 ν (best-fit)3+2 ν (2σ)
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
1+3+1, Normal, SNSa 1+3+1, Inverted, SISa
3 ν (best-fit)3 ν (2σ)1+3+1 ν (best-fit)1+3+1 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)1+3+1 ν (best-fit)1+3+1 ν (2σ)
0.001 0.01 0.1
mlight
(eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
1+3+1, Normal, SNSb 1+3+1, Inverted, SISb
3 ν (best-fit)3 ν (2σ)1+3+1 ν (best-fit)1+3+1 ν (2σ)
0.001 0.01 0.1
3 ν (best-fit)3 ν (2σ)1+3+1 ν (best-fit)1+3+1 ν (2σ)
Barry, W.R., Zhang, JHEP 1107
30
Sterile Neutrinos, Seesaw and 0νββ
• if the eV-steriles are from seesaw: individual cancellations in flavor symmetrymodels, e.g.:
U2e2 m2 + U2e4 m4 = 0
• if seesaw scale is below 100 MeV: No double beta decay!
6∑
i=1
U2ei mi = 0 since M =
0 mD
mTD MR
= U
mdiagν 0
0 MdiagR
UT
Barry, W.R., Zhang, JCAP 1201
31
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
WL
WR
NR
NR
νL
WL
dL
dL
uL
e−R
e−L
uL
d̃R
χ/g̃
d̃Rχ/g̃
dc
dc
uL
e−L
e−L
uL
W
W
∆−−
dL
dL
uL
e−L
e−L
uL
√
2g2vL hee
ũL
ũL
χ/g̃
χ/g̃
dc
dc
e−L
uL
uL
e−L
W
W
dL
dL
uL
e−L
χ0
χ0
e−L
uL
Clear experimental signature:
KATRIN and/or cosmology see nothing but 0νββ does
32
Schechter-Valle theorem: no matter what process, neutrinos are Majorana:
νe
W
e−
d u u
e−
d
νe
W
is 4 loop diagram: mν ∼1
(16π2)4MeV5
m4W
mechanism physics parameter current limit test
light neutrino exchange∣
∣
∣U2eimi
∣
∣
∣ 0.4 eV
oscillations,
cosmology,
neutrino mass
heavy neutrino exchange
∣
∣
∣
∣
∣
S2ei
Mi
∣
∣
∣
∣
∣
2 × 10−8 GeV−1LFV,
collider
heavy neutrino and RHC
∣
∣
∣
∣
∣
∣
V2ei
Mi M4WR
∣
∣
∣
∣
∣
∣
4 × 10−16 GeV−5flavor,
collider
Higgs triplet and RHC
∣
∣
∣
∣
∣
∣
(MR)ee
m2∆R
M4WR
∣
∣
∣
∣
∣
∣
10−15 GeV−5flavor,
collider
e− distribution
λ-mechanism with RHC
∣
∣
∣
∣
∣
∣
Uei S̃eiM2
WR
∣
∣
∣
∣
∣
∣
1.4 × 10−10 GeV−2flavor,
collider,
e− distribution
η-mechanism with RHC tan ζ∣
∣
∣Uei S̃ei
∣
∣
∣ 6 × 10−9flavor,
collider,
e− distribution
short-range /R
∣
∣
∣λ′2111
∣
∣
∣
Λ5SUSY
ΛSUSY = f(mg̃, mũL, m
d̃R, mχi
)
7 × 10−18 GeV−5collider,
flavor
long-range /R
∣
∣
∣
∣
∣
∣
∣
sin 2θb λ′131 λ′113
1
m2b̃1
− 1m2
b̃2
∣
∣
∣
∣
∣
∣
∣
∼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 . . . 1
spectrum,
cosmology
34
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+,. . .)
35
1.) Distinguishing via other Observables
0.01 0.1mβ (eV)
10-3
10-2
10-1
100
<m
ee>
(eV
)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.01 0.1
Inverted
CPV(+)(-)
θ12
10-3
10-2
10-1
100
<m
ee>
(eV
)0.1 1
Σ mi (eV)
Normal
CPV(+,+)(+,-)(-,+)(-,-)
0.1 1
Inverted
CPV(+)(-)
standard mechanism: KATRIN, cosmology
36
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
if new heavy particles are exchanged:
Ah ≃c
M5
⇒ for 0νββ holds:
1 eV = 1 TeV
⇒ Phenomenology in colliders, LFV
37
Examples
• R-parity violating supersymmetry (Allanach, Paes, Kom)
• TeV seesaw neutrinos (Ibarra, Petcov et al.; Mitra, Senjanovic, Vissani)
• Left-right symmetric theories (Senjanovic et al.; Goswami et al.)
