Neutrinoless double beta decay
with light sterile neutrinos
Kaori Fuyuto
Los Alamos National Laboratory

W. Dekens, J. de Vries, KF, E. Mereghetti, G. Zhou
JHEP06(2020)097

February 14, 2021
NDBD Workshop
LA-UR-21-21157

Outline :1. Introduction
2. Neutrinoless double beta decay- EFT approach with light sterile neutrino

3. Standard vs Non-standard interactions
4. Summary

Introduction

4

Neutrino massνe

ν3

ν1∆ m2atmν μ
ν τ∆ m2solν2ν2ν1Normal hierarchy

ν3

Inverted hierarchy∆m2solThe observation of neutrino oscillation confirms
neutrinos have mass.

5

Neutrino mass
The observation of neutrino oscillation confirms
neutrinos have mass.
Ex) Electron : 0.5 MeV

< 1eV

ν

e
Open question :What is the origin of the tiny but non-vanishing masses of the neutrinos?

Neutrinoless double beta decay

6

Double βdecay without neutrino emission(A, Z) ! (A, Z + 2) + 2e

Nucleie⌫¯e

The process can occur if neutrino is a Majorana particle.

7

Majorana mass
Right-handed neutrino : ⌫R~ Gauge singlet (Sterile neutrino)

L ⌫R =L=✓Yukawa

Majorana MassY⌫ L̄H̃⌫R1 c⌫R MR ⌫R + H.C2◆⌫L, H=eLc⌫R= C⌫R T✓+◆G, v ' 246 GeV
12 (v + h)

C : charge conjugation matrix8

Majorana mass
Right-handed neutrino : ⌫R~ Gauge singlet (Sterile neutrino)

L ⌫R =Yukawa

Majorana MassY⌫ L̄H̃⌫R

1 c⌫R MR ⌫R + H.C2vv: Mass insertion

νRνLνLv : Higgs VEV

9

Majorana mass
Right-handed neutrino : ⌫R~ Gauge singlet (Sterile neutrino)

L ⌫R =

YukawaMajorana MassY⌫ L̄H̃⌫R1 c⌫R MR ⌫R + H.C
2Majorana mass term is induced.
v

νv

ν

1Lmass =⌫¯m⌫ ⌫2(⌫ = ⌫ c )10

Majorana mass
Right-handed neutrino : ⌫R
~ Gauge singlet (Sterile neutrino)

L ⌫R =

YukawaMajorana MassY⌫ L̄H̃⌫R

1 c⌫R MR ⌫R + H.C
2

If MR is much heavier than EW scale,vνv

νY⌫2 v 2m⌫ ⇠MR

11

Majorana mass
Right-handed neutrino : ⌫R~ Gauge singlet (Sterile neutrino)
YukawaMajorana Mass1 cL⌫R = Y⌫ L̄H̃⌫R⌫R MR ⌫R + H.C
2If neutrinos are Majorana particles,0ν2β is induced.
v)* ThreelightMajorana
neutrinoThis
diagramleads
to a Majorana
masscaseterm (Mfor Rneutrinos.
v

νv

νY⌫2 v 2m⌫ ⇠MR

12Standard caseThree light Majorana neutrinos : νi=1~3due-W±

νi=1~3deu

W±: Mass insertion
Left-handed vector operator :L(6)GF(6)= p ūL µ dL ēL µ CVLL ⌫2(6)CVLL =2Vud Uei

13Standard caseThree light Majorana neutrinos : νi=1~3pnνqν

nA0⌫23X

eep

1mi2
⇠ 2
⇠
Uei 2
2q + miqi=1O(100) MeV

3X
i=12
Uei
mi!

14

Standard caseThree light Majorana neutrinos : νi=1~3pn
νq
νn

eep
Oscillation data

A0⌫23X

1mi2
⇠ 2
⇠
Uei 2
2q + miqi=1O(100) MeV

3X
i=12
Uei
mi!

