Neutrinoless Double Beta Decay
Michael Duerr
Max-Planck-Institut für Kernphysik, Heidelberg, Germany
Kanazawa University, 17 February 2012
Based on JHEP 06 (2011) 091,
Phys. Rev. D84 (2011) 093004, and
arXiv:1201.3031 [hep-ph]
together with: S. Choubey, M. Lindner, A. Merle,
M. Mitra, W. Rodejohann, K. Zuber
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
1
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
2
Basics of neutrino physics and neutrinoless double beta decay
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
3
Basics of neutrino physics and neutrinoless double beta decay
Neutrinos are massive
9
-5
8
2
2
∆m21 [10 eV ]
8.5
7.5
★
★
7
6.5
0.3
0.5
0.4
0.6
0.7
0
0.01 0.02 0.03 0.04 0.05 0.06
2
2
sin θ13
tan θ12
-3
2.5
2
2
2
∆m31 [10 eV ]
3
-2
★
★
-2.5
-3
0.3
0.5
1
2
3
0
0.01 0.02 0.03 0.04 0.05 0.06
2
2
tan θ23
sin θ13
Neutrino oscillation
experiments show
that neutrinos have
a mass.
180
120
δCP
60
Oscillation parameters
0
★
-60
Mohapatra et al., arXiv:hep-ph/0412099
-120
-180
0
0.01 0.02 0.03 0.04 0.05 0.06
2
sin θ13
Gonzalez-Garcia et al., JHEP 04 (2010) 056
?
⇔
Michael Duerr (MPIK)
Is lepton number conserved
in Nature?
→ 0νββ
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
4
Basics of neutrino physics and neutrinoless double beta decay
Basics of neutrinoless double beta decay
Modes of ββ decay:
(Z , A) → (Z + 2, A) + 2e − + 2ν̄e
(Z , A) → (Z + 2, A) + 2e −
Total decay rate of 0νββ:
2
uL
N(E ) 6
W
νL
νL
(0νββ)
mee =
0ν −1
Γ0ν / ln 2 = (T1/2
) = |mee |2 M0ν G 0ν (Q, Z )
dL
(2νββ)
P
i
2
Uei
mi
M0ν : nuclear matrix element
G 0ν (Q, Z ): phase space factor
2νββ
0νββ
eL−
eL−
W
dL
Michael Duerr (MPIK)
-
uL
Neutrinoless Double Beta Decay
Q
E
Kanazawa University, 17 Feb 2012
5
Basics of neutrino physics and neutrinoless double beta decay
Basics of neutrinoless double beta decay
Modes of ββ decay:
(Z , A) → (Z + 2, A) + 2e − + 2ν̄e
(Z , A) → (Z + 2, A) + 2e −
(2νββ)
(0νββ)
Total decay rate of 0νββ:
mee =
Nucleus
76 Ge
100 Mo
130 Te
136 Xe
G 0ν (Q, Z )/10−25 y−1 eV
0.30
2.19
2.12
2.26
−2
i
2
Uei
mi
M0ν : nuclear matrix element
2
0ν −1
Γ0ν / ln 2 = (T1/2
) = |mee |2 M0ν G 0ν (Q, Z )
P
G 0ν (Q, Z ): phase space factor
Experiment
Nucleus
Heidelberg-Moscow
IGEX
CUORICINO
NEMO-3
NEMO-3
NEMO-3
NEMO-3
NEMO-3
76 Ge
76 Ge
130 Te
48 Ca
82 Se
96 Zr
100 Mo
150 Nd
0ν
T1/2
≥ 1.9 × 1025 y
≥ 1.57 × 1025 y
≥ 0.3 × 1025 y
≥ 1.3 × 1022 y
≥ 2.1 × 1023 y
≥ 8.6 × 1021 y
≥ 5.8 × 1023 y
≥ 1.8 × 1022 y
0νββ in colored seesaw model
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
5
Basics of neutrino physics and neutrinoless double beta decay
Basics of neutrinoless double beta decay
Modes of ββ decay:
(Z , A) → (Z + 2, A) + 2e − + 2ν̄e
(Z , A) → (Z + 2, A) + 2e −
Total decay rate of 0νββ:
2
uL
N(E ) 6
W
νL
νL
