Nuclear Transition Matrix Elements for Neutrinoless
D bl β Decay
Double-β
D
off 76Ge
G and
d 82Se
S Isotopes
I t
Theoretical Approaches
((1)) Phenomenological
g
(2) Quark model
(3) EFT
(4) Chiral EFT
(5) Lorentz invariant description
(6) Lattice QCD
Gauge theoretical models
1
2.
3.
4.
5.
6
6.
7.
Left-right
L
f
i h Symmetric
S
i models
d l
Sterile neutrinos
Majoron
j
models
SUSY models
Lepto-quark models
Compositeness
Extra-dimensional Scenario
Nuclear Structure Aspects
((1) Structure of NTMEs (nonperturbative QCD)
)
(
p
Q )
(Simkovic et al., Vegados, Faessler, Civitarese and Suhonen, Mendez)
(2) Models: ISM, QRPA, DQRPA, PHFB, EDF CDFT, IBM
(4) FNS, SRC (5) gA‐Problem
FNS
( ) Dipole
(1)
po e form
o factor
ac o
(2) Structure of nucleons
(3) ……
(4) ……….
………………
SRC
((1))
(2)
(3)
(4)
(5)
Jastrow correlations
l i
(Miller-Spencer,
( ill
CCM))
UCOM
CCM (Argonne and CD-Bonn)
FhCh
Meson exchange
Uncertainties in NTMEs
(1)
(2)
(3)
(4)
(5)
Spread (Vogel)
Global average (Bahcall, Avignone III)
Model independent (Bilenky and Grifols)
Model specific (Tuebingen, Jyväskylä)
Engel’s proposal
Experimental NTMEs
Nuclear Structure Aspects
Calculation of as many
yp
physical
y
observables as p
possible
--PRC 41, 1315 (1990)
( ) Yrast spectra
(1)
p
(2) Occupation Numbers
(3) Deformation parameter (Reduced B(E2:0+→2+) transition)
(4) Static quadrupole moments Q(2+)
(5) g-factors g(2+)
(6) M2ν
PARAMETERS
 2 : e p  1  eeff , en  eeff
( a ) gl  1.0, gl  0.0, g s


 /

eff
 0.6g s
(b) gl , g s , g p   0.89,3.18,0.73

g , g , g   0.07,1.52,0.89

l
s
p
 /

bare
Rath and Sharma, PRC 38, 2928 (1988).
Occupation Numbers
Spin-Tensor Decomposition
T1 / 2  6.1  10 ( yr ) (90%C.L.))
19
SUMMARY
(1) Relationship between ISM and MFT Approaches
(2) Structure of effective two-body effective interaction
(3) Renormalization of gA