Effective mass : mββ15Standard case
Oscillation data : PRD98(2018)030001 [PDG]
0c12 c13
UPMNS = @ · · ····

s12 c13······

i1

s13 e··· A···

m221 = m22

m21 = 7.39 ⇥ 10 5 [eV2 ]m231 = m23

m21 = ±2.5 ⇥ 10 3 [eV2 ]Ex) Normal hierarchy case✓A0⌫2 / c213 m1 c212 + ei↵ s212q

m21 +

m221

◆

+ ei s213q

m21 + The amplitude is described by the lightest neutrino mass.

m231

16

Standard case
Oscillation data : PRD98(2018)030001 [PDG]
0c12 c13
UPMNS = @ · · ····

s12 c13······i1s13 e··· A···

m221 = m22

m21 = 7.39 ⇥ 10 5 [eV2 ]m231 = m23

m21 = ±2.5 ⇥ 10 3 [eV2 ]⇣0⌫
Inverse half-life : T1/2

⌘ 1

4= gA
G0⌫ |A0⌫2 |2gA = 1.27, G0⌫ : Phase space factor

17

Search for 0ν2β0⌫ 136
T1/2
Xe > 1.06 ⇥ 1026 yr

KamLAND-Zen
PRL117(2016)+082503

18

Current limit on half-life
Standard caseNormal Hierarchy (NH)m1 < m2 < m3
Inverted Hierarchy (IH)

m3 < m1 < m2* Bands1) Majorana phase2) Matrix elements
QRPAShell

19

Current limit on half-life
Standard caseNormal Hierarchy (NH)m1 < m2 < m3
Inverted Hierarchy (IH)

m3 < m1 < m2
Future sensitivity⇠ 1027 yr : KamLAND2-Zen⇠ 1028 yr : nEXO

20Current limit on half-life
Standard caseNormal Hierarchy (NH)m1 < m2 < m3
Inverted Hierarchy (IH)

m3 < m1 < m2
Future sensitivity
27⇠
10: KamLAND2-Zenv)
Standard case : Three light Majorana neutrinosyr(MR⇠ 1028 yr : nEXO

What about light MR case?

Beyond the standard caseFor more details, see
M. Drewes, 1303.6912

Other phenomenological aspects:
MR& 10 GeV

Leptogenesis

9BAU

E. K. Akhmedov, et al, PRL81(1998)1359
T. Asaka, et al, PLBB620, 17 (2005),

⇠ TeV
⇠ keV

W. Buchmuller, et al , Ann.Rev.Nucl.Part.Sci.
55 (2005)311,

DM

DM candidate
S. Dodelson, L. M. Widrow, PRL72(1994)17
T. Asaka, et al, PLBB638, 401 (2006),

Short-baseline neutrino oscillation⇠ eV
Wide mass range!

Anomalies

LSND : PRD64(2001)112007
MiniBooNE : PRL110(2013)161801
Reactor anomaly : PRD83(2011)073006
MiniBooNE : PRL121(2018)221801
PRL102(2009)101802⌫¯µ ! ⌫¯e⌫µ ! ⌫e21

Beyond the standard caseFor more details, see
M. Drewes, 1303.6912* Need theoretical analysis in light of light sterile neutrinos

MR& 10 GeV

Leptogenesis

9BAU

E. K. Akhmedov, et al, PRL81(1998)1359
T. Asaka, et al, PLBB620, 17 (2005),

⇠ TeV
⇠ keV

W. Buchmuller, et al , Ann.Rev.Nucl.Part.Sci.
55 (2005)311,

DM

DM candidate
S. Dodelson, L. M. Widrow, PRL72(1994)17

Short-baseline neutrino oscillation⇠ eVAnomalies

LSND : PRD64(2001)112007
MiniBooNE : PRL110(2013)161801
Reactor anomaly : PRD83(2011)073006
MiniBooNE : PRL121(2018)221801
PRL102(2009)101802⌫¯µ ! ⌫¯e⌫µ ! ⌫e22

23

Our study
Model-independent analysis in the light νR scenario~ Effective Field Theory

24

Our study
Model-independent analysis in the light νR scenario~ Effective Field Theory* Non-standard interactions (d = 6)
L=Y⌫ L̄H̃⌫R

1 c
1 (6) (6)
⌫ R MR ⌫ R + 2 C ⌫ R O2⇤C⌫(6)
RGF
⌫L
⌫R ×
⌫L

⌫RVS×
⌫R

25

Our study
Model-independent analysis in the light νR scenario~ Effective Field Theory* Non-standard interactions (d = 6)
L=Y⌫ L̄H̃⌫R

1 c1 (6) (6)⌫ R MR ⌫ R + 2 C ⌫ R O
2⇤* Derive the master formula depending on MReV

Mass range : MR1015 GeV

Capture the behavior of light- and high-mass neutrino

SM + Light sterile neutrinos EFT

EFT approach⇤newG. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)
V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, JHEP 12, 082(2017)
V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, JHEP 12, 097(2018)