• Color seesaw (Choubey, Duerr, Mitra, W.R.)
. . .focus only on one example here. . .
38
Left-right symmetry
WR
WR
dR
dR
uR
e−R
e−R
uR
NRi
WR WR
ūR
dR
e−R e−
R
dR
ūR
NRi
Senjanovic et al., 1011.3522; 1103.1627
39
WR WR
ūR
dR
e−R e−
R
dR
ūR
NRi[T
eV
]
Nm
0
1
2
[TeV] RW
m1 1.5 2 2.5
-1Ldt = 2.1 fb∫
, Expectedµ+eµµWith mixing, ee+, Observedµ+eµµWith mixing, ee+
, ExpectedµµNo mixing, ee+, ObservedµµNo mixing, ee+
SS+OS
MajoranaN
= 7 TeVs
forbid
den
RWm ≥
Nm
ATLAS
40
Left-right symmetry
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
W
W
dL
dL
uL
e−L
e−L
uL
NRi
WR
WR
dR
dR
uR
e−R
e−R
uR
NRi
WL
WL
δ−−L
dL
dL
uL
e−L
e−L
uL
√
2g2vL hee
WR
WR
δ−−R
dR
dR
uR
e−R
e−R
uR
√
2g2vR hee
WL
WR
NR
NR
νL
WL
dL
dL
uL
e−R
e−L
uL
WR
NR
NR
νL
WL
dR
dL
uR
e−R
e−L
uL
41
Left-right symmetry
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
W
W
dL
dL
uL
e−L
e−L
uL
NRi
WR
WR
dR
dR
uR
e−R
e−R
uR
NRi
U2ei miS2eiMi
V 2eiM4WR Mi
WL
WL
δ−−L
dL
dL
uL
e−L
e−L
uL
√
2g2vL hee
WR
WR
δ−−R
dR
dR
uR
e−R
e−R
uR
√
2g2vR hee
WL
WR
NR
NR
νL
WL
dL
dL
uL
e−R
e−L
uL
WR
NR
NR
νL
WL
dR
dL
uR
e−R
e−L
uL
≤ U2ei miM2∆L
V 2ei MiM4WR M
2∆R
Uei Tei tan ζUei TeiM2WR
42
Left-right symmetry
W
νi
νi
W
dL
dL
uL
e−L
e−L
uL
Uei
q
Uei
W
W
dL
dL
uL
e−L
e−L
uL
NRi
WR
WR
dR
dR
uR
e−R
e−R
uR
NRi
0.4 eV 2× 10−8 GeV−1 4× 10−16 GeV−5
WL
WL
δ−−L
dL
dL
uL
e−L
e−L
uL
√
2g2vL hee
WR
WR
δ−−R
dR
dR
uR
e−R
e−R
uR
√
2g2vR hee
WL
WR
NR
NR
νL
WL
dL
dL
uL
e−R
e−L
uL
WR
NR
NR
νL
WL
dR
dL
uR
e−R
e−L
uL
— 10−15 GeV−5 6× 10−9 1.4× 10−10 GeV−2
43
Simple and interesting scenario
mν = ML −mD M−1R mTD = vL h−mD (vR f)−1 mTDsuppose ML dominates in mν and h = f : ⇒ MR ∝ mν
Triplet can mediate µ → 3e at tree-level: m∆ ≫ Mi
⇒ ANR ≃ G2F(
mWMWR
)4 ∑ V 2eiMi
∝∑ U2ei
mi
Tello et al., 1011.3522
44
Interplay of diagrams in left-right symmetry
Interference of diagrams, constraints from LFV, neutrino data,. . .