(0νββ)
mee =
0ν −1
Γ0ν / ln 2 = (T1/2
) = |mee |2 M0ν G 0ν (Q, Z )
dL
(2νββ)
P
i
2
Uei
mi
M0ν : nuclear matrix element
G 0ν (Q, Z ): phase space factor
2νββ
0νββ
eL−
eL−
W
dL
Michael Duerr (MPIK)
-
uL
Neutrinoless Double Beta Decay
Q
E
Kanazawa University, 17 Feb 2012
5
Basics of neutrino physics and neutrinoless double beta decay
Basics of neutrinoless double beta decay
Modes of ββ decay:
(Z , A) → (Z + 2, A) + 2e − + 2ν̄e
(Z , A) → (Z + 2, A) + 2e −
Total decay rate of 0νββ:
dL
Michael Duerr (MPIK)
(0νββ)
mee =
2
0ν −1
Γ0ν / ln 2 = (T1/2
) = |mee |2 M0ν G 0ν (Q, Z )
dL
(2νββ)
uL
N(E ) 6
P
i
2
Uei
mi
M0ν : nuclear matrix element
G 0ν (Q, Z ): phase space factor
2νββ
0νββ
eL−
eL−
-
uL
Neutrinoless Double Beta Decay
Q
E
Kanazawa University, 17 Feb 2012
5
Basics of neutrino physics and neutrinoless double beta decay
New Physics mechanisms for the black box
Higgs triplet
model
Mass mechanism
dL
uL
dL
uL
νL
W
e−
ũ
u
G̃
νL
uL
Michael Duerr (MPIK)
G̃
δ −−
eL−
W
W
dL
dc
eL−
W
eL−
SUSY
dL
Neutrinoless Double Beta Decay
eL−
uL
u
ũ
dc
Kanazawa University, 17 Feb 2012
e−
6
On the quantitative impact of the Schechter–Valle theorem
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
7
On the quantitative impact of the Schechter–Valle theorem
The Schechter–Valle theorem
Assumptions:
Connects 0νββ and a non-zero
Majorana neutrino mass.
u quark, d quark and e are
massive
standard left-handed
interaction exists:
(νeL γµ eL + uL γµ dL ) W µ
Schechter and Valle, Phys. Rev. D25 (1982) 2951
W
W
d
u
u
d
0νββ
νe
Michael Duerr (MPIK)
e−
e−
Neutrinoless Double Beta Decay
νe
Kanazawa University, 17 Feb 2012
8
On the quantitative impact of the Schechter–Valle theorem
No symmetry can protect zero Majorana mass
Assume an unbroken discrete symmetry:
νeL → ην νeL ,
qL → ηq qL (q = u, d),
eL → ηe eL ,
WL+µ → ηW WL+µ .
Majorana mass term forbidden: ην2 6= 1
Invariance of the left-handed interaction: ην∗ ηe ηW = ηu∗ ηd ηW = 1
Existence of 0νββ: ηu2 ηd∗2 ηe2 = 1
These equations cannot be solved simultaneously!
Takasugi, Phys. Lett. B149 (1984) 372, Nieves, Phys. Lett. B147 (1984) 375
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
9
On the quantitative impact of the Schechter–Valle theorem
Size of the neutrino mass
W
W
d
u
u
d
0νββ
e−
νe
e−
νe
How big is this mass?
Estimation: mν ∼
Michael Duerr (MPIK)
1
MeV5
4
(16π 2 )4 MW
Neutrinoless Double Beta Decay
≈ 10−23 eV
Kanazawa University, 17 Feb 2012
10
On the quantitative impact of the Schechter–Valle theorem
Parameterization of the black box
Most general Lorentz-invariant Lagrangian for 0νββ (point-like operators):
L=
GF2 −1
m (1 JJj + 2 J µν Jµν j + 3 J µ Jµ j + 4 J µ Jµν j ν + 5 J µ Jjµ )
2 p
with J = u (1 ± γ5 ) d, J µ = uγ µ (1 ± γ5 ) d etc.
|1 |
from [Pas et. al, 2001]
our calc.
