Transcript Nuclear
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
O νββ -Decay (forbidden in Standard Model) Neutrino Mass e 1
P Left n
e 2
P ν Left n Phase Space 10 6 x 2 νββ
W 1 = cos q W L + sin q W R n = n c Majorana Neutrino W 2 = -sin q W L + cos q W R Neutrino must have a Mass n Majorana , N L , N R
Neutrinoless Double Beta Decay Probability Amand Faessler, Tuebingen
• • • • 1. Different Methods for the 0 nbb -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-Fock Bogoliubov (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.).
128 Te Not in QRPA 82 Se Increasing Admixtures in the Ground State Amand Faessler, Tuebingen
Basis Size Effect for 82 Se 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 0 bbn 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 0 nbb 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 76 Ge Amand Faessler, Tuebingen
Fermi and Gamow-Teller 0 nbb Transition Operator with Closure 0 nbb 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 + |DIAS> = |T, T-2> T 0 + 0 + T |IAS> = |T, T-1> T |g.s.
i > =|T, T> |T-2,T-2> |g.s.
f >=|0 f + > + e |DIAS> Amand Faessler, Tuebingen
Fermi 0
nbb
Transition Operator
Amand Faessler, Tuebingen
Transition Matrix Elements for Fermi Transitions: First Leg Second Leg 0 + 0 + T |IAS> = |T, T-1> Exp. (d, 2 He): Frekers; T Sakai; Zegers |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 o nbb Light left handed Majorana n ?
Exchange Heavy left handed Majorana n Heavy right handed Majorana n Exchange 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 u d W L n kM mass U n ek=1,2,3 e e W L 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. 76 Ge, 100 Mo, 130 Te; | h| 2 > 0 and our matrix element for g A = 1.25 Due to ratios only minimal changes for g A =1.00
Amand Faessler, Tuebingen
Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino Three different transitions needed, e.g. 76 Ge, 100 Mo, 130 Te, to determine the three parameters.
Amand Faessler, Tuebingen
Neutrino Mass from
0nbb
Experiment Klapdor et al. 76 Ge Mod. Phys. Lett. A21,1547(2006) ; T(1/2; 0
nbb
) = (2.23 +0.44 -0.31) x 10 25 years; 6
s •
Matrix Elements: QRPA Tuebingen
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 T T Amand Faessler, Tuebingen
3) Summary
Search for the Leading Mechanism One Leading Mechanism: Determine the h 1 ( m n ?) in two systems. Is it the same? Two leading non-interfering mechanisms: Determine h 1 and h 2 in three systems Two interfering mechanisms: Determine h 1 , h 2 and the relative phase theta in three nuclei and verify it in three nuclei with at least one other.
Amand Faessler, Tuebingen