Description of Double Beta Decay,
Nuclear Structure and Physics
beyond the Standard Model Status and Prospects.
Amand Faessler
University of Tuebingen
Nuclear Phy sics in Astrophysics-V.
Eilat, April 5th. 2011
Oνββ-Decay (forbidden in
Standard Model)  Neutrino Mass
e2
P
e1
P
Left
ν
Left
Phase Space
106 x 2νββ
n
n
W1 = cos q WL+ sin q WR
n = nc Majorana Neutrino
Neutrino must have a Mass
W2 = -sin q WL + cos q WR
nMajorana, NL, NR
Amand Faessler, Tuebingen
Neutrinoless Double BetaDecay Probability
Amand Faessler, Tuebingen
1. Different Methods for the
0nbb-Matrix Elements for the
Light Majorana Neutrino Exchange.
A. Escuderos, A. Faessler, V. Rodin, F. Simkovic, J. Phys.
G37 (2010) 125108; arXiv: 1001.3519 [nucl-th]
• Quasi-Particle Random Phase Approximation
(QRPA; Tübingen).
• Shell Model (Strasbourg-Madrid).
• Angular Momentum Projected Hartee-FockBogoliubov (Tuebingen; P. K. Rath et al.).
• Interacting Boson Model (Barea and Iachello).
Amand Faessler, Tuebingen
a) QRPA all the Ring
diagrams:
Ground State: 0, 4, 8, 12
, … quasi- particles
(seniority)
b) The Shell Model
Ground state: 0, 4, 6, 8, ….
Problem for SM: Size of the Single Particle Basis.
Amand Faessler, Tuebingen
Additive Contributions of 0, 4, 6, …
Quasi-Particle States in the SM (Poves et al.).
128Te
Not in QRPA
82Se
Increasing Admixtures
in the Ground State
Amand Faessler, Tuebingen
Basis Size Effect for 82Se on the
Neutrinoless Double Beta Decay.
4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2
4levels: Ikeda Sum rule 50 %; 5 levels 60 %;
6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2
9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2
Amand Faessler, Tuebingen
Contribution of Higher Angular
Momentum Pairs in Projected HFB.
HFB
0bbn
Only even Angular Momentum Pairs
with Positive Parity can contribute.
IBM: = 0+ and 2+ Pairs
Amand Faessler, Tuebingen
QRPA (TUE), Shell Model
IBM2, PHFB
Amand Faessler, Tuebingen
2. Can one measure the Matrix
Elements of the 0nbb Decay?
V. Rodin, A. F. , Phys. Rev. C80 (2009), arXiv: 0906.1759
and 1012.5176 [nucl-th] to be published.
Fermi part: Shell Model = (1/5) QRPA in 76Ge
Amand Faessler, Tuebingen
Fermi and Gamow-Teller 0nbb
Transition Operator with Closure
0nbb Transition Matrix Element
with Closure Relation:
Amand Faessler, Tuebingen
Fermi Strength concentrated in the Isobaric Analogue
State |IAS> and Double Isobaric Analogue State |DIAS>
Isotensor force needed: T  T-2; Coulomb Interaction
0+
0+
T-
|DIAS> = |T, T-2>
T-
0+
|g.s.i> =|T, T>
|IAS> = |T, T-1>
T|T-2,T-2>
|g.s.f>=|0f+> + e|DIAS>
Amand Faessler, Tuebingen
Fermi 0nbb Transition Operator
Amand Faessler, Tuebingen
Transition Matrix Elements
for Fermi Transitions:
First Leg
Second Leg
0+
T-
|IAS> = |T, T-1>
Exp. (d,2He): Frekers;
T- Sakai; Zegers
0+
|g.s.i> =|T, T>
|g.s.f> = |T-2,T-2> + e|DIAS>
Amand Faessler, Tuebingen
3. How to find the Leading
Mechanism for the onbb ?
•
•
•
•
Light left handed Majorana n Exchange
Heavy left handed Majorana n Exchange
Heavy right handed Majorana n Exchange
SUSY Lepton Number Violating Mechanis.
F. Simkovic, J. Vergados, A. Faessler,
Phys. Rev. D82, 055502 (2010)
A. Faessler, A. Meroni, S. T. Petcov, F.
Simkovic, J. Vergados, to be published.
Amand Faessler, Tuebingen
GUT: Light and Heavy left handed
Majorana Neutrino Exchange
d
u
WL
NkM
n
kL
mass
eUNnek=1,2,3
ek=4,5,6
e-
WL
d
u
Amand Faessler, Tuebingen
SUSY: R-Parity Breaking
Lepton Number-Violating
Minimal Supersymmetric Model
Superfields:
Amand Faessler, Tuebingen
Neutrinoless Inverse Half Life
propto Transition Probability
Amand Faessler, Tuebingen
Transition Probability prop to Inverse
Half Life; SUSY Contribution l‘.
Dominance of Gluino echange in short range part assumed.
Similar expression for Dominance of Neutralino exchange.
Amand Faessler, Tuebingen
Two leading non-interfering Mechanisms:
Light Majorana and Heavy R Neutrino
i = different nuclei, e.g. 76Ge, 100Mo, 130Te;
|h|2 > 0 and our matrix element for gA = 1.25
Due to ratios only minimal
changes for gA=1.00
Amand Faessler, Tuebingen
Two interfering Mechanisms:
Light Majorana and Heavy Left Neutrino
Three different transitions needed, e.g. 76Ge,
100Mo, 130Te, to determine the three parameters.
Amand Faessler, Tuebingen
Neutrino Mass from 0nbb
Experiment Klapdor et al. 76Ge
Mod. Phys. Lett. A21,1547(2006) ;
T(1/2; 0nbb) = (2.23 +0.44 -0.31) x 1025 years; 6s
Matrix Elements: QRPA Tuebingen
• <m(n)> = 0.24 [eV]
(exp+-0.02; theor+-0.01) [eV]
Amand Faessler, Tuebingen
1) Summary
Comparing four different approaches
for the 0nbb matrix elements:
a. Shell model only small basis; violates the Ikeda
sum rule by 50 to 60%.
b. Interacting boson Model: only s (0+) and d (2+)
pairs.
c. Projected Hartee Fock Bogoliubov: Only 0+ pairs.
d. QRPA large basis; fulfils Ikeda sum rule; realistic
forces.
Amand Faessler, Tuebingen
2) Summary
Shell model for Fermi Transition
~ 1/5 of QRPA
0+
IAS
TTAmand Faessler, Tuebingen
3) Summary
Search for the Leading Mechanism
One Leading Mechanism: Determine the
h1(mn ?) in two systems. Is it the same?
Two leading non-interfering mechanisms:
Determine h1 and h2 in three systems
Two interfering mechanisms: Determine h1, h2
and the relative phase theta in three nuclei and
verify it in three nuclei with at least one other.
THE END
Amand Faessler, Tuebingen