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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+

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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