0.0001 0.001 0.01 0.1
mlight (eV)
1026
1028
1030
1032
[T1
/2] δ
R (
yrs)
GERDA 40kg
GERDA 1T
Normal
0.0001 0.001 0.01 0.1
Inverted
0.0001 0.001 0.01 0.1
mlight (eV)
1024
1026
1028
1030
[T1
/2] N
R (
yrs)
GERDA 40kg
GERDA 1T
Normal
0.0001 0.001 0.01 0.1
Excluded by HDM
InvertedmδR = 3.5 TeVmδR
= 2 TeV
mδR = 1 TeV
0.0001 0.001 0.01 0.1
mlight (eV)
1024
1026
1028
1030
[T1
/2] t
yp
e I
I (yrs)
GERDA 40kg
GERDA 1T
Normal
mδR = 3.5 TeV
mδR = 2 TeV
mδR = 1 TeV
[T1/2]ν+NR
0.0001 0.001 0.01 0.1
Inverted
mδR = 3.5 TeV
mδR = 2 TeV
mδR = 1 TeV
[T1/2]ν+NR
Barry, W.R., to appear; see also Goswami et al., 1204.2527
45
Cleanest Probe: e− e− collisions: “inverse 0νββ”
• LR-symmetry: (Barry, Dorame, W.R., 1204.3365)
WR
NR
NR
νL
WL
dR
dL
uR
e−R
e−L
uL
NRi
νLi
NRi
e−
e−
WR
WL
T ∗ei
Uei
2500. 2600. 2700. 2800. 2900. 3000.
10-6
10-5
10-4
0.001
0.01
0.1
e−e− → W−L W−
R , s = 9 TeV2
σ[fb]
mWR[GeV]
• SUSY: (Kom, W.R., 1110.3220)
χ̃0
uLdc
ẽL
eL
λ′∗111
uLdc
ẽL
eL
λ′∗111
χ̃0
uL
dc
ẽL
eLλ′111
uL
dcẽL
eLλ′111
100 125 150 175 200 225 250 275
m∼χ0 [GeV]
100
125
150
175
200
225
250
275
m∼ eL [
GeV]
-6
-4
-2
0
2
BR
E(beam)
√s=500GeV
log10(σ/fb)
46
“Inverse 0νββ”
this is not
76Se++ + e− + e− → 76Ge
but rather
e− + e− → W− +W−
Rizzo; Heusch, Minkowski; Gluza, Zralek; Cuypers, Raidal;. . .
47
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=
G2F32π
{∑
(mν)i U2ei(
t
t− (mν)i+
u
u− (mν)i
)}2
48
Inverse Neutrinoless Double Beta Decay
Extreme limits:
• light neutrinos:
σ(e−e− → W−W−) = G2F
4π|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 (S2ei/Mi
5 · 10−8GeV−1)2
fb
⇒ too small• √s → ∞:
σ(e−e− → W−W−) = G2F
4π
(∑
U2ei (mν)i)2
⇒ amplitude grows with √s? Unitarity??
49
Unitarity
high energy limit√s → ∞:
σ(e−e− → W−W−) = G2F
4π
(∑
U2ei (mν)i)2
↔ amplitude grows with √s?Answer: exact see-saw relation U2ei (mν)i = 0
M =
0 mD
mTD MR
= U
mdiagν 0
0 MdiagR
UT
if Higgs triplet is present: unitarity also conserved
σ(e−e− → W−W−) = G2F
4π
((U2ei (mν)i − (mL)ee
)2= 0
W.R., PRD 81
50
Inverse 0νββ and RPV SUSY
W = λ′111L1Q1Dc1 ⇒ e−e− → 4 jets
χ̃0
uLdc
ẽL
eL
λ′∗111
uLdc
ẽL
eL
λ′∗111
χ̃0
uL
dc
ẽL
eLλ′111
uL
dcẽL
eLλ′111
0νββ resonant selectron production
via gauge interactions
51
Cross section
σ(e−Le−L → ẽ−L ẽ−L ) =
πα2|gL|4s
2m2χ̃0
s+ 2m2χ̃0 − 2m2ẽL
[
L+2λ
(s+ 2m2χ̃0 − 2m2ẽL)2 − λ2
]
where
L = lns+ 2m2χ̃0 − 2m2ẽL + λs+ 2m2χ̃0 − 2m2ẽL − λ
λ = λ(s,m2ẽL ,m2ẽL) =
√
s2 − 4sm2ẽLKeung, Littenberg, 1983
adjustable parameters
mχ̃0 , mg̃ , mẽL , mũL , md̃R , λ′111
squarks and gluinos decoupled;
competing decays ẽL → e χ̃0 and ẽL → jj
52
competing decays ẽL → e χ̃0 and ẽL → jj:
• 0νββ-limit goes with Λ5SUSY ⇒ λ′111 can be O(1) and thus BR(ẽL → jj) >BR(ẽL → e χ̃0)
• even for low masses, large BR(ẽL → jj) possible for narrow band aroundmẽL −mχ̃0 ≪ mẽL
reconstruction:
• mass and width of ẽL: dijet invariant mass distribution
• BR(ẽL → jj) and thus λ′111: ẽL decays
• mass of χ̃0: rate of e−Le−L → ẽ−L ẽ−L
53
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)
250 500 750 1000 1250 1500 1750
m∼χ0 [GeV]
250
500
750
1000
1250
1500
1750
m∼ e L
[G
eV]
-3
-2
-1
0
BR
E(beam)
√s=3000GeV
log10(σ/fb)
1.9× 1025 yrs 1.0× 1027 yrsKom, W.R., 1110.3220
54
Summary
55
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 e
ven
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 e
ven
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!
