Experimental Aspects of DBDs beyond
the standard model and Nuclear matrix elements
Hiro Ejiri RCNP Osaka

Greenary Nimph 翠の精Experimental Aspects of DBDs
1. DBDs beyond the Standard Mdel.
2. The light Majorana n mass
3. Nuclear matrix elements (NMEs)

4. Experimental approaches to NMES
5. Remarks and perspectives

Thanks Prof. Hinohara and the organizers.

1. Ejiri H 2005 J. Phys. Soc Jpn. 74 2101

2. Vergados J, Ejiri H , Simkovic F 2012 Rep. Prog. Phys. 75 ,106301
3. Ejiri H, Suhonen J and Zuber Z 2019 Phys. Rep. 797 1
1. Hashim I, Ejiri H, Shima T, et al., Phys. Rev, 2018 97, 014617.
2. Ejiri H 2019 Frontiers in Physics 10.3389/fphys. 0003

3. Ejiri H, 2019 J. Phys. G. Nucl. Part. Phys. 46 125202
4. Jokiniemi L, Suhonen J, Ejiri H, Hashim I, PL B 2019 795 143.
5. Ejiri H , CER collaboration . 2020 J. Phys. 47 LT 01.
6. Ejiri H, Universe 2020 6, 225

7 . Ejiri H, Advances High Energy Phys. 2021 ID 6666720
8. Ejiri H, Frontiers Physics, 2021 650421

I. DBDs beyond the standard EW modelNeutrino-less bb decays
0nbb A = B + b + b

Lepton number DL=2 beyond SM.
.
Particle astro physics
Majorana n, mn CP, RHC

T0n = G0n [M0n fn]2EXP
Kinematic
Phase Space

NNR,Nucl. phys. gA
short-range, D, pt s correlation

Why DBD : s~10-83 cm2 T~10-36/sec
A femto (10 -15cm) nuclear collider
Luminosity/3 t L~1076/cm2 /sec = 3 10 83/cm2 /ynnt, tseent,tsnppnn

3 ton 10 30 neutrons with 1/3 light velocity in a bahn area
A few counts per ton year in case of IH 20 meV M=2LHC L~1033 /cm2 /sec
2021/2/11

1. Energy spectra to select the 0nbb 2-3 body processes

n matrix and masses

m3

m2
m1

DmS ~9 meV
DmA ~45meV

m2
m1

n e nmnt
m3

NHn e nmnt

IH
Absolute mass scale< mn> = |S Ui2 exp(i fi) mi|

fi=a2-a1, fi = a2-2d

is given by using Ui DmS, DmA given by n oscillations

Mass hierarchy
IfIH

meff is>15 meV IH< 12 meV NH➢
Need meff , M0nwithin 30 %NH=lowest mass

J. Vergados, H. Ejiri, F. Simkovic, ROPP. 75 (2012) 106301.
H. Ejiri, J. Phys. Soc. Jpn. 74 (2005) 2101.

IH mass m3 << m1 < m 2<m> ~ m(A) (1-sin2 2 q12 sin2a12) ½60

Neutrino mass m eff meV50403020
10003060

a2-a190deg.

Phase difference = a2-a1 to be measured . 0-p/2 : m= 50-18 meV± 5 meV, i.e.NME ± 15 % to get the phase difference ±p/12

L-R symmetric model : Left right weak currentsRHC L/R weak boson mass ratio l and mixing q<m>=|SmjUej|
2021/2/11<l>=(ML/MR)2|SUejVej|<h>=tanqLR|SUejVej|

C. Q21 and E12 correlations to identify LHC/RHC<m>～0.3 eV, <l> ~ 7 10-7, <h> ~ 4 10-9

H. Ejiri , N. Kudomi et al
ELEGANTPR C 63 2001 065501
100Mo tracking detector
2021/2/11

II. Majorana n mass IH and NH

A. Non-zero 0nbb :Majorana and [Mass×M0n]
B. Limits on T ½ Dirac orMaj. limit on [Mass × NME]

Neutrino massmeV100102７ y

IH mass
10IH

m0=20 meV( 2/M0n)
Se, Mo, Te, Xe

1029 yNH mass

11031 y0.1
110NME

Key elements for n-mass by DBD
T0n =G[Mmneff ]2mneff : m0 phase, mass hierarchy

T0n , M are 2 key elements for mneff G phase spacen- mass –sensitivity ( m to be measured)
m=[ k /M] [ B/N]¼ k=G-1/2 M=NME•

M = NME, B=BG/ty N=Isotope mass ton• A: T0n Exp. 10-27-30/y. N- multi-ton B 1/t y
B : M No direct exp. No accurate theory yet
Exp. to help theory evaluate M

