Neutrinoless double beta decay with light sterile neutrinos

Kaori Fuyuto

Los Alamos National Laboratory

W. Dekens, J. de Vries, KF, E. Mereghetti, G. Zhou February 14, 2021 JHEP06(2020)097 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 mass The observation of neutrino oscillation confirms neutrinos have mass.

ν3 ν2 2 sol

ν m e ∆ ν1

νμ 2 atm m ∆ ν τ

ν2 2 sol m ∆ ν1 ν3

Normal hierarchy Inverted hierarchy 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? 6 Neutrinoless double beta decay

Double βdecay without neutrino emission

(A, Z) (A, Z + 2) + 2e ! e

Nuclei ⌫¯

e

The process can occur if neutrino is a Majorana particle. 7 Majorana mass

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

Yukawa Majorana Mass 1 = Y L¯H˜ ⌫ ⌫c M ⌫ +H.C L⌫R ⌫ R 2 R R R

+ ⌫L G L = , H = 1 , v 246 GeV eL (v + h) ' ✓ ◆ ✓ 2 ◆ c T ⌫R = C⌫R C : charge conjugation matrix 8 Majorana mass

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

Yukawa Majorana Mass 1 = Y L¯H˜ ⌫ ⌫c M ⌫ +H.C L⌫R ⌫ R 2 R R R

v v : Mass insertion νR v : Higgs VEV νL νL 9 Majorana mass

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

Yukawa Majorana Mass 1 = Y L¯H˜ ⌫ ⌫c M ⌫ +H.C L⌫R ⌫ R 2 R R R

Majorana mass term is induced.

v v 1 = ⌫¯m ⌫ Lmass 2 ⌫ (⌫ = ⌫c) ν ν 10 Majorana mass

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

Yukawa Majorana Mass 1 = Y L¯H˜ ⌫ ⌫c M ⌫ +H.C L⌫R ⌫ R 2 R R R

If MR is much heavier than EW scale,

v v 2 2 Y⌫ v m⌫ ⇠ MR ν ν 11 Majorana mass

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

Yukawa Majorana Mass 1 c ⌫ = Y⌫ L¯H˜ ⌫R ⌫ MR⌫R +H.C LIf neutrinosR are Majorana particles,2 R 0ν2β is induced. * Three light Majorana neutrino case (M v) This diagram leads to a Majorana mass term for Rneutrinos. v v 2 2 Y⌫ v m⌫ ⇠ MR ν ν 12 Standard case

Three light Majorana neutrinos : νi=1~3 d u W± e-

νi=1~3 e- W± d u : Mass insertion

Left-handed vector operator :

(6) GF µ (6) (6) = u¯L dLe¯LµC ⌫ C = 2VudUei L p2 VLL VLL 13 Standard case

Three light Majorana neutrinos : νi=1~3

n p ν e- q ν e- n p

3 m 1 3 U 2 i U 2 m A0⌫2 ⇠ ei q2 + m2 ⇠ q2 ei i i=1 i i=1 ! X O(100) MeV X 14 Standard case

Three light Majorana neutrinos : νi=1~3

n p ν e- q ν e- n p Oscillation data 3 m 1 3 U 2 i U 2 m A0⌫2 ⇠ ei q2 + m2 ⇠ q2 ei i i=1 i i=1 ! X X O(100) MeV Effective mass : mββ 15 Standard case Oscillation data : PRD98(2018)030001 [PDG]

i c12c13 s12c13 s13e U = PMNS 0 ··· ··· ··· 1 ··· ··· ··· @ A 2 2 2 5 2 m = m m =7.39 10 [eV ] 21 2 1 ⇥ 2 2 2 3 2 m = m m = 2.5 10 [eV ] 31 3 1 ± ⇥ Ex) Normal hierarchy case

c2 m c2 + ei↵s2 m2 + m2 + eis2 m2 + m2 A0⌫2 / 13 1 12 12 1 21 13 1 31  ✓ q ◆ q The amplitude is described by the lightest neutrino mass. 16 Standard case Oscillation data : PRD98(2018)030001 [PDG]

i c12c13 s12c13 s13e U = PMNS 0 ··· ··· ··· 1 ··· ··· ··· @ A 2 2 2 5 2 m = m m =7.39 10 [eV ] 21 2 1 ⇥ 2 2 2 3 2 m = m m = 2.5 10 [eV ] 31 3 1 ± ⇥