3×
10−7
2.0 ×
|2 |
2×
10−7
RLz
|LRz
3 |, |3 |
1×
10−8
e c (p + k1 )
|4 |
2×
10−8
|5 |
2 × 10−7
10−8
d(q1 ) d(q2 )
u(k1 + q1 )
Michael Duerr (MPIK)
4×
10−8
1.5 ×
W (k1 )
ν c (p)
10−9
RRz
|LLz
3 |, |3 |
Pas et al., Phys. Lett. B498 (2001) 35
W (k2 )
u(k2 + q2 )
e(p − k2 )
Neutrinoless Double Beta Decay
ν(p)
Kanazawa University, 17 Feb 2012
11
On the quantitative impact of the Schechter–Valle theorem
Decay mediated by the operator JRσ JσR jL
Choose JRσ JRσ jL ∝ uγ σ PR duγσ PR dePL e c
Mass correction
δmν =
128g 4 GF2 3 mu2 me2 md2 2
2
F
M
/µ
W
(16π 2 )4 mp
For µ = 100 MeV:
d(q1 ) d(q2 )
W (k1 )
u(k1 + q1 )
ν c (p)
Michael Duerr (MPIK)
δmν = 9.4 × 10−25 eV
e c (p + k1 )
W (k2 )
u(k2 + q2 )
e(p − k2 )
Neutrinoless Double Beta Decay
ν(p)
Kanazawa University, 17 Feb 2012
12
On the quantitative impact of the Schechter–Valle theorem
Discussion
The radiatively generated masses are many orders of magnitude
smaller than the observed neutrino masses.
Lepton number violating New Physics (at tree-level not necessarily
related to neutrino masses) may induce black box operators which
explain an observed rate of 0νββ.
The smallness of the black box contributions implies that other
neutrino mass terms (Dirac/Majorana) must exist.
ν’s mainly Majorana: Mass mechanism is the dominant part of the
black box operator.
ν’s mainly Dirac: Other lepton number violating New Physics
dominates 0νββ. Translating an observed rate of 0νββ into neutrino
masses would be completely misleading.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
13
Consistency test of 0νββ
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
14
Consistency test of 0νββ
The problem
Assume, a line is seen in 0νββ experiments.
Question: Is it due to 0νββ or some other nuclear physics process?
Usual solution: Do a second experiment with another isotope.
But: Expensive for ton-scale experiments.
Can 0νββ be confirmed within the same experiment?
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
15
Consistency test of 0νββ
0νββ to excited states
All 0νββ isotopes have an
accessible excited 0+ state.
76 As
@
β
@
@
0+
76 Ge PP
6
@ PP
PP
@
PP
+
@
PP
q 01
P
@ ββ
6
@
Q
γ
@
+
@
? 21 E (0+ )
@
1
@ γ
@
R ? g.s. ? ?
@
76 Se
Michael Duerr (MPIK)
Ratio of decay rates:
Γ0+
1
Γg.s.
=
n
(Q−E (0+
1 ))
Qn
×
0+
M1
Mg.s.
2
n = 11 (2νββ) n = 5 (0νββ)
N(E ) 6
2νββ
0νββ
2νββ + 2γ
0νββ + 2γ
Q − E (0+
1)
Neutrinoless Double Beta Decay
-
Q
E
Kanazawa University, 17 Feb 2012
16
Consistency test of 0νββ
Which isotopes are best?
0+
Decay mode
Q [keV]
E (0+
1 ) [keV]
Mg.s.
0ν
M0ν1
Γ0+ /Γg.s.