¼m= 1.5 m0[B/N] for 0.5 detector efficiency
N: Isotopes ton, B : BG per ton year T=5 y
m0 = k/M M=NME
m0 ~ 20 meV in case of M=2
B=1, N=1,30 meV IH

B=0.01. N=100
3 meV NH

2021/2/11

DBD 0nbb NMEs and DBD mass sensitivity¼m= k [m ] [ B/N]
0M0n=k2 M(QRPA) ~ 2 , m0 =18 meV e~0.5

IH 20 meVLimits on [Mass × NME] < k/T 1/2Neutrino massmeV

1000
136Xe

1026 y76Ge76Ge1026 y>1026 y

100

IH mass
IH>1028y101110NME

Current 0.8 -0.5 1026 for Ge and Xe. To reach IH mass,A factor >10 in n-mass and >104 in NT/B

3 DBD nuclear matrix element (NME)DBD 0nbb NME
Model NMEsQuenching
due toeffects
not in model

H(r12)~1/r12 neutrino potential for 2 n for n-exchange .

M0n= SJ M(J) J= 1+ GT, 2- SD, 3+ SQ multipole sum
M(J) = Sk Mk(J), Sum over all k state with spin J

DBD NME : Three major problems , A. B. C.
A: Very small fraction of the strengthts YReduction rate k=M EXP/MQP

Initial and final (ground state) nuclei and nucleons
are very different , reduce overlap between them
10.8
0.6
0.4
0.2
00

1

M(EXP)/M(QP ) (Quasi-particle)
Single b k=k(ts) k(NM)~0.25
Double b M ~ 0.05

23Multipolarity

45

Very small fraction ofthe strength

GSGSSingle bDBD b|M(GS) |2= 1 10-2 Sum|M(GS) |2= 4 10-4 Sum

Closure approximation <i|T|GS>
GS should pick up 10-4 strengthB: Weak int.: spin isospin ts N-1N GR and N-1D GR
GR= s t flip
S [Ni-1 Dj＋]]

nstNnucleon s t N
quark ts Dj

GR=S [Ni-1 Pj]

nt- sb-Nucleus[N1-1 P1] [0+|I> = |NP> - e |GRn> - d |GR D>

Mb~ keff M0

keff (ts)~ 1/(1+ cts)

keff (D)~ 0.6

cts: susceptibility

Nuclear medium
ts polarization
+12

WW
W

N N-1
Single N

Coherent
Nucleon t s flipc=k( N-Z~10)

D N-1
Coherent
Quark t s flipc=k(N+Z~100)

Nucleonic and D ts polarization and susceptivility may
be tested in FB. March APFB by Prof. Hiyama

C: Real NME M (Nuclei) ≠ model NME M(nucleons)
Strongly interacting many hadron system , not like model
Suhonen

M0n =(gA )2 M(model).
A factor ~ 10, depending on models and parameters
Experimental inputs are indispensable

NME M = k(gA)2T= k(gA)4
N ton= k(gA)8. Ejiri H, Suhonen J and Zuber Z 2019 Phys. Rep. 797 1

4. Experimental approaches to DBD NMEs
2021/2/11

Double b decay, single b&n and CERs

DBD M1 and M2 via neutrino potential by single b NMEs
M(a, b±)= (gAeff)± M(QRPA a b±) a=GT, SD. SQ,・・(gAeff) for renormalization effects due to non-nucleonicand nuclear medium effects which are not in pnQRPA.

(gAeff)- ~ (gAeff)+ for b = (gAeff) for bb
M(a, bb) = (g eff)2 M(QRPA bb)

Response experiments by RCNP/Osakam

RCNP Osaka p,He,MuSIC m

Spring-8 GeV- MeV pol. gJ-PARC 3-50 GeV p, n, m

MLF MUSE m

Oto under gr. bb-n,High E resolution (3He,t) CERs at RCNP Osaka

DE/E ~ 2 10-5t
3Heq~ 20-200 MeV/cCER (m,nm, xn g) n-b+
E~ 5-30 MeV
q~100~50 MeV/c 2– 3+J PARC 3 GeV p(m, nm )97Nb

b,gb,g

m99Nb

100Nb

100Mo

gi from 100-iNb: relative strengthLife time : the absolute strength

H. Ejiri Proc. e-g conference Sendai 1972, H. Ejiri et al., JPSJ 2014
NNR19:I. Hashim , Hashim H. Ejiri et al., PRC 97 (2018) 014617

Nuclear p rIASGTSDmWm GRB(m)= [gA MA + gV MV+ gp Mp ]2
QRPA
EXP

Strength B( m) 10 -3706060504040302020
1000102030 nergy
40Excitation

MeV50

Jokiniemi L, Suhonen J, Ejiri H, Hashim I, PL B 2019 795 143.