1 Inverse half-life : T 0⌫ = g4 G 2 1/2 A 0⌫ |A0⌫2| ⇣ ⌘

gA =1.27,G0⌫ : Phase space factor 17 Search for 0ν2β

KamLAND-Zen T 0⌫ 136Xe > 1.06 1026 yr 1/2 ⇥ PRL117(2016)+082503 Current limit on half-life 18

Standard case Normal Hierarchy (NH) m1

Inverted Hierarchy (IH)

m3

* Bands 1) Majorana phase 2) Matrix elements

QRPA Shell Current limit on half-life 19

Standard case Normal Hierarchy (NH) m1

Inverted Hierarchy (IH)

m3

Future sensitivity

27 10 yr : KamLAND2-Zen ⇠ 1028 yr : nEXO ⇠ Current limit on half-life 20

Standard case Normal Hierarchy (NH) m1

Inverted Hierarchy (IH)

m3

Future sensitivity

27 10 yr : KamLAND2-Zen Standard case : Three light Majorana ⇠neutrinos (MR v) 1028 yr : nEXO What about light MR case?⇠ For more details, see 21 Beyond the standard case M. Drewes, 1303.6912 Other phenomenological aspects:

MR Leptogenesis 9 & 10 GeV W. Buchmuller, et al , Ann.Rev.Nucl.Part.Sci. BAU 55 (2005)311, E. K. Akhmedov, et al, PRL81(1998)1359 TeV T. Asaka, et al, PLBB620, 17 (2005), ⇠ DM candidate keV DM S. Dodelson, L. M. Widrow, PRL72(1994)17 ⇠ T. Asaka, et al, PLBB638, 401 (2006), Short-baseline neutrino oscillation

eV LSND : PRD64(2001)112007 ⌫¯ ⌫¯ ⇠ Anomalies MiniBooNE : PRL110(2013)161801 µ e Reactor anomaly : PRD83(2011)073006 ! MiniBooNE : PRL121(2018)221801 ⌫µ ⌫e PRL102(2009)101802 ! Wide mass range! For more details, see 22 Beyond the standard case M. Drewes, 1303.6912 * Need theoretical analysis in light of light sterile neutrinos

MR Leptogenesis 9 & 10 GeV W. Buchmuller, et al , Ann.Rev.Nucl.Part.Sci. BAU 55 (2005)311, E. K. Akhmedov, et al, PRL81(1998)1359 TeV T. Asaka, et al, PLBB620, 17 (2005), ⇠

keV DM DM candidate ⇠ S. Dodelson, L. M. Widrow, PRL72(1994)17 Short-baseline neutrino oscillation

eV LSND : PRD64(2001)112007 ⌫¯ ⌫¯ ⇠ Anomalies MiniBooNE : PRL110(2013)161801 µ e Reactor anomaly : PRD83(2011)073006 ! MiniBooNE : PRL121(2018)221801 ⌫µ ⌫e PRL102(2009)101802 ! 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) 1 1 = Y L¯H˜ ⌫ ⌫c M ⌫ + C(6) (6) L ⌫ R 2 R R R ⇤2 ⌫R O

(6) GF C⌫R

⌫L ⌫R ⌫R × VS × ⌫R ⌫L 25 Our study

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

* Non-standard interactions (d = 6) 1 1 = Y L¯H˜ ⌫ ⌫c M ⌫ + C(6) (6) L ⌫ R 2 R R R ⇤2 ⌫R O