48 Ca→48 Ti
20
22
76 Ge→76 Se
32
34
82 Se→82 Kr
34
36
96 Zr→96 Mo
40
42
100 Mo→100 Ru
42
44
110 Pd→110 Cd
46
48
116 Cd→116 Sn
48
50
124 Sn→124 Te
50
52
130 Te→130 Xe
52
54
136 Xe→136 Ba
54
56
150 Nd→150 Sm
60
62
4274 ± 4
2039.04 ± 0.16
2995.5 ± 1.9
3347.7 ± 2.2
3034.40 ± 0.17
2004 ± 11
2809 ± 4
2287.8 ± 1.5
2527.518 ± 0.013
2457.83 ± 0.37
3371.38 ± 0.20
2997
1122
1488
1148
1130
1473
1757
1657
1794
1579
740
5.465
4.412
2.530
3.732
3.623
2.782
3.532
4.059
3.352
2.321
2.479
1.247
0.044
0.419
1.599
1.047
2.721
3.090
1.837
0.395
3.79 × 10−3
2.58 × 10−3
3.70 × 10−5
1.23 × 10−3
2.54 × 10−4
1.04 × 10−3
9.46 × 10−4
1.19 × 10−3
1.76 × 10−3
8.39 × 10−3
1
Q-values from [Audi et al., 2002; Rahaman et al., 2008; Redshaw et al., 2007, 2009; McCowan and Barber, 2010;
Kolhinen et al., 2010]
IBM-2 nuclear matrix elements from [Barea and Iachello, 2009; Iachello, 2010]
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
17
Consistency test of 0νββ
Which isotopes are best?
0+
Decay mode
Q [keV]
E (0+
1 ) [keV]
Mg.s.
0ν
M0ν1
Γ0+ /Γg.s.
48 Ca→48 Ti
20
22
76 Ge→76 Se
32
34
82 Se→82 Kr
34
36
96 Zr→96 Mo
40
42
100 Mo→100 Ru
42
44
110 Pd→110 Cd
46
48
116 Cd→116 Sn
48
50
124 Sn→124 Te
50
52
130 Te→130 Xe
52
54
136 Xe→136 Ba
54
56
150 Nd→150 Sm
60
62
4274 ± 4
2039.04 ± 0.16
2995.5 ± 1.9
3347.7 ± 2.2
3034.40 ± 0.17
2004 ± 11
2809 ± 4
2287.8 ± 1.5
2527.518 ± 0.013
2457.83 ± 0.37
3371.38 ± 0.20
2997
1122
1488
1148
1130
1473
1757
1657
1794
1579
740
5.465
4.412
2.530
3.732
3.623
2.782
3.532
4.059
3.352
2.321
2.479
1.247
0.044
0.419
1.599
1.047
2.721
3.090
1.837
0.395
3.79 × 10−3
2.58 × 10−3
3.70 × 10−5
1.23 × 10−3
2.54 × 10−4
1.04 × 10−3
9.46 × 10−4
1.19 × 10−3
1.76 × 10−3
8.39 × 10−3
1
Q-values from [Audi et al., 2002; Rahaman et al., 2008; Redshaw et al., 2007, 2009; McCowan and Barber, 2010;
Kolhinen et al., 2010]
IBM-2 nuclear matrix elements from [Barea and Iachello, 2009; Iachello, 2010]
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
17
Consistency test of 0νββ
Results for
76
Ge and
150
Nd
0+
Decay mode
Q [keV]
E (0+
1 ) [keV]
Mg.s.
0ν
M0ν1
Γ0+ /Γg.s.
76 Ge→76 Se
32
34
150 Nd→150 Sm
60
62
2039.04 ± 0.16
3371.38 ± 0.20
1122
740
5.465
2.321
2.479
0.395
3.79 × 10−3
8.39 × 10−3
1
Q-values from [Audi et al., 2002; Rahaman et al., 2008; Redshaw et al., 2007, 2009; McCowan and Barber, 2010;
Kolhinen et al., 2010]
IBM-2 nuclear matrix elements from [Barea and Iachello, 2009; Iachello, 2010]
76 Ge:
917 keV electron energy, 2 gammas with 559.1 keV and 563.2
keV; 1–2 excited state transitions correspond to 264–528 ground state
transitions.