New Physics

ē

ū
Xnewd

⌫R27

28

EFT approach⇤new

New Physics
SM + sterile neutrino EFTEx)

ē

ū
C⌫(6)
⇠Rd

⌫R

1m2X

29

EFT approach⇤new

New Physics
SM + sterile neutrino EFT
LNC dim 6 operators†L̄⌫R H̃ H H⇣⌘(¯⌫R µ e) H̃ † iDµ H

L̄ µµ ⌫R ⌧ I H̃W Id¯ µ u (¯⌫R µ e)Q̄u (¯⌫R L)

L̄⌫R ✏ Q̄R dL̄d ✏ Q̄R ⌫R* 7 independent operators
Y. Liao and X.-D. Ma, Phys. Rev. D96, 015012 (2017)

30

EFT approach⇤new

New Physics
SM + sterile neutrino EFT⇠ 100 GeVMixing
1 c
Lmass =N M⌫ N + h.c.
2
✓ ◆✓
0⌫L
N=,M⌫ =
†c
⌫RMD

⇤
MDMR†

◆

✔︎ Diagonalize Mν with an unitary matrix U✔︎ Integrate out heavy SM particles

31

EFT approach
New Physics⇤new

SM + sterile neutrino EFTMixing⇠ 100 GeVEx)

L(6)

(6)

CVLL



GF
(6)
(6)
= p ūL µ dL ēL µ CVLL ⌫ + ūL dR ēL CSRR ⌫22Vud Uij ⌫j(i = 1, 2, 3)

Unitary matrix(6)

CSRRv 2 (6)⇤CLdQ⌫ Ukl
⌫l2

⇣

(6)
OLdQ⌫ = L̄a d✏ab Q̄bR ⌫R⌘#32

EFT approach
New Physics⇤newSM + sterile neutrino EFTMixing⇠ 100 GeV

If 1 GeV . mi . v , ⌫i should also be integrated out.
C⌫(6)
R⌫iC⌫(6)R⇠hC⌫(6)
Ri2miq2 + m2iSterile neutrino mass

33EFT approach
New Physics⇤newSM + sterile neutrino EFTMixing⇠ 100 GeV

If 1 GeV . mi . v , ⌫i should also be integrated out.
C (9)

h(6)

C (9) ⇠ C⌫Ri2 1mi* Described by Dim 9 operator

34

EFT approach⇠ 1 GeV

Nucleon and pion interactions~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

Ex)

n⌫ep

⇠ gLEC C (6)Low energy constant

35

EFT approach
Nucleon and pion interactions⇠ 1 GeV~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

⌫epne
⇡

±

⇠ gLEC C (6)Short-range contributions
e±en
⇡epnp

⇡

±npee

* Hard-neutrino contributions:
V. Cirigliano, et al., PRL120(2018)20, 202001; PRC100(2019)055504

36

EFT approach
Nucleon and pion interactions⇠ 1 GeV~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

pn
⌫inee

⇣

Ann!ppee gLEC , C (6)
p⌘

37

EFT approach
Nucleon and pion interactions⇠ 1 GeV~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

pn⌫in⇠ 1 MeVee⇣

Ann!ppee gLEC , C (6)pTransition amplitudes :

A0⌫2

⌦ +↵
+= 0 |Ann!ppee | 0

Initial and final nuclei states

⌘

38

EFT approach⇠ 1 GeV

Nucleon and pion interactions~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

⇠ 1 MeVTransition amplitudes :A0⌫2⇣gLEC , C (6) , MNME

⌘Nuclear matrix element(Many-body methods )39EFT approach⇠ 1 GeV

Nucleon and pion interactions~ Chiral Perturbation Theory
G. Prezeau, M. Ramsey-Musolf, and P.Vogel, PRD68, 034016 (2003)

⇠ 1 MeVTransition amplitudes :A0⌫2⇣gLEC , C (6) , MNME⌘

Inverse half-life :⇣⌘ 120⌫
4T1/2= gA G0⌫ |A0⌫2 |gA = 1.27, G0⌫ : Phase space factor

NMEs

40

NMEs obtained with different nuclear-structure
approaches differ by factors of two or three.
8760ν5M

4NR-EDFR-EDFQRPA Jy
QRPA TuQRPA CH
IBM-2SM Mi
SM St-M,Tk32J. Engel, J. Menendez
Rept.Prog.Phys. 80(2017)046301

102T1/2 mββ [y meV ]10310ν

21030

10291028

4876 82

96 100

A116 124 130 136

150

LECs41
Well determined byexperiments or Lattice

Lattice

Several LECs are still unknown.