* Derive the master formula depending on MR

Mass range : MR eV 1015GeV

Capture the behavior of light- and high-mass neutrino SM + Light sterile neutrinos EFT G. Prezeau, M. Ramsey-Musolf, and P. Vogel, PRD68, 034016 (2003) 27 V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, JHEP 12, 082(2017) EFT approach V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, JHEP 12, 097(2018) e¯ u¯ ⇤new New Physics Xnew

d ⌫R 28 EFT approach

⇤new New Physics

SM + sterile neutrino EFT Ex) e¯ u¯ (6) 1 C⌫R 2 ⇠ mX d ⌫R 29 EFT approach

⇤new New Physics

SM + sterile neutrino EFT

LNC dim 6 operators

µ d¯ u (¯⌫Rµe) L¯⌫R H˜ H†H ¯ µ Qu (¯⌫RL) (¯⌫R e) H˜ †iDµH ¯ ¯ ⇣ ⌘ L⌫R ✏ QRd I I L¯µµ⌫R ⌧ HW˜ Ld¯ ✏ Q¯R⌫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 GeV Mixing ⇠ 1 = N cM N +h.c. Lmass 2 ⌫

⌫L 0 MD⇤ N = c ,M⌫ = ⌫ M † M † ✓ R◆ ✓ D R◆

✔ ︎ Diagonalize Mν with an unitary matrix U

✔ ︎ Integrate out heavy SM particles 31 EFT approach

⇤new New Physics

SM + sterile neutrino EFT

100 GeV Mixing ⇠

(6) GF µ (6) (6) Ex) = u¯L dLe¯LµCVLL⌫ +¯uLdRe¯LCSRR⌫ L p2 # 

C(6) 2V U ⌫ (i =1, 2, 3) VLL ud ij j Unitary matrix

2 (6) v (6) (6) ¯a ¯b C C U ⇤ ⌫ = L d✏abQ ⌫R SRR 2 LdQ⌫ kl l OLdQ⌫ R ⇣ ⌘ 32 EFT approach

⇤new New Physics

SM + sterile neutrino EFT

100 GeV Mixing ⇠

If 1 GeV . mi . v , ⌫i should also be integrated out.

C(6) ⌫R 2 m C(6) i ⌫i ⌫R 2 2 ⇠ q + mi C(6) h i ⌫R Sterile neutrino mass 33 EFT approach

⇤new New Physics

SM + sterile neutrino EFT

100 GeV Mixing ⇠

If 1 GeV . mi . v , ⌫i should also be integrated out.

C(9) 2 (9) (6) 1 C C⌫R ⇠ mi h i * 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) ⌫ e g C(6) ⇠ LEC n p Low energy constant 35 EFT approach

1 GeV Nucleon and pion interactions ⇠ ~ Chiral Perturbation Theory G. Prezeau, M. Ramsey-Musolf, and P. Vogel, PRD68, 034016 (2003) ⌫ e g C(6) ⇠ LEC n p Short-range contributions e e e ⇡ n p ± e e e n p ⇡± ⇡± n p * Hard-neutrino contributions: V. Cirigliano, et al., PRL120(2018)20, 202001; PRC100(2019)055504 36 EFT approach

1 GeV Nucleon and pion interactions ⇠ ~ Chiral Perturbation Theory

G. Prezeau, M. Ramsey-Musolf, and P. Vogel, PRD68, 034016 (2003)

n p e (6) ⌫i nn ppee gLEC,C e A ! n p ⇣ ⌘ 37 EFT approach

1 GeV Nucleon and pion interactions ⇠ ~ Chiral Perturbation Theory

G. Prezeau, M. Ramsey-Musolf, and P. Vogel, PRD68, 034016 (2003)

n p e (6) ⌫i nn ppee gLEC,C e A ! n p ⇣ ⌘

1 MeV Transition amplitudes : ⇠ + + 0⌫2 = 0 nn ppee 0 A |A ! | ⌦ ↵ 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 MeV Transition amplitudes : ⇠ g ,C(6),M A0⌫2 LEC NME ⇣ ⌘ Nuclear matrix element (Many-body methods ) 39 EFT approach

1 GeV Nucleon and pion interactions ⇠ ~ Chiral Perturbation Theory

G. Prezeau, M. Ramsey-Musolf, and P. Vogel, PRD68, 034016 (2003)

1 MeV Transition amplitudes : ⇠ g ,C(6),M A0⌫2 LEC NME ⇣ ⌘ Inverse half-life : 1 T 0⌫ = g4 G 2 1/2 A 0⌫ |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.

