Neutrinoless Double Beta Decay v Werner Rodejohann m v = m L - m D - - PowerPoint PPT Presentation

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Neutrinoless Double Beta Decay

Werner Rodejohann XVIII LNF Spring School May 2016

MANITOP

Massive Neutrinos: Investigating their Theoretical Origin and Phenomenology

mv = mL - mD M -1 mD

v

T R

1

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Contents

III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem

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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

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Interpretation of Experiments

Master formula: Γ0ν = Gx(Q, Z) |Mx(A, Z) ηx|2

• Gx(Q, Z): phase space factor, typically Q5
• Mx(A, Z): nuclear physics; factor 2-3 uncertainty
• ηx: particle physics; many possibilities

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Contents

III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem

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III1) Basics

• 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

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• Standard Interpretation:

W νi νi W dL dL uL e−

L

e−

L

uL Uei q Uei

• Non-Standard Interpretations:

WL WR NR NR νL WL dL dL uL e

− R

e

− L

uL

˜ dR χ/˜ g ˜ dR χ/˜ 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

7

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Non-Standard Interpretations

clear experimental signature: KATRIN (or cosmology) sees nothing but “|mee| > 0.5 eV” 0νββ decoupled from cosmology limits on neutrino mass!

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Energy Scale:

• standard amplitude for light Majorana neutrino exchange:

Al ≃ G2

F

|mee| q2 ≃ 7 × 10−18 |mee| 0.5 eV

• GeV−5 ≃ (2.7 TeV)−5
• 9

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Energy Scale:

• standard amplitude for light Majorana neutrino exchange:

Al ≃ G2

F

|mee| q2 ≃ 7 × 10−18 |mee| 0.5 eV

• GeV−5 ≃ (2.7 TeV)−5
• if new heavy particles are exchanged:

Ah ≃ c M 5

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Energy Scale:

• standard amplitude for light Majorana neutrino exchange:

Al ≃ G2

F

|mee| q2 ≃ 7 × 10−18 |mee| 0.5 eV

• GeV−5 ≃ (2.7 TeV)−5
• if new heavy particles are exchanged:

Ah ≃ c M 5 ⇒ for 0νββ holds:

1 eV = 1 TeV

⇒ Phenomenology in colliders, LFV

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Schechter-Valle theorem: observation of 0νββ implies Majorana neutrinos

νe W e− d u u e− d νe W

is 4 loop diagram: mBB

ν

∼ G2

F

(16π2)4 MeV5 ∼ 10−25 eV explicit calculation: Duerr, Lindner, Merle, 1105.0901

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mechanism physics parameter current limit test light neutrino exchange

• U2

ei mi

• 0.5 eV
• scillations,

cosmology, neutrino mass heavy neutrino exchange

• S2

ei Mi

• 2 × 10−8 GeV−1

LFV, collider heavy neutrino and RHC

• V2

ei Mi M4 WR

• 4 × 10−16 GeV−5

flavor, collider Higgs triplet and RHC

• (MR)ee

m2 ∆R M4 WR

• 10−15 GeV−1

flavor, collider e− distribution λ-mechanism with RHC

• Uei ˜

Sei M2 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′2

111

• Λ5

SUSY ΛSUSY = f(m˜ g, m˜ uL , m˜ dR , mχi ) 7 × 10−18 GeV−5 collider, flavor long-range / R

• sin 2θb λ′

131 λ′ 113    1 m2 ˜ b1 − 1 m2 ˜ b2   

• ∼ GF

q mb

• λ′

131 λ′ 113

• Λ3

SUSY 2 × 10−13 GeV−2 1 × 10−14 GeV−3 flavor, collider Majorons |gχ| or |gχ|2 10−4 . . . 1 spectrum, cosmology

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Some features

• Majoranas and no RHC:

A ∝ m q2 − m2 →          m for q2 ≫ m2 1 m for q2 ≪ m2

1 m² 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/vector boson:

A ∝ 1 q2 − m2 → 1 m2

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Dib et al., hep-ph/0006277

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Chiralities

W νi νi W dL dL uL e−

L

e−

L

uL Uei q Uei

A ∝ PL / q + mi q2 − m2

i

PL ∝ mi q2 − m2

i

≃    mi/q2 (m2

i ≪ q2)

1/mi (m2

i ≫ q2)