42

EFT approach
Interpolation formula of MNME (mi ) and gLEC (mi )Dim 9⇠ 100 GeV

Smoothly connect⇠ 1 GeVLong⇠ 1 MeVShort⌫igLEC* This makes it possible to analyze NDBD in any mass spectrum.

43

NMEs and LECs
Mass dependence of the amplitude : |A0⌫2 (mi )|136 XeūL µ dL ēL µ ⌫136

- Two different NMEsQRPAShell

Xe- Peak around O(100) MeV

miq2 + m2i
O(100) MeV- Similar behavior in literature
J.Barea, et al PRD92(2015)093001

mi [MeV]- Large uncertainty in LECs

44NMEs and LECs
Mass dependence of the amplitude : |A0⌫2 (mi )|136 Xe(ūL µ dL ⇥ ūR µ dR ) ēL µ ⌫QRPAShell

136

Xe- Two different NMEs- Peak around O(1) GeV* Nontrivial behavior
due to LECs
- Not discussed in literature- Large uncertainty in LECs

mi [MeV]3 + 1 Standard vs Non-standard case(Leptoquark)46

3+1 scenario
One sterile neutrino : m4
L ⌫R =Y⌫ L̄H̃⌫R

1 c⌫R MR ⌫R + H.C
2* Standard interactions

47

3+1 scenario
One sterile neutrino : m4Lmass =1 c
N M⌫ N + h.c.
2N=✓⌫Lc⌫R◆

Assumption : Two parameters MD and MR00B 0M⌫ = B@ 0⇤
MD000⇤
MD000⇤MD1⇤MD⇤CMDC⇤AMDMR

m1 = m2 = 0i
1 hp
m3,4 =|MR |2 + 12|MD |2 ± |MR |2Yukawa
Majorana(m4 > m3 )483+1 scenario
One sterile neutrino : m4Lmass =1 cN M⌫ N + h.c.
2N=✓⌫Lc⌫R◆

Assumption : Two parameters MD and MR

00B 0M⌫ = B@ 0⇤
MD000⇤
MD000⇤
MD1

⇤
MD
⇤CMDC
⇤AMDMR

YukawaMajorana* Not satisfy oscillation data but good example
to understand behaviors of 0ν2β49

3+1 scenario
One sterile neutrino : m4L(6)2GF(6)µpūL dL ēL µ CVLL ⌫=2(6)CVLL =2Vud Uij* Cancellation of LO contribution in light-mass region
M. Blennow, et al, JHEP07(2010)096

(6)

CVLLq
(6)

CVLLq ⇠ O(100)MeV

For q2m2i✓◆
2
mi 2mi⇠ q2 Uei 1 + q2 + · · ·LO vanishes
2mi Uei= (M⌫ )11 = 0

m4vs Half-life (136Xe)

The half-life is well above experimental reach.

50

LeptoquarkJ. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)
J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)
I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Leptoquark (LQ) couples to the SM quark and lepton+ sterile neutrinos (1, 2 flavors)51

LeptoquarkJ. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)
J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)
I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Leptoquark (LQ) couples to the SM quark and lepton+ sterile neutrinos (1, 2 flavors)
Scalar LQ : R̃ (3, 2, 1/6)

LLQ =All possible scalar LQs: PRD43(1991)225

y RL d¯R R̃✏L + y LR Q̄R̃⌫R

52

LeptoquarkJ. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)
J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)
I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Leptoquark (LQ) couples to the SM quark and lepton+ sterile neutrinos (1, 2 flavors)
Scalar LQ : R̃ (3, 2, 1/6)

LLQ =Q̄

L̄

Gauge-invariant dim6 operator:
(6)

L(6)
⌫R = CLdQ⌫ L̄dR ✏ Q̄⌫RR̃
dR

y RL d¯R R̃✏L + y LR Q̄R̃⌫R⌫R(6)
CLdQ⌫ =1 LR RL⇤
y y2mLQ

53

LeptoquarkJ. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)
J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)
I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Leptoquark (LQ) couples to the SM quark and lepton+ sterile neutrinos (1, 2 flavors)
Scalar LQ : R̃ (3, 2, 1/6)