150 Nd:
2631 keV electron energy, 2 gammas with 334 keV and 406
keV; 1–2 excited state transitions correspond to 120–240 ground state
transitions.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
18
Consistency test of 0νββ
Results for
76
Ge and
150
Nd
76 Ge
150 Nd
background free
Mt = 2.0 t y
Mt = 3.4 t y
background limited
Mt = 121 t y
Mt = 30.9 kt y
background free
Mt = 48.3 t y
Mt = 14.2 t y
background limited
Mt = 69.9 kt y
Mt = 543 kt y
0ν = 2.23 × 1025 y
Klapdor’s claim T1/2
|mee | = 50 meV
Half-life sensitivities:
(T1/2
(T1/2
)−1
)−1
M: detector mass
∝ aMt (background free)
q
∝ a
Michael Duerr (MPIK)
Mt
B∆E
(background limited)
Neutrinoless Double Beta Decay
a: isotopical abundance
: efficiency for detection
B: background index
∆E : energy resolution @ peak
Kanazawa University, 17 Feb 2012
19
Consistency test of 0νββ
Reach of the consistency test
|mee | [eV]
1
0.1
0.01
sin2θ13= 0.013
HD-Moscow
1000 kg Ge consistency test
1000 kg Ge
0.001
0.0001
0.001
0.01
m1 [eV]
0.1
⇒ Method works down to 100 meV.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
20
LNV and LFV through color octets
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
21
LNV and LFV through color octets
Motivation
TeV-scale particles can lead to the same contribution to 0νββ as
sub-eV-scale neutrinos:
Al '
(Mee = |
P
GF2
X U 2 m −5
ei i ' (2.7 TeV)
2 i − m2 hp
i
i
Uei2 mi | ' 0.5 eV and hp 2 i ' 0.01 GeV−2 mi2 )
contribution of two heavy scalars or vectors with mass M1 and a
heavy fermion with mass M2 :
A∝
Michael Duerr (MPIK)
1
M14 M2
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
22
LNV and LFV through color octets
Colored seesaw scenario – the model
Extend SM by color octet scalar and fermions
Φ ∼ (8, 2, +1) and Ψi ∼ (8, 1, 0)
Lagrangian of the new sector:
1
−Lν = Yναi L̄α iσ2 Tr(Φ∗ Ψi ) + MΨi Tr(Ψ̄ci Ψi ) + λΦH Tr(Φ† H)2 + H.c.
2
⇒ no neutrino mass at tree-level.
Coupling of Φ to quarks:
LQ = d̄R κD Φ† QL + ūR κU QL Φ + H.c.
Perez, Wise, Phys. Rev. D 80 (2009) 053006, Perez et al., JHEP 01 (2011) 046.
Color octets ⇒ sizable cross sections at LHC expected.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
23
LNV and LFV through color octets
Colored seesaw scenario – neutrino mass
One-loop neutrino mass matrix
hH 0 i
hH 0 i
Φ0
Mναβ =
X
v2
i
λΦH αi βi
Y Y I(MΦ , MΨi )
16π 2 ν ν
Φ0
νβ
να
Ψi
with loop function Ii ≡ I(MΦ , MΨi ) = MΨi
2 −M 2 +M 2 ln(
MΦ
Ψ
Ψ
i
i
2 −M 2 )2
(MΦ
Ψi
Ψi
M2
Ψi
M2
Φ
)
Express Yukawas as
Yν =
q
16π 2 1
λΦH v
U
q
Mνd R
q

(I d )−1

ĉ2 ĉ3
ĉ2 ŝ3
ŝ2


with Casas–Ibarra matrix R = −ĉ1 ŝ3 − ŝ1 ŝ2 ĉ3 ĉ1 ĉ3 − ŝ1 ŝ2 ŝ3 ŝ1 ĉ2 
ŝ1 ŝ3 − ĉ1 ŝ2 ĉ3 −ŝ1 ĉ3 − ĉ1 ŝ2 ŝ3 ĉ1 ĉ2
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
24
LNV and LFV through color octets
Neutrinoless double beta decay
direct contribution
indirect contribution
u
d
Φ
d
u
−
W
e
Ψi
−
ν
Ψi
e−
e−
W
Φ−
u
d
A'
2
y11
4
MΦ
Al '
i MΨ
i
for Rij = δij : A '
2
16π 2 y11
4
λPhiH v 2 MΦ
76 Ge:
u
d
P (Yνei )2
Current limit for
e−
ν
P mi Uei2
Mee
GF2 hp
2i
i MΨ Ii
i
T1/2 ≥ 1.9 × 1025 yrs
Half-life formula
Klapdor-Kleingrothaus et al., Eur. Phys. J. A12 (2001) 147
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
25
LNV and LFV through color octets
Lepton flavor violation
γ
Br(lα → lβ γ) =
3αem
4
4πGF2 MΦ
P
2
i Yνβi (Yναi )∗ F(xi )
Φ−
Φ−
Ψi
lα
with F(xi ) =
1−6xi +3xi2 +2xi3 −6xi2 ln(xi )
12(xi −1)4
and xi =
2
MPsi
2
MΦ
i
lβ
.