8 NR-EDF 7 R-EDF QRPA Jy 6 QRPA Tu QRPA CH 5 IBM-2

ν SM Mi 0 4

M SM St-M,Tk 3

2

1 J. Engel, J. Menendez 0 Rept.Prog.Phys. 80(2017)046301

1031 ] 2

1030 [y meV 2 ββ m

ν 29 0 1/2 10 T

1028 48 76 82 96 100 116 124 130 136 150 A LECs 41 Well determined by experiments or Lattice Lattice

Several LECs are still unknown. 42 EFT approach

Interpolation formula of M NME ( m i ) and gLEC(mi)

Dim 9 100 GeV ⇠

1 GeV Smoothly connect ⇠ Long Short

⌫i 1 MeV ⇠ gLEC

* This makes it possible to analyze NDBD in any mass spectrum. NMEs and LECs 43

Mass dependence of the amplitude : 0⌫2(mi) 136 |A | Xe u¯ µd e¯ ⌫ L L L µ - Two different NMEs 136Xe QRPA Shell - Peak around O(100) MeV

mi 2 2 q + mi O(100) MeV - Similar behavior in literature J.Barea, et al PRD92(2015)093001

- Large uncertainty in LECs mi [MeV] NMEs and LECs 44

Mass dependence of the amplitude : 0⌫2(mi) 136 |A | Xe (¯u µd u¯ µd )¯e ⌫ L L ⇥ R R L µ - Two different NMEs QRPA 136Xe Shell - 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) 3+1 scenario 46

One sterile neutrino : m4 1 = Y L¯H˜ ⌫ ⌫c M ⌫ +H.C L⌫R ⌫ R 2 R R R * Standard interactions 3+1 scenario 47

One sterile neutrino : m4 1 ⌫ = N cM N +h.c. N = L Lmass 2 ⌫ ⌫c ✓ R◆

Assumption : Two parameters MD and MR

000MD⇤ Yukawa 000MD⇤ M⌫ = 0 1 000MD⇤ BM ⇤ M ⇤ M ⇤ M C Majorana B D D D RC @ A m1 = m2 =0 1 m = M 2 + 12 M 2 M (m >m ) 3,4 2 | R| | D| ±| R| 4 3 hp i 3+1 scenario 48

One sterile neutrino : m4 1 ⌫ = N cM N +h.c. N = L Lmass 2 ⌫ ⌫c ✓ R◆

Assumption : Two parameters MD and MR

000MD⇤ Yukawa 000MD⇤ M⌫ = 0 1 000MD⇤ BM ⇤ M ⇤ M ⇤ M C Majorana B D D D RC @ A * Not satisfy oscillation data but good example to understand behaviors of 0ν2β 3+1 scenario 49

One sterile neutrino : m4

(6) 2GF µ (6) (6) = u¯L dLe¯LµC ⌫ C = 2VudUij L p2 VLL VLL

* Cancellation of LO contribution in light-mass region M. Blennow, et al, JHEP07(2010)096 (6) C 2 2 VLL For q m i q 2 mi 2 mi Uei 1+ + ⇠ q2 q2 ··· (6) ✓ ◆ CVLL LO vanishes q O(100)MeV 2 ⇠ miUei =(M⌫ )11 =0 136 50 m4 vs Half-life ( Xe)

The half-life is well above experimental reach. J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013) 51 J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013) Leptoquark 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) J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013) 52 J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013) Leptoquark 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 : R˜ (3, 2, 1/6) All possible scalar LQs: PRD43(1991)225 = yRLd¯ R˜✏L + yLRQ¯R˜⌫ LLQ R R J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013) 53 J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013) Leptoquark 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 : R˜ (3, 2, 1/6) = yRLd¯ R˜✏L + yLRQ¯R˜⌫ LLQ R R