WR NR NR νL W dR dL uR e

− R

e

− L

uL

A ∝ PR / q + mi q2 − m2

i

PL ∝ / q q2 − m2

i

≃    1/q (m2

i ≪ q2)

q/m2

i

(m2

i ≫ q2) 16

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Heavy neutrinos

W νi νi W dL dL uL e−

L

e−

L

uL ei q ei

if heavier than 100 MeV: Ah = G2

F

S2

ei

Mi ≡ G2

F 1

m ⇒ 1 m < ∼ 10−8 GeV−1 dimensionless LNV parameter: ηh = mp 1 m ≤ 1.7 × 10−8

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Faessler, Gonzalez, Kovalenko, Simkovic, 1408.6077

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An exact See-Saw Relation

Full mass matrix: M =   mD mT

D

MR   = U   mdiag

ν

M diag

R

  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

upper left 0 in M gives exact see-saw relation Uαi (mν)i Uiβ = 0, or: |N 2

ei mi| = |S2 ei Mi| <

∼ 0.3 eV compare with S2

ei

Mi < ∼ 10−8 GeV−1 and |Sei|2 ≤ 0.0052

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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

|Sei|

2 |Sei|

2 M_i

|Sei|

2 /M_i

⇒ cancellations required to make heavy neutrinos contribute significantly to 0νββ

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TeV scale seesaw with sizable mixing

mν = m2

D/MR ≃ v2/MR

with mν ≃

• ∆m2

A it follows that MR ≃ 1015 GeV and

S = mD/MR =

• mν/MR ≃ 10−13

then, heavy neutrino contribution to 0νββ negligible: S2/MR = m2

D/M 3 R ≃ 10−41 GeV−1

can make MR TeV, but then mixing

• mν/MR ≃ 10−7 and still

m2

D/M 3 R ≃ 10−17 GeV−1 21

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TeV scale seesaw with sizable mixing

not necessarily correct, mD and MR are matrices and cancellations can occur. . . e.g. mD = v     h1 h2 h3 ω h1 ω h2 ω h3 ω2 h1 ω2 h2 ω2 h3     MR = M0

1 (here ω = e2iπ/3)

gives mν = 0, add (very) small corrections. . . mD = v, MR = TeV, mixing mD/MR large, 0νββ contribution large

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TeV scale seesaw with sizable mixing

can also make everything smaller: MD = m     fǫ2 gǫ 1     , M −1

R

= 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

• Al

Ah

• =

G2

F

q2 |mee|

G2

F 1

m ≃ 10−4 GeV2 q2 ≃ 10−2

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Higgs triplets (type II seesaw)

W W ∆−− dL dL uL e−

L

e−

L

uL √ 2g2vL hee

A∆ ≃ G2

F

hee vL m2

∆

< ∼ G2

F

(mν)ee m2

∆

= G2

F

|mee| m2

∆

plays no role in 0νββ

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Inverse Neutrinoless Double Beta Decay

this is not

76Se++ + e− + e− → 76Ge

but rather e− + e− → W − + W −

Rizzo; Heusch, Minkowski; Gluza, Zralek; Cuypers, Raidal;. . .

N e−

L

e−

L

W − W − N e−

L

e−

L

W − W − ∆−− e−

L

e−

L

W − W −

(a) (b) (c)

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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

|V

ei| 2 = 1.0

|V

ei| 2 = 0.0052

|V

ei| 2 = 5.0 10

• 8 (Mi /GeV)

dσ d cos θ = G2

F

32 π

• (mν)i U2

ei

• t

t − (mν)i + u u − (mν)i 2

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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

• U2

ei (mν)i

2 ⇒ amplitude grows with √s? Unitarity??

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Unitarity

high energy limit √s → ∞: σ(e−e− → W −W −) = G2

F

4π

• U2

ei (mν)i

2 ↔ amplitude grows with √s? Answer: exact see-saw relation U2

ei (mν)i = 0

M =   mD mT

D

MR   = U   mdiag

ν

M diag

R

  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

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Contents

III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem

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III2) Left-right symmetric theories

very simple extension of SM gauge group to SU(2)L × SU(2)R × U(1)B−L usual particle content: LLi =  ν′

L

ℓL  

i

∼ (2, 1, −1) , LRi =  νR ℓR  

i

∼ (1, 2, −1) QLi =  uL dL  

i

∼ (2, 1, 1

3) ,

QRi =  uR dR  

i

∼ (1, 2, 1

3)

for symmetry breaking: ∆L ≡  δ+

L/

√ 2 δ++

L

δ0

L

−δ+

L/

√ 2   ∼ (3, 1, 2) , ∆R ≡  δ+

R/

√ 2 δ++

R

δ0

R

−δ+

R/

√ 2   ∼ (1, 3, 2) φ ≡  φ0

1

φ+

2

φ−

1

φ0

2

  ∼ (2, 2, 0)