For choice Rij = δij
3αem (16π 2 )2
Br(µ → eγ) =
4πGF2 MΦ4 λ2ΦH v 4
2
X F(x )
i
∗
Uei Uµi mi Ii
i
Current limit at 90% C.L.:
Br(µ → eγ) ≤ 2.4 × 10−12
MEG Collaboration, Phys. Rev. Lett. 107 (2011) 171801
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
26
LNV and LFV through color octets
Case of three color octet fermions – setup
Minimal deviation
from tri-bimaximal mixing with
non-zero θ13 :


−iδ
√1
λe
− √26
3
 1

√
√λ iδ
√1 + √λ e iδ
√1  diag(1, e iα , e i(β+δ) )
−
UPMNS ' 
 6 − 3e
3
6
2
√1 + √λ e iδ
√1 − √λ e iδ
√1
6
6
3
6
2
G2
•Al ' F2
hp i
y 2 16π 2
•A ' 114
MΦ λΦH v 2
2m1 m2 i2α
+
e + m3 λ2 e i2β
3
3
2m1
m2 e i2α
m3 λ2 e i2β
+
+
3I1 MΨ1
3I2 MΨ2
I3 MΨ3
!
√ m1 F(x1 )
2)
I1
√
m2 F(x2 )
m3 F(x3 ) 2
+( 2e i2α + λe i2α+iδ )
− 3e i2β+iδ λ
I2
I3
• Br(µ → eγ) ∝ (2e iδ λ −
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
27
LNV and LFV through color octets
Case of three color octet fermions – results 1
Ratio of particle physics amplitudes A/Al
normal hierarchy
inverted hierarchy
sin2 θ13 6= 0
10000
100
100
1
1
0.01
0.01
0.0001
0.0001
10−3
10−2
10−1
10−3
m1 [eV]
Michael Duerr (MPIK)
λΦH = 10−8
λΦH = 10−5
λΦH = 10−2
10000
A/Al
A/Al
sin2 θ13 6= 0
λΦH = 10−8
λΦH = 10−5
λΦH = 10−2
10−2
10−1
m3 [eV]
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
28
LNV and LFV through color octets
Case of three color octet fermions – results 2
Effective masses
effective mass Mee =
P
i
Uei2 mi
“color effective mass”
2
sin θ13 = 0.013
100
102
10
hp2 i
A [eV]
G2F
|Mee | [eV]
10−1
10−2
10−3
10−4
0.0001
hp 2 i
A
GF2
sin2 θ13 6= 0
inverted hierarchy
normal hierarchy
0
10−2
10−4
10−6
10−8
10−3
0.001
0.01
0.1
0.3
10−2
10−1
m1 [eV]
m1 [eV]
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
29
Summary
Contents
1
2
3
4
5
Basics of neutrino physics and neutrinoless double beta decay
On the quantitative impact of the Schechter–Valle theorem
(MD, M. Lindner, A. Merle, JHEP 06 (2011) 091)
Consistency test of neutrinoless double beta decay with one isotope
(MD, M. Lindner, K. Zuber, Phys. Rev. D84 (2011) 093004)
Lepton number and lepton flavor violation through color octet states
(S. Choubey, MD, M. Mitra, W. Rodejohann, arXiv:1201.3031 [hep-ph])
Summary
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
30
Summary
Summary
Neutrinoless double beta decay is a sensitive test for lepton number
violating New Physics.
The black box theorem is valid, but it is only of academic interest:
Radiatively generated masses are far too small to account for the
neutrino masses observed in oscillation experiments.
Other operators must give the leading contribution to neutrino masses,
which could be of Dirac or Majorana type.
Using 0νββ to the first excited 0+ final state in addition to the
ground state transition, it is possible to perform a crosscheck and
discriminate unknown nuclear background lines from 0νββ within one
experiment.