56
2.) 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
WL
dR
dL
uR
e−R
e−L
uL
dΓdE1 dE2 d cos θ
∝ (1− β1 β2 cos θ) dΓdE1 dE2 d cos θ ∝ (E1 − E2)2 (1 + β1 β2 cos θ)
Arnold et al., 1005.1241
57
2.) Distinguishing via decay products
Defining asymmetries
Aθ = (N+ −N−)/(N+ +N−) and AE = (N> −N +N
3.) Distinguishing via nuclear physics
Gehman, Elliott, hep-ph/0701099
3 to 4 isotopes necessary to disentangle mechanism
59
to better estimate error range: correlations need to be understood:
Faessler, Fogli et al., PRD 79
ellipse major axis: SRC (blue, red) and gA
ellipse minor axis: gpp
60
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
WL
dR
dL
uR
e−R
e−L
uL
dΓdE1 dE2 d cos θ
∝ (1− β1 β2 cos θ) dΓdE1 dE2 d cos θ ∝ (E1 − E2)2 (1 + β1 β2 cos θ)
Arnold et al., 1005.1241
61
Supersymmetry: short range
ẽL
χ
ẽL
χ
dc
dc
uL
e−L
e−L
uL
ẽL
χ
ũL
χ
dc
dc
uL
e−L
uL
e−L
ũL
ũL
χ/g̃
χ/g̃
dc
dc
e−L
uL
uL
e−L
d̃R
χ
χ
ẽL
dc
dc
uL
e−L
e−L
uL
d̃R
χ/g̃
χ/g̃
ũL
dc
dc
uL
e−L
uL
e−L
d̃R
χ/g̃
d̃Rχ/g̃
dc
dc
uL
e−L
e−L
uL
A/R1 ≃λ′2111Λ5SUSY
62
Supersymmetry: short range
interplay with LHC:
ẽL
χ
ũL
χ
dc
dc
uL
e−L
uL
e−L
ẽL ũL
u
dc
e−L u
dc
e−L
χ
“resonant selectron production”
σ̂ ∝ λ′2111
ŝ
Allanach, Kom, Paes, 0903.0347
63
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
64
Supersymmetry: long range
b̃
νe
b̃c
W
dc
dL
uL
e−L
e−L
uL
ν̃e
d
bc
b
dc
Ab/R2 ≃ GF1
qUei mb
λ′131 λ′113
Λ3SUSY
λ′131 λ′113
Λ2SUSY0νββ B0-B̄0 mixing
65
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 + 2zif z = y + x/2, then:
m1 = x− y , m2 = x+ 2y , m3 = 2x+ y
and one has a neutrino mass sum-rule
m1 +m2 = m3
66
The Zoo (of A4 models)
Barry, W.R., PRD 81, updated regularly on
http://www.mpi-hd.mpg.de/personalhomes/jamesb/Table_A4.pdf
67
Sum-rules in Models and 0νββ
constrains masses and Majorana phases
Barry, W.R., NPB 842
68
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 = ǫmmaxstable: new solutions not before ǫ ≃ 0.2
69