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Left-right Symmetry

• very rich Higgs sector (13 extra scalars)
• rich gauge boson sector (Z′, MW ±

R ) with

MZ′ =

• 2

1−tan2 θW MWR ≃ 1.7 MWR

• ’sterile’ neutrinos νR
• type I + type II seesaw for neutrino mass
• right-handed currents with strength GF
• gR

gL

2

mW MWR

2

• mν ∝ 1/vR ∝ 1/MWR: maximal parity violation ↔ smallness of neutrino

mass

(Note: in case of modified symmetry breaking gL = gR and MZ′ < MWR possible. . .)

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Left-right Symmetry

6 neutrinos, flavor states n′

L = (ν′ L, νRc)T , mass states nL = (νL, N c R)T

n′

L =

  ν′

L

νRc   =  KL KR   nL =  U S T V     νL N c

R

  right-handed currents: Llep

CC =

g √ 2

• ℓLγµKLnL(W −

1µ + ξeiαW − 2µ) + ℓRγµKRnc L(−ξe−iαW − 1µ + W − 2µ)

• (KL and KR are 3 × 6 mixing matrices)

plus: gauge boson mixing  W ±

L

W ±

R

  =   cos ξ sin ξ eiα − sin ξ e−iα cos ξ    W ±

1

W ±

2

 

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Connection to neutrinos

Majorana mass matrices ML = fL vL from ∆L and MR = fR vR from ∆R (with fL = fR = f) Lν

mass = − 1 2

• ν′

L ν′ R c

 ML MD M T

D

MR    ν′

L c

ν′

R

  ⇒ mν = ML − MD M −1

R M T D

useful special cases (i) type I dominance: mν = MD M −1

R M T D = MD f −1 R /vR M T D

(ii) type II dominance: mν = fL vL for case (i): mixing of light neutrinos with heavy neutrinos of order |Sαi| ≃ |T T

αi| ≃

mν Mi < ∼ 10−7 TeV Mi 1/2 small (or enhanced up to 10−2 by cancellations)

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Right-handed Currents in Double Beta Decay (A, Z) → (A, Z + 2) + 2e−

Llep

CC =

g √ 2

3

• i=1
• eLγµ(UeiνLi + SeiN c

Ri)(W − 1µ + ξeiαW − 2µ)

+ eRγµ(T ∗

eiνc Li + V ∗ eiNRi)(−ξe−iαW − 1µ + W − 2µ)

• Lℓ

Y = − L ′c Liσ2∆LfLL′ L − L ′c Riσ2∆RfRL′ R

classify diagrams:

• mass dependent diagrams (same helicity of electrons)
• triplet exchange diagrams (same helicity of electrons)
• momentum dependent diagrams (different helicity of electrons)

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Mass Dependent Diagrams

electrons either both left- or both right-handed: leading diagrams:

W νi νi W dL dL uL e−

L

e−

L

uL Uei q Uei WR WR dR dR uR e−

R

e−

R

uR NRi

Aν ≃ G2

F

mee q2 AR

NR ≃ G2 F

mWL MWR 4

i

V ∗

ei 2

Mi < ∼ 0.3 eV < ∼ 4 · 10−16 GeV−5 ∝ L2 R ∝ L4 R5

35

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Triplet exchange diagrams

leading diagrams:

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

AδL ≃ G2

F

heevL m2

δL

AδR ≃ G2

F

mWL MWR 4

i

V 2

eiMi

m2

δR

−− < ∼ 4 · 10−16 GeV−5 (negligible) ∝ L4 R5

36

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Momentum Dependent Diagrams

electrons with opposite helicity leading diagrams (light neutrino exchange, long range):

WR NR NR νL WL dR dL uR e−

R

e−

L

uL WL WR NR NR νL WL dL dL uL e−

R

e−

L

uL

Aλ ≃ G2

F

mWL MWR 2

i

UeiT ∗

ei

1 q Aη ≃ G2

F tan ξ

• i

UeiT ∗

ei

1 q < ∼ 1 · 10−10 GeV−2 < ∼ 6 · 10−9 ∝ L3 R3q ∝ L3 R3q

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Tests of left-right symmetric diagrams

suppose ML dominates in mν and h = f: ⇒ MR ∝ mν ⇒ ANR ≃ G2

F

mW MWR 4 V 2

ei

Mi ∝ U 2

ei

mi

Tello et al., 1011.3522

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Tests of left-right symmetric diagrams