In the colored seesaw model, “direct” and “indirect” contributions to
0νββ exist: Depending on the model parameters, either of the
contributions can be dominant.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
31
Summary
Thank You!
Thanks for your attention!
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
32
Backup slides
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
1
Oscillation parameters
parameter
2 [10−5 eV2 ]
∆m21
best fit ±1σ
7.59+0.20
−0.18
2σ
7.24–7.99
3σ
7.09–8.19
2 [10−3 eV2 ]
∆m31
2.50+0.09
−0.16
−(2.40+0.08
−0.09 )
2.25 − 2.68
−(2.23 − 2.58)
2.14 − 2.76
−(2.13 − 2.67)
sin2 θ12
0.312+0.017
−0.015
0.28–0.35
0.27–0.36
sin2 θ23
0.52+0.06
−0.07
0.52 ± 0.06
0.41–0.61
0.42–0.61
0.39–0.64
sin2 θ13
0.013+0.007
−0.005
0.016+0.008
−0.006
0.004–0.028
0.005–0.031
0.001–0.035
0.001–0.039
0 − 2π
0 − 2π
δ
−0.61+0.75
−0.65 π
−0.41+0.65
−0.70 π
upper (lower) values refer to normal (inverted) hierarchy
back
Schwetz et al., New J. Phys. 13 (2011) 109401
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
2
Effective mass |mee |
Normal hierarchy:
m2 =
mee =
q
2 und m =
m12 + ∆m21
3
2
c13
2
m1 c12
+
2
e i2α s12
q
m12
q
+
2
m12 + ∆m31
2
∆m21
+
sin2 θ13 = 0
best fit values range
3σ values range
10−1
|mee | [eV]
|mee | [eV]
2
m12 + ∆m31
100
10−2
10−3
10−4
0.0001
q
sin2 θ13 = 0.053
100
10−1
2
e i2β s13
0.001
0.01
0.1
0.3
10−2
10−3
10−4
0.0001
m1 [eV]
Michael Duerr (MPIK)
best fit values range
3σ values range
0.001
0.01
0.1
0.3
m1 [eV]
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
3
SV – decay mediated by the operator JL JL jL
Choose JL JL jL ∝ uPL duPL dePL e c
Mass correction
δmν = Σ(p/ = mν ) ∝ p 2 p/=mν
Physical neutrino mass mν is solution of
p/ − Σ(p/)|p/=mν = 0
Result:
δmν = 0
d(q1 ) d(q2 )
W (k1 )
u(k1 + q1 )
ν c (p)
Michael Duerr (MPIK)
e c (p + k1 )
W (k2 )
u(k2 + q2 )
e(p − k2 )
Neutrinoless Double Beta Decay
ν(p)
Kanazawa University, 17 Feb 2012
4
Consistency test – experimental considerations
What do we have to look for?
0+
1 final state: two e and two γ
ground state transition: only two e
⇒ Detector geometry must be such that both transitions can be
distinguished.
Excited 0+
1 states de-excite via
+
+
0 → 2 → 0+
⇒ γγ angular correlation
5
W (θ) = × (1 − 3 cos2 θ + 4 cos4 θ)
8
Michael Duerr (MPIK)
1.2
W (θ)
1.0
0.8
0.6
0.4
0.2
0
−π
Neutrinoless Double Beta Decay
−π/2
0
π/2
π
Kanazawa University, 17 Feb 2012
5
Consistency test – possible backgrounds
β decay of intermediate nucleus [may be produced by (p, n) reactions]
to excited states will lead to the same gamma signature and energy
spectra will overlap
→ solution: measure electron energy very accurately, or build detector
which can distinguish one or two electrons (tracking capabilities).
External backgrounds: signal of the decay to excited states is a triple
coincidence, with well-defined energies of all involved particles.
Additionally, angular correlations exist.
⇒ hard to be mimicked by some other process
Major background: 2νββ decay into the 0+
1 excited state
⇒ crucial experimental quantity: energy resolution.
Michael Duerr (MPIK)
Neutrinoless Double Beta Decay
Kanazawa University, 17 Feb 2012
6