Neutrinoless Double Beta Decay and Particle PhysicsNeutrinoless Double Beta Decay is mediated by...

Neutrinoless Double Beta Decay and Particle Physics

Werner Rodejohann

(MPIK, Heidelberg)

01/10/2012

1

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


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


0.001 0.01 0.1


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


0.001 0.01 0.1


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


0.001 0.01 0.1


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


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


0.001 0.01 0.1


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


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


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

Neutrinoless Double Beta Decay and Particle PhysicsNeutrinoless Double Beta Decay is mediated by...

Documents

Transcript of Neutrinoless Double Beta Decay and Particle PhysicsNeutrinoless Double Beta Decay is mediated by...