WR WR dR dR uR e−

R

e−

R

uR NRi WR WR δ−−

R

dR dR uR e−

R

e−

R

uR √ 2g2vR hee

Keung, Senjanovic, 1983

39

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Example: Left-right symmetric theories

WR WR dR dR uR e−

R

e−

R

uR NRi WR WR δ−−

R

dR dR uR e−

R

e−

R

uR √ 2g2vR hee WR WR ¯ uR dR e

− R

e

− R

dR ¯ uR NRi

δ−−

L

µ−

L

e+

L

e−

L

e−

L

heµ hee

40

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Lindner, Queiroz, W.R., 1604.07419

LHC assumes that MWR > MN, BR = 1, cuts don’t see low MN regime indirect limits from WR → jj (Helo, Hirsch, 1509.00423) and Z′ → ℓℓ MZ′ MWR = √ 2δ

• δ2 − tan2 θW

and

gR

• 1 − δ2 tan2 θW

Z′

µ ¯

f

• T R

3 + (T L 3 − Q)δ2 tan2 θW

• f

where δ = gL/gR

41

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Da (far and uncertain) future:

Lindner, Queiroz, W.R., Yaguna, 1604.08596

42

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LHC vs. 0νββ

WR WR ¯ uR dR e−

R

e−

R

dR ¯ uR NRi

• LHC assumptions: MN < MWR, BR(MN → ee) = 1, gR = gL
• cuts result in weak sensitivities for low MN
• background processes?
• QCD corrections?
• (LNV at LHC and baryogenesis)

43

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Background

1000 2000 3000 4000 5000 0.2 0.4 0.6 0.8 1.0

MeffGeV geff

Helo et al., PRD 88

• ne should include e.g.
• “jet fake” (high-pT jet registered as electron)
• “charge flip” (e− from opposite sign pair transfer pT to e+ via conversion)

Peng, Ramsey-Musolf, Winslow, 1508.04444

44

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Background

• ne should include e.g.
• “jet fake” (high-pT jet registered as electron)
• “charge flip” (e− from opposite sign pair transfer pT to e+ via conversion)

1000 2000 3000 4000 5000 0.2 0.4 0.6 0.8 1.0

MeffGeV geff

Peng, Ramsey-Musolf, Winslow, 1508.04444

45

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QCD corrections

• matrix element multiplied with αs/(4π) ln M 2

W /µ2, match with eff. diagram

• run that down to 0νββ scale p2 = (100 MeV)2 ⇒ αs/(4π) ln M 2

W /p2 = 10%

• creates color non-singlet operators, (’operator mixing’), Fierz them for NMEs
• creates new operator with different matrix element, e.g.

(V − A) × (V + A) → (S − P) × (S + P)

• can give for alternative mechanisms large effect in either direction. . .
• (makes limit on right-handed diagrams slightly weaker)

Mahajan, PRL 112; Gonzalez, Kovalenko, Hirsch, PRD 93

46

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Observation of LNV at LHC implies washout effects in early Universe!

Example TeV-scale WR: leading to washout e±

R e± R → W ± R W ± R and

e±

R W ∓ R → e∓ R W ± R . Further, e± RW ∓ R → e∓ R W ± R stays long in equilibrium

(Frere, Hambye, Vertongen; Bhupal Dev, Lee, Mohapatra; U. Sarkar et al.) More model-independent (Deppisch, Harz, Hirsch): washout: log10 ΓW (qq → ℓ+ℓ+ qq) H > ∼ 6.9 + 0.6 MX TeV − 1

• + log10

σLHC fb (TeV-0νββ, LFV and YB: Deppisch, Harz, Huang, Hirsch, Päs) ↔ post-Sphaleron mechanisms, τ flavor effects,. . .