LLQ =Q̄L̄R̃
dR⌫Ry RL d¯R R̃✏L + y LR Q̄R̃⌫R

LQ parameters :mLQ = 10 TeV

y LR y RL⇤ = 1.054

Leptoquark
Scalar and tensor operators show up below EW scale:L(6)2GF(6)(6)µ⌫p=ūL dR ēL CSRR ⌫i + ūLdR ēL µ⌫ CTRR ⌫i22v
N⇤ = 4(5)
(6)
(6)
(6)
⇤⇤UN4ii + U5i )CSRR = 4CTRR = CLdQ⌫ (U2i = 1 ⇠ 4(5)

55

56

LeptoquarkScalar and tensor operators show up below EW scale:
L

(6)

2GF
(6)
(6)
µ⌫p=ūL dR ēL CSRR ⌫i + ūLdR ēL µ⌫ CTRR ⌫i22v
N⇤ = 4(5)
(6)
(6)
(6)
⇤⇤UN4ii + U5i )CSRR = 4CTRR = CLdQ⌫ (U2i = 1 ⇠ 4(5)2GF(6)µ+ p ūL dL ēL µ CVLL ⌫2(6)CVLL =2Vud Uij

Induced by mixing(No LQ interaction)i = 1 ⇠ 3, j = 1 ⇠ 4(5)57

Leptoquark
Scalar and tensor operators show up below EW scale:
L

(6)

2GF
(6)
(6)
µ⌫p=ūL dR ēL CSRR ⌫i + ūLdR ēL µ⌫ CTRR ⌫i22v
N⇤ = 4(5)
(6)
(6)
(6)
⇤⇤UN4ii + U5i )CSRR = 4CTRR = CLdQ⌫ (U2i = 1 ⇠ 4(5)Neutrino exchangepn
νineepPion exchangennpπeπep* πN and NN interactions are neglected in our analyses.

58

3+1 : m4 vs Half-life* Dominant contribution : m4Standard interactions(6)

CSRR,TRR⌫4(6)CSRR,TRR

Pink : No LQ interaction(vector contribution)* LQ interactions dominate
over standard contributions.

59

3+1 : m4 vs Half-life* Dominant contribution : m4
Standard interactions(6)

CSRR,TRR⌫4(6)CSRR,TRR0⌫ 136
T1/2
Xe > 1.06 ⇥ 1026 yr
KamLAND-Zen : PRL117(2016)+082503

Ruled out
0.1 MeV . m4 . 100 GeV

60

3+1 : m4 vs Half-life* Dominant contribution : m4Standard interactions(6)

CSRR,TRR⌫4(6)CSRR,TRR

Future sensitivity⇠ 1027 yr : KamLAND2-Zen⇠ 1028 yr : nEXO
m4 & 10 keV

3 + 2 Standard vs Non-standard case
(Leptoquark)62

3 + 2 scenario
Two sterile neutrinos : m4 and m5* Normal hierarchy is assumed.
Oscillation parameters [PDG]PRD98, 030001(2018) and update (2019)
m232 = 2.5 · 10 3 [eV2 ]m221 = 7.39 · 10 5 [eV2 ]sin2 ✓12 = 3.10 · 10 1sin2 ✓13 = 2.241 · 10 2
[3 + 2]✓45 = ⇡/8sin2 ✓23 = 5.58 · 10 1
Dirac = 1.23⇡
45 = 0.5

Majorana phases = 0m4,5 : free parameters63

3+2 standard : m4 vs Half-life
Three choices of m5 :Blue : m5 = 30 MeV
Pink : m5 = 100 MeV
Green : m5 = 500 MeV
Future sensitivity⇠ 1028 yr : nEXO
⇠ 1027 yr : KamLAND2-Zen

64

3+2 LQ : m4 vs Half-life
Three choices of m5 :Blue : m5 = 10 eV
Red : m5 = 1 keVGreen : m5 = 1 MeVFor the two-light cases,
the excluded region is0.1 MeV . m4 . 100 GeV

65

Summary

Search for neutrinoless double beta decay is a probe of Majorana mass.
Sterile neutrinos are motivated by various phenomena.

eVMass range : MR

1015 GeV

Our study : Model-independent analyses with light νR - Possible to analyze NDBD in any mass spectrumwith interpolation formulae- Non-standard interactions can dominate✔︎ Applicable to models with light sterile neutrinos!