neutrinoless double beta decay · 2016. 5. 11. · neutrinoless double beta decay is mediated by...

Neutrinoless Double Beta Decay

Werner Rodejohann

XVIII LNF Spring School

May 2016MANITOP

Massive Neutrinos: Investigating their

Theoretical Origin and Phenomenology

mv = mL - mD M -1

mD

v

T

R

1

Contents

III) Neutrinoless double beta decay: non-standard interpretations

III1) Basics

III2) Left-right symmetry

III3) SUSY

III4) The inverse problem

2

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

3

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

4

Contents


III1) Basics


III3) SUSY


5

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

6

• 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

Non-Standard Interpretations

clear experimental signature:

KATRIN (or cosmology) sees nothing but “|mee| > 0.5 eV”

0νββ decoupled from cosmology limits on neutrino mass!

8

Energy Scale:

• standard amplitude for light Majorana neutrino exchange:

Al ≃ G2F

|mee|q2

≃ 7× 10−18

( |mee|0.5 eV

)

GeV−5 ≃ (2.7 TeV)−5

•

9

Energy Scale:


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

10

Energy Scale:


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

11

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

νe

W

e−

d u u

e−

d

νe

W

is 4 loop diagram: mBBν ∼ G2

F

(16π2)4MeV5 ∼ 10−25 eV

explicit calculation: Duerr, Lindner, Merle, 1105.0901

12

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

1

m2b1

− 1

m2b2

∣

∣

∣

∣

∣

∣

∣

∼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

13

Some features

• Majoranas 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/vector boson:

A ∝ 1

q2 −m2→ 1

m2

14

Dib et al., hep-ph/0006277

15

Chiralities

W

νi

νi

W

dL

dL

uL

e−L

e−L

uL

Uei

q

Uei

A ∝ PL/q +mi

q2 −m2i

PL ∝ mi

q2 −m2i

≃

mi/q2 (m2

i ≪ q2)

1/mi (m2i ≫ q2)

WR

NR

NR

νL

W

dR

dL

uR

e−R

e−L

uL

A ∝ PR/q +mi

q2 −m2i

PL ∝ /q

q2 −m2i

≃

1/q (m2i ≪ q2)

q/m2i (m2

i ≫ q2)

16

Heavy neutrinos

W

νi

νi

W

dL

dL

uL

e−L

e−L

uL

S ei

q

S ei

if heavier than 100 MeV:

Ah = G2F

S2ei

Mi≡ G2

F 〈 1m〉 ⇒ 〈 1m 〉 <∼ 10−8 GeV−1

dimensionless LNV parameter:

ηh = mp 〈1

m〉 ≤ 1.7× 10−8

17

Faessler, Gonzalez, Kovalenko, Simkovic, 1408.6077

18

An exact See-Saw Relation

Full mass matrix:

M =

0 mD

mTD MR

= U

mdiagν 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

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

|N2ei mi| = |S2

eiMi| <∼ 0.3 eV

compare withS2ei

Mi

<∼ 10−8 GeV−1 and |Sei|2 ≤ 0.0052

19

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

⇒ cancellations required to make heavy neutrinos contribute significantly to

0νββ

20

TeV scale seesaw with sizable mixing

mν = m2D/MR ≃ v2/MR

with mν ≃√

∆m2A it follows that MR ≃ 1015 GeV and

S = mD/MR =√

mν/MR ≃ 10−13

then, heavy neutrino contribution to 0νββ negligible:

S2/MR = m2D/M3

R ≃ 10−41 GeV−1

can make MR TeV, but then mixing√

mν/MR ≃ 10−7 and still

m2D/M3

R ≃ 10−17 GeV−1

21


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 = M01 (here ω = e2iπ/3)

gives mν = 0, add (very) small corrections. . .

mD = v, MR = TeV, mixing mD/MR large, 0νββ contribution large

22


can also make everything smaller:

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

∣

∣

∣

∣

Al

Ah

∣

∣

∣

∣

=

G2F

q2 |mee|G2

F 〈 1m〉≃ 10−4 GeV2

q2≃ 10−2

23

Higgs triplets (type II seesaw)

W

W

∆−−

dL

dL

uL

e−L

e−L

uL

√

2g2vL hee

A∆ ≃ G2F

hee vLm2

∆

<∼ G2F

(mν)eem2

∆

= G2F

|mee|m2

∆

plays no role in 0νββ

24

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)

25


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

|Vei|2 = 1.0

|Vei|2 = 0.0052

|Vei|2 = 5.0 10

-8 (M

i /GeV)

dσ

d cos θ=

G2F

32π

{

∑

(mν)i U2ei

(

t

t− (mν)i+

u

u− (mν)i

)}2

26


Extreme limits:

• light neutrinos:

σ(e−e− → W−W−) =G2

F

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−) =G2

F

4π

(

∑

U2ei (mν)i

)2

⇒ amplitude grows with√s? Unitarity??