Gauge-invariant dim6 operator: L¯ Q¯ R˜ (6) = C(6) Ld¯ ✏ Q¯⌫ L⌫R LdQ⌫ R R 1 C(6) = yLRyRL d ⌫ LdQ⌫ 2 ⇤ R R mLQ J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013) 54 J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013) Leptoquark 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 : R˜ (3, 2, 1/6) = yRLd¯ R˜✏L + yLRQ¯R˜⌫ LLQ R R

L¯ Q¯ R˜ LQ parameters : LR RL mLQ = 10 TeV y y ⇤ =1.0 dR ⌫R Leptoquark 55 Scalar and tensor operators show up below EW scale:

(6) 2GF (6) µ⌫ (6) = u¯LdRe¯LC ⌫i +¯uL dRe¯Lµ⌫ C ⌫i L p2 SRR TRR  2 (6) (6) v (6) N = 4(5) CSRR =4CTRR = CLdQ⌫ (UUNi⇤4⇤i + U5⇤i) 2 i =1 4(5) ⇠ Leptoquark 56 Scalar and tensor operators show up below EW scale:

(6) 2GF (6) µ⌫ (6) = u¯LdRe¯LC ⌫i +¯uL dRe¯Lµ⌫ C ⌫i L p2 SRR TRR  2 (6) (6) v (6) N = 4(5) CSRR =4CTRR = CLdQ⌫ (UUNi⇤4⇤i + U5⇤i) 2 i =1 4(5) ⇠

2GF µ (6) Induced by mixing + u¯L dLe¯LµC ⌫ p2 VLL (No LQ interaction)

(6) C = 2VudUij i =1 3,j=1 4(5) VLL ⇠ ⇠ Leptoquark 57 Scalar and tensor operators show up below EW scale:

(6) 2GF (6) µ⌫ (6) = u¯LdRe¯LC ⌫i +¯uL dRe¯Lµ⌫ C ⌫i L p2 SRR TRR  2 (6) (6) v (6) N = 4(5) CSRR =4CTRR = CLdQ⌫ (UUNi⇤4⇤i + U5⇤i) 2 i =1 4(5) ⇠

Neutrino exchange Pion exchange n p n p e π e νi e π e n p n p

* πN and NN interactions are neglected in our analyses. 58 3+1 : m 4 vs Half-life

* Dominant contribution : m4 Standard interactions (6) CSRR,TRR

⌫4

(6) CSRR,TRR

Pink : No LQ interaction (vector contribution) * LQ interactions dominate over standard contributions. 59 3+1 : m 4 vs Half-life

* Dominant contribution : m4 Standard interactions (6) CSRR,TRR

⌫4

(6) CSRR,TRR

T 0⌫ 136Xe > 1.06 1026 yr 1/2 ⇥ KamLAND -Zen : PRL117(2016)+082503 Ruled out 0.1 MeV . m4 . 100 GeV 60 3+1 : m 4 vs Half-life

* Dominant contribution : m4 Standard interactions (6) CSRR,TRR

⌫4

(6) CSRR,TRR

Future sensitivity 27 10 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)

2 5 2 2 3 2 m =7.39 10 [eV ] m =2.5 10 [eV ] 21 · 32 · 2 1 2 1 sin ✓12 =3.10 10 sin ✓ =5.58 10 · 23 · 2 2 sin ✓ =2.241 10 Dirac =1.23⇡ 13 ·

[3 + 2] ✓45 = ⇡/8 45 =0.5 Majorana phases = 0

m4,5 : free parameters 63 3+2 standard : m 4 vs Half-life

Three choices of m5 :

Blue : m5 = 30 MeV

Pink : m5 = 100 MeV

Green : m5 = 500 MeV

Future sensitivity 1028 yr : nEXO ⇠ 27 10 yr : KamLAND2-Zen ⇠ 64 3+2 LQ : m 4 vs Half-life

Three choices of m5 :

Blue : m5 = 10 eV

Red : m5 =1keV

Green : m5 =1MeV

For the two-light cases, the excluded region is 0.1 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.

Mass range : MR eV 1015GeV

Our study : Model-independent analyses with light νR - Possible to analyze NDBD in any mass spectrum with interpolation formulae

- Non-standard interactions can dominate

✔ ︎ Applicable to models with light sterile neutrinos!