47

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Constraints from Lepton Flavor Violation

WR WR δ−−

R

dR dR uR e−

R

e−

R

uR √ 2g2vR hee δ−−

R

µ−

R

e+

R

e−

R

e−

R

heµ hee

0.0001 0.001 0.01 0.1 mlight (eV) 10

26

10

28

10

30

10

32

[T1/2]ν (yrs)

GERDA 40kg GERDA 1T

Normal 0.0001 0.001 0.01 0.1

Excluded by KamLAND-Zen

Inverted

mδR = 3.5 TeV mδR = 2 TeV mδR = 1 TeV

Barry, W.R., JHEP 1309

48

SLIDE 49

Adding diagrams

WR WR dR dR uR e−

R

e−

R

uR NRi W νi νi W dL dL uL e−

L

e−

L

uL Uei q Uei

⇒ lower bound on m(lightest) > ∼ meV

49

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Xe vs. Ge

10

24

10

25

10

26

T1/2[

136Xe] (yrs)

10

24

10

25

10

26

T1/2[

76Ge] (yrs)

GERDA HM Ge Combined EXO KamLAND-Zen Xe Combined

IBM (M-S) QRPA (CCM)

10

24

10

25

10

26

T1/2[

136Xe] (yrs)

10

24

10

25

10

26

T1/2[

76Ge] (yrs)

GERDA HM Ge Combined EXO KamLAND-Zen Xe Combined

QRPA (Tü) QRPA (HD)

WR WR dR dR uR e−

R

e−

R

uR NRi

W WR NR NR νL W dL dL uL e−

R

e−

L

uL

Barry, W.R., JHEP 1309

50

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λ-diagram and inverse 0νββ

WR NR NR νL W dR dL uR e−

R

e−

L

uL

NRi νLi NRi e− e− WR WL T ∗

ei

Uei

0νββ W-WR production

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]

Barry, Dorame, W.R., 1204.3365

51

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Contents

III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem

52

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III3) Supersymmetry

L/

R = λijk ˆ

Li ˆ Lj ˆ ec

k + λ′ ijk ˆ

Li ˆ Qj ¯ dc

k + λ′′ ijkˆ

uc

i ˆ

dc

j ˆ

dc

k + ǫi ˆ

Li ˆ Hu λ′′ violates B, the rest violates L by one unit gives rise to two mechanisms for 0νββ:

• short range, or neutralino/gluino exchange, or λ′

111 mechanism

• long-range, or squark exchange, or λ′

131 λ′ 113 mechanism

Hirsch, Kovalenko, Paes, Klapdor, Babu, Mohapatra, Vergados,. . .

53

SLIDE 54

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 ˜ dR χ/˜ g dc dc uL e−

L

e−

L

uL

A/

R1 ≃

λ′2

111

Λ5

SUSY 54

SLIDE 55

Supersymmetry: short range

• Actually. . .

η˜

g

= πα3 6 λ′2

111

G2

F

mp m˜

g

• 1

m4

˜ uL

+ 1 m4

˜ dR

− 1 2m2

˜ uLm2 ˜ dR

• ηχ

= πα2 2 λ′2

111

G2

F 4

• i=1

mp mχi

• V 2

Li(u)

m4

˜ uL

+ V 2

Ri(d)

m4

˜ dR

− VLi(u)VRi(d) m2

˜ uLm2 ˜ dR

• η′

˜ g

= 2πα3 3 λ′2

111

G2

F

mp m˜

g

1 m2

˜ uLm2 ˜ dR

ηχ˜

e

= 2πα2 λ′2

111

G2

F 4

• i=1

mp mχi V 2

Li(e)

m4

˜ eL

ηχ ˜

f

= πα2 λ′2

111

G2

F 4

• i=1

mp mχi

• VLi(u)VRi(d)

m2

˜ uLm2 ˜ dR

− VLi(u)VLi(e) m2

˜ uLm2 ˜ eL

− VLi(e)VRi(d) m2

˜ eLm2 ˜ dR

• 55

SLIDE 56

Supersymmetry: short range

gluino dominance: η˜

g / R1 ≃ πα3

6 λ′2

111

G2

F

mp m˜

g m4 ˜ dR

• 1 +

m ˜

dR

m˜

uL

22 ≤ 7.5 × 10−9 translates into λ′2

111

m˜

g m4 ˜ dR(1 + m2 ˜ dR/m2 ˜ uL)2 <

∼ 1.8 × 10−17 GeV−5

56

SLIDE 57

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” ˆ σ ∝ λ′2

111

ˆ s

Allanach, Kom, Paes, 0903.0347

57

SLIDE 58

tan β = 10, A0 = 0, 10 fb−1 M0/GeV M1/2/GeV T 0νββ

1/2

(Ge) < 1.9 × 1025 yrs 100 > T 0νββ

1/2 (Ge)/1025 yrs > 1.9

T 0νββ

1/2

(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

58

SLIDE 59

RPV SUSY and inverse 0νββ

˜ χ0 uL dc ˜ eL eL λ′∗

111

uL dc ˜ eL eL λ′∗

111

˜ χ0 uL dc ˜ eL eL λ′

111

uL dc ˜ eL eL λ′

111

0νββ resonant ˜ eL production → 4j

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

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∼

eL [GeV]

• 3
• 2
• 1

BR E(beam)

√s=3000GeV log10(σ/fb)

Kom, W.R., 1110.3220

59

SLIDE 60

Cool effect somewhere else

d-squarks resonantly produced νedL → ˜ dR → νedL, euL

Dev, W.R.