27

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

mdiagν 0

0 MdiagR

UT

if Higgs triplet is present: unitarity also conserved

σ(e−e− → W−W−) =G2

F

4π

(

(U2ei (mν)i − (mL)ee

)2= 0

W.R., PRD 81

28

Contents


III1) Basics


III3) SUSY


29

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, 13)

for symmetry breaking:

∆L ≡

δ+L/√2 δ++

L

δ0L −δ+L/√2

∼ (3,1,2) , ∆R ≡

δ+R/√2 δ++

R

δ0R −δ+R/√2

∼ (1,3,2)

φ ≡

φ01 φ+

2

φ−1 φ0

2

∼ (2,2,0)

30

Left-right Symmetry

• very rich Higgs sector (13 extra scalars)

• rich gauge boson sector (Z ′,MW±R

) with

MZ′ =√

21−tan2 θW

MWR ≃ 1.7MWR

• ’sterile’ neutrinos νR

• type I + type II seesaw for neutrino mass

• right-handed currents with strength GF

(

gRgL

)2 (mW

MWR

)2

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

mass

(Note: in case of modified symmetry breaking gL 6= gR and MZ′ < MWR

possible. . .)

31

Left-right Symmetry

6 neutrinos, flavor states n′L = (ν′L, νR

c)T , mass states nL = (νL, NcR)

T

n′L =

ν′L

νRc

=

KL

KR

nL =

U S

T V

νL

N cR

right-handed currents:

LlepCC =

g√2

[

ℓLγµKLnL(W

−1µ + ξeiαW−

2µ) + ℓRγµKRn

cL(−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

32

Connection to neutrinos

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

Lνmass = − 1

2

(

ν′L ν′Rc)

ML MD

MTD MR

ν′Lc

ν′R

⇒ mν = ML −MD M−1R MT

D

useful special cases

(i) type I dominance: mν = MD M−1R MT

D = MD f−1R /vR MT

D

(ii) type II dominance: mν = fL vL

for case (i): mixing of light neutrinos with heavy neutrinos of order

|Sαi| ≃ |T Tαi| ≃

√

mν

Mi

<∼ 10−7

(

TeV

Mi

)1/2

small (or enhanced up to 10−2 by cancellations)

33

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

LlepCC =

g√2

3∑

i=1

[

eLγµ(UeiνLi + SeiN

cRi)(W

−1µ + ξeiαW−

2µ)

+ eRγµ(T ∗

eiνcLi + V ∗

eiNRi)(−ξe−iαW−1µ +W−

2µ)]

LℓY =− 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)

34

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 ≃ G2F

mee

q2AR

NR≃ G2

F

(

mWL

MWR

)4∑

i

V ∗ei

2

Mi

<∼ 0.3 eV <∼ 4 · 10−16 GeV−5

∝ L2

R∝ L4

R5

35

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 ≃ G2F

heevLm2

δL

AδR ≃ G2F

(

mWL

MWR

)4∑

i

V 2eiMi

m2δR

−− <∼ 4 · 10−16 GeV−5

(negligible) ∝ L4

R5

36

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 ≃ G2F

(

mWL

MWR

)2∑

i

UeiT∗ei

1

qAη ≃ G2

F tan ξ∑

i

UeiT∗ei

1

q

<∼ 1 · 10−10GeV−2 <∼ 6 · 10−9

∝ L3

R3q∝ L3

R3q

37

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∝∑ U2

ei

mi

Tello et al., 1011.3522

38

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

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

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 θWand

gR√

1− δ2 tan2 θWZ ′µ f(

TR3 + (TL

3 −Q)δ2 tan2 θW)

f

where δ = gL/gR

41

Da (far and uncertain) future:

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

42

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

Background

1000 2000 3000 4000 5000

0.2

0.4

0.6

0.8

1.0

Meff HGeVL

gef

f

Helo et al., PRD 88

one 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

Background

one 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

Meff HGeVL

geff

Peng, Ramsey-Musolf, Winslow, 1508.04444

45

QCD corrections

• matrix element multiplied with αs/(4π) lnM2W /µ2, match with eff. diagram

• run that down to 0νββ scale p2 = (100 MeV)2 ⇒ αs/(4π) lnM2W /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

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

Example TeV-scale WR: leading to washout e±R e±R → W±RW±

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: log10ΓW (qq → ℓ+ℓ+ qq)

H>∼ 6.9 + 0.6

(

MX

TeV− 1

)

+ log10σLHC

fb

(TeV-0νββ, LFV and YB: Deppisch, Harz, Huang, Hirsch, Päs)

↔ post-Sphaleron mechanisms, τ flavor effects,. . .

