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

P

P

n n

Left

Left

ν Phase Space

106 x 2νββ

Amand Faessler, Tuebingen

e1

e2

= c Majorana Neutrino

Neutrino must have a Mass

W1 = cos WL+ sin WR

W2 = -sin WL + cos WR

Majorana, NL, NR

Neutrinoless Double Beta-

Decay Probability

Amand Faessler, Tuebingen

• Quasi-Particle Random Phase Approximation (QRPA; Tübingen).

• Shell Model (Strasbourg-Madrid).

• Angular Momentum Projected Hartee-Fock-Bogoliubov (Tuebingen; P. K. Rath et al.).

• Interacting Boson Model (Barea and Iachello).Amand Faessler, Tuebingen

1. Different Methods for the 0-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]

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.

Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.).

Amand Faessler, Tuebingen

128Te

82SeNot in QRPA

Increasing Admixtures in the Ground State

Basis Size Effect for 82Se on the Neutrinoless Double Beta Decay.

Amand Faessler, Tuebingen

4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2

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

4levels: Ikeda Sum rule 50 %; 5 levels 60 %;

Contribution of Higher Angular Momentum Pairs in Projected HFB.

Only even Angular Momentum Pairs with Positive Parity can contribute.

IBM: = 0+ and 2+ Pairs

HFB 0

Amand Faessler, Tuebingen

Amand Faessler, Tuebingen

QRPA (TUE), Shell Model IBM2, PHFB

Amand Faessler, Tuebingen

2. Can one measure the Matrix Elements of the 0 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

Fermi and Gamow-Teller 0 Transition Operator with Closure

Amand Faessler, Tuebingen

0 Transition Matrix Element with Closure Relation:

|DIAS> = |T, T-2> |IAS> = |T, T-1>0+

|g.s.i> =|T, T> |T-2,T-2>

|g.s.f>=|0f+> + |DIAS>Amand Faessler, Tuebingen

T-

T-

T-

0+

0+

Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS>

Isotensor force needed: T T-2; Coulomb Interaction

Fermi 0 Transition Operator

Amand Faessler, Tuebingen

|IAS> = |T, T-1>0+

|g.s.i> =|T, T>

|g.s.f> = |T-2,T-2> + |DIAS>Amand Faessler, Tuebingen

T-

0+

Transition Matrix Elements for Fermi Transitions:

First Leg

Second Leg

T-Exp. (d,2He): Frekers; Sakai; Zegers

• Light left handed Majorana Exchange • Heavy left handed Majorana Exchange • Heavy right handed Majorana Exchange • SUSY Lepton Number Violating Mechanis.

Amand Faessler, Tuebingen

3. How to find the Leading Mechanism for the o ?

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

d u

d u

WL

WL

kM mass

e-

e-

GUT: Light and Heavy left handed Majorana Neutrino Exchange

Uek=1,2,3

kL mass

Uek=4,5,6

Amand Faessler, Tuebingen

SUSY: R-Parity Breaking Lepton Number-Violating

Minimal Supersymmetric Model

Superfields:

Amand Faessler, Tuebingen

Neutrinoless Inverse Half Life propto Transition Probability

Transition Probability prop to Inverse Half Life; SUSY Contribution

‘.

Amand Faessler, Tuebingen

Dominance of Gluino echange in short range part assumed. Similar expression for Dominance of Neutralino exchange.

Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino

Amand Faessler, Tuebingen

i = different nuclei, e.g. 76Ge, 100Mo, 130Te;| and our matrix element for gA = 1.25

Due to ratios only minimal changes for gA=1.00

Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino

Amand Faessler, Tuebingen

Three different transitions needed, e.g. 76Ge, 100Mo, 130Te, to determine the three parameters.

Neutrino Mass from Experiment Klapdor et al. 76Ge Mod. Phys. Lett. A21,1547(2006) ; T(1/2; 0) = (2.23 +0.44 -0.31) x 1025 years; 6

Matrix Elements: QRPA Tuebingen

• <m()> = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV]

Amand Faessler, Tuebingen

1) Summary Comparing four different approaches

for the 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

Amand Faessler, Tuebingen

T-

0+

2) Summary

T-

Shell model for Fermi Transition ~ 1/5 of QRPA

IAS

Amand Faessler, Tuebingen

3) Summary Search for the Leading Mechanism

One Leading Mechanism: Determine the m ?) in two systems. Is it the same?

Two leading non-interfering mechanisms: Determine 1 and 2 in three systems

Two interfering mechanisms: Determine 1, 2 and the relative phase theta in three nuclei and verify it in three nuclei with at least one other.THE END