geffA = 0.8
gｐ ＝7.3
Pseudscalar
Exp/QRPA suggests geffA~0.5 geffA/gA~0.4

Universal reductions of axial vector b & g i
Ejiri Fujita PR 176 1968,
PR 34 85 1978
1k=MEXP/MQR

0.8
0.6mbbg

0.4
0.200123Spin J

45H, Ejiri J. Suhonen J. Phys. G. 42 2015H. Ejiri N. Soucouti, J. Suhonen PL B 729 2014 .
L. Jokiniemi J. Suhonen H. Ejiri AHEP2016 ID8417598
L. Jokiniemi, J. Suhonen, H. Ejiri, I. Hashim PL B 794 143 2019

8.0

M0n(F)

M 0n(GT)+M 0n(T)76Ge

DBD NMEs with exp. k=gAeff/gA= 0.5

M 0n76Ge 130Te

130Te

6.0
4.0
2.0
0.0
-2.000.2

0.4

0.6
gAeff

0.8

11.2/ gAQRPA Jokinieni, Ejiri, Frekers, Suhonen Phys. Rev. C 98 2018 024608

NMEas are very sensitive tonuclear models and parameters
Suhonen 2010Ejiri 2021

Exp. NMEs

Present with gAeff/gA=0.5

QRPA Jokinieni, Ejiri, Frekers, Suhonen Phys. Rev. C 98 2018 024608

5. Perspectives and Remarks

A: Possible DBD detector with IH mass 20 meV
n-mass from 200 to 20 meV by 104 in (N/B)
1. Multi-ton enriched isotopes
2. BG 1ton year , E-resolution =0.1-2 %m0M

BG/t yN tonIsotope A

40

20.1

3Ge 76 Semiconductor

20212Se/82Mo 100 Bolometer

201130

Xe 136 TPC/Scintillator•

Coordinated collaboration works on
3 possible detectors are highly promoted.

B. Nuclear matrix elements
1. CER: nuclear (3He,t) and leptonic (m,nm) provide

single-b NMEs with J= 0-2, p=5-100 MeV/c,associated with DBD NMEs.
2. NMEs (EXP)/NME(QRPA )= quenching /renormalization

kNM=gAeff/gA~0.5 for GT, SD, m 30-80 MeV/c
3. Using the experimental gAeff/gA and QRPA, DBD NMES ~24 . Extensive experimental works on (3He,t), (d,2He) and m-CERs tostudy k=geffA multipole and nuclear dependences.
5. Extensive theoretical works on D & non-nucleonic effects
and nuclear medium effects.

C: New experimental ways for NMES
1 Neutrino beam experiments
p+A=np+ p+ →m+ + nm

SourceE GeV

SNS
1J－PARC 3

Np

Nn /s

6 1015
1.2 1015

1 10155 1014

H. Ejiri NIM. 503 (2003) 276 – 278.

m+ →e+ + ne + nm

2. Photon LEPS
Laser electron photon Sources
Pol.Laser
GeV e

H. Ejiri PRL 21 1968, PR 38 ’78

Scattered e
- =S

Pol. Laser electron photon
Eg ~ 4 g2 El = 2 108 El ~ 20 MeV,

,Tz-1,,z=5,5bgNbT,Tz=6,6A PAggbb ,z=4,4

T- isospin rotationb+ ｒesponses via IAS<f |g Mb| i> = g/e (2T)1/2 <f | emg | IAS>

Thanks for your attension

Hadronic ( D, p) *Effect on low bb 0+ - 0+P(D)2 ~ (10-2)2 ~ 10-4n

D- D0 D+ pp pp nnD-nnnD0ppppnnp-*Pontecorvo; Haxton, Stephenson, Kotani Doi .

p0np+ p

Photo nuclear reaction
Isovector component byIAS isospin T fromGround state with T-1

Ejiri H, et al. Phys. Rev. Lett. 2119 1968 373
Ejiri H, Titov. A, et al., Phys. Rev, C 88 2013 054610

Nuclear structures on 2n and 0nbb NMEs

QRPA 0nbb NMEs (Engel et al. PRC 89 (2014) 064308

2nbb NMEs triangle exp, tsquare FSQP(Ejiri) J. Phys. 2017

Single nucleon in a nucleus is 0.5 probability, NMS ~ 0.7
1. Nucleon knock-out (e,e’p) Lipikas PR C 86 2012 047304
2. Nucleon transfer reactions

B.P. kay , J.P. Schiffer , S. J. Freeman Phys. Rev> Lett. 111 201