60

SLIDE 61

Supersymmetry: long range

˜ b νe ˜ bc W dc dL uL e−

L

e−

L

uL

Ab

/ R2 ≃ GF

1 q Uei mb Λ3

SUSY

λ′

131 λ′ 113 61

SLIDE 62

Supersymmetry: long range

Test with B0- ¯ B0 mixing

˜ νe d bc b dc

constrains λ′

131 λ′ 113/Λ4 SUSY

gives currently stronger constraint than 0νββ

62

SLIDE 63

Contents

III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem

63

SLIDE 64

III4) The inverse problem

identify mechanism via 1.) other observables (LHC, LFV, KATRIN, cosmology,. . .) 2.) decay products (individual e− energies, angular correlations, spectrum,. . .) 3.) nuclear physics (multi-isotope, 0νECEC, 0νβ+β+,. . .)

64

SLIDE 65

Distinguishing via decay products

SuperNEMO

2000 4000 6000 8000 10000 12000 0.5 1 1.5 2 2.5 3

E2e (MeV) Number of events/0.05 MeV

(a)

100Mo

7.369 kg.y 219,000 bbevents S/B = 40

NEMO 3 (Phase I) 2000 4000 6000 8000 10000 12000

• 1
• 0.5

0.5 1

cos(Θ) Number of events

(b)

100Mo

7.369 kg.y 219,000 bbevents S/B = 40

NEMO 3 (Phase I)

• source foils in between plastic scintillators
• individual electron energy, and their relative angle!

65

SLIDE 66

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

dΓ dE1 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

66

SLIDE 67

Distinguishing via decay products

Defining asymmetries Aθ = (N+ − N−)/(N+ + N−) and AE = (N> − N<)/(N> + N<)

4 2 2 4 50 100 150 200 250 300 Λ 107 mΝ meV 4 2 2 4 50 100 150 200 250 300 Λ 107 mΝ meV 67

SLIDE 68

Distinguishing via nuclear physics

challenging, but possible if nuclear physics is under control (sic!) recall: 1 T 0ν

1/2(A, Z) = G(Q, Z) |M(A, Z) η|2

if you measured two isotopes: T 0ν

1/2(A1, Z1)

T 0ν

1/2(A2, Z2) = Gx(Q2, Z2) |Mx(A2, Z2)|2

Gx(Q1, Z1) |Mx(A1, Z1)|2 particle physics drops out, ratio of NMEs sensitive to mechanism ⇒ third reason for multi-isotope determination

68

SLIDE 69

Distinguishing via nuclear physics

Gehman, Elliott, hep-ph/0701099

3 to 4 isotopes necessary to disentangle mechanism

69

SLIDE 70

Distinguishing via nuclear physics

• standard interpretation: suppressed by 2 to 3 orders of magnitude
• ratio sensitive to mechanism
• 0+

1 easier to identify; 2+ 1 very sensitive to RHC 70

SLIDE 71

Distinguishing via nuclear physics

Observation of (A, Z) → (A, Z − 2) + 2 e+ (0νβ+β+) e−

b + (A, Z) → (A, Z − 2) + e+

(0νβ+EC) 2 e−

b + (A, Z) → (A, Z − 2)∗

(0νECEC) rate to 0νββ is sensitive to mechanism

71

SLIDE 72

Dircet vs. indirect contribution

Example: introduce Ψi = (8, 1, 0) and Φ = (8, 2, 1

2)

να νβ Ψi Ψi Φ Φ H0 H0

Φ Φ Ψi Ψi d d u e− e− u

mν ∝ λΦH yαiyβi indirect contribution to 0νββ: direct contribution to 0νββ: Al ≃ G2

F

|mee| q2 A ≃ c2

ud

y2

eα

MΨi M 4

Φ 72

SLIDE 73

Dircet vs. indirect contribution

new contribution can dominate over standard one:

Choubey, Dürr, Mitra, W.R., JHEP 1205

73

SLIDE 74

Summary

74