47

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)

1026

1028

1030

1032

[T1

/2] ν

(yrs

)

GERDA 40kg

GERDA 1T

Normal

0.0001 0.001 0.01 0.1

Excluded by KamLAND-Zen

InvertedmδR

= 3.5 TeV

mδR = 2 TeV

mδR = 1 TeV

Barry, W.R., JHEP 1309

48

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

Xe vs. Ge

1024

1025

1026

T1/2[136

Xe] (yrs)

1024

1025

1026

T1/

2[76G

e] (

yrs) GERDA

HM

Ge Combined

EX

OK

amLA

ND

-Zen

Xe

Com

bine

d

IBM (M-S)QRPA (CCM)

1024

1025

1026

T1/2[136

Xe] (yrs)

1024

1025

1026

T1/

2[76G

e] (

yrs) GERDA

HM

Ge Combined

EX

OK

amLA

ND

-Zen

Xe

Com

bine

d

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

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

Contents


III1) Basics


III3) SUSY


52

III3) Supersymmetry

L/R = λijk Li Lj eck + λ′

ijk Li Qj dck + λ′′

ijkuci d

cj d

ck + ǫi LiHu

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

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

Λ5SUSY

54


Actually. . .

ηg =πα3

6

λ′2111

G2F

mp

mg

(

1

m4uL

+1

m4dR

− 1

2m2uL

m2dR

)

ηχ =πα2

2

λ′2111

G2F

4∑

i=1

mp

mχi

(

V 2Li(u)

m4uL

+V 2Ri(d)

m4dR

− VLi(u)VRi(d)

m2uL

m2dR

)

η′g =2πα3

3

λ′2111

G2F

mp

mg

1

m2uL

m2dR

ηχe = 2πα2λ′2111

G2F

4∑

i=1

mp

mχi

V 2Li(e)

m4eL

ηχf = πα2λ′2111

G2F

4∑

i=1

mp

mχi

(

VLi(u)VRi(d)

m2uL

m2dR

− VLi(u)VLi(e)

m2uL

m2eL

− VLi(e)VRi(d)

m2eLm2

dR

)

55


gluino dominance:

ηg/R1≃ πα3

6

λ′2111

G2F

mp

mg m4dR

(

1 +

(

mdR

muL

)2)2

≤ 7.5× 10−9

translates into

λ′2111

mg m4dR

(1 +m2dR

/m2uL

)2<∼ 1.8× 10−17 GeV−5

56


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

57

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

58

RPV SUSY and inverse 0νββ

χ0

uLdc

eL

eL

λ′∗111

uLdc

eL

eL

λ′∗111

χ0

uL

dc

eL

eLλ′111

uL

dceL

eLλ′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∼ 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)

Kom, W.R., 1110.3220

59

Cool effect somewhere else

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

Dev, W.R.

60

Supersymmetry: long range

b

νe

bc

W

dc

dL

uL

e−L

e−L

uL

Ab/R2

≃ GF1

qUei

mb

Λ3SUSY

λ′131 λ

′113

61

Supersymmetry: long range

Test with B0-B0 mixing

νe

d

bc

b

dc

constrains λ′131 λ

′113/Λ

4SUSY

gives currently stronger constraint than 0νββ

62

Contents


III1) Basics


III3) SUSY


63


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

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!

65


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

66


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

67

Distinguishing via nuclear physics

challenging, but possible if nuclear physics is under control (sic!)

recall:

1

T 0ν1/2(A,Z)

= G(Q,Z) |M(A,Z) η|2

if you measured two isotopes:

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

⇒ third reason for multi-isotope determination

68


Gehman, Elliott, hep-ph/0701099

3 to 4 isotopes necessary to disentangle mechanism

69


• 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


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

Dircet vs. indirect contribution

Example: introduce Ψi = (8, 1, 0) and Φ = (8, 2, 12 )

να νβΨi 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 ≃ G2F

|mee|q2

A ≃ c2udy2eα

MΨi M4Φ

72

Dircet vs. indirect contribution

new contribution can dominate over standard one:

Choubey, Dürr, Mitra, W.R., JHEP 1205

73

Summary

74

neutrinoless double beta decay · 2016. 5. 11. · neutrinoless double beta decay is mediated by...

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