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 P P n n Left ν Phase Space 10 6 x 2 νββ Amand Faessler, Tuebingen e1e1 e2e2  = c Majorana Neutrino Neutrino must have a Mass W 1 = cos  W L + sin  W R W 2 = -sin  W L + cos  W R Majorana, N L, N R

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) ; arXiv: [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 128 Te 82 Se Not in QRPA Increasing Admixtures in the Ground State

Basis Size Effect for 82 Se 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 %;

Amand Faessler, Tuebingen Basis Size Effect for 128 Te on the Neutrinoless Double Beta Decay. 5 levels (Shell Model): 0g7/2, 1d572, 2s1/2, 1d3/2, 0h11/2 7 levels: 0g7/2, 1d572, 2s1/2, 1d3/2, 0h11/2, 0g9/2, 0h9/2 13 levels: N=3, N=4, 0h11/2, 0h9/2, 1f7/2, 1f5/2 Ikeda sum Rule: 60 %

Amand Faessler, Tuebingen

Different Seniority Contributions s for 82 Se and 128 Te in QRPA and the Shell Model Amand Faessler, Tuebingen M 0 s=0 s= 4, (6), 8,… total ISR% 82 Se 4lev QRPA Se 4lev SM Se 6lev QRPA Se 9lev QRPA Te 5lev QRPA Te 5lev SM Te 7lev QRPA Te 13lev QRPA level basis: p 3/2, f 5/2, p 1/2, g 9/2 6 level basis: f 7/2, p 3/2, f 5/2, p 1/2, g 9/2, g 7/2 9 level basis: d 5/2, s 1/2, d 3/2, f 7/2, p 3/2, f 5/2, p 1/2, g 9/2, g 7/2

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

QRPA (TUE), Shell Model (Madrid-Strassburg), IBM2, PHFB 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: and [nucl-th] to be published. Fermi part: Shell Model = (1/5) QRPA in 76 Ge

Amand Faessler, Tuebingen 3. Can one measure the Matrix Elements of the 0  Decay?

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 >=|0 f + > +  |DIAS> Amand Faessler, Tuebingen T-T- T-T- T-T Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS> Isotensor force needed: T  T-2; Coulomb Interaction

Gamow Teller Strength not concentrated in one State broad Resonance. Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0  S=0  Gamow-Teller: g A s a s b |Pair> = - g A 3|Pair> Fermi: g V |Pair> = 1 |Pair> Shell Model for Fermi ~ (1/5) of QRPA Amand Faessler, Tuebingen

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-T Transition Matrix Elements for Fermi Transitions: First Leg Second Leg T-T- Exp. (d, 2 He): 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, (2010) A. Faessler, A. Meroni, S. T. Petcov, F. Simkovic, J. Vergados, to be published.

5/2/2015Fedor Simkovic22 n Smallness of neutrino masses - Seesaw mnmn mDmD MRMR T. Yanagida, M. Gell-Mann, P. Ramond, R. Slansky If n R exists  then neutrino are naturaly massive  mass is unprotected by symmetry, can be large at a scale of LNV Sterile neutrinos n R Familiar light masses N m 1 =m D 2 /M R «m D m 2 ≈M R n 1 = n L -m D /M R ( n R ) c n 2 =n R +m D /M R ( n L ) c Assumption M R » m D Eigenvalues and eigenvectors

Amand Faessler, Tuebingen du d u WLWL WLWL kM mass e-e- e-e- GUT: Light and Heavy left handed Majorana Neutrino Exchange U ek=1,2,3  kL mass U  ek=4,5,6

Amand Faessler, Tuebingen du d u WRWR WRWR NRNR e-e- e-e- Light and Heavy left handed Majorana Neutrino Exchange V N ek

Amand Faessler, Tuebingen SUSY: R-Parity Breaking Lepton Number-Violating Minimal Supersymmetric Model Superfields:

5/2/2015Fedor Simkovic26 R-parity Breaking MSSM R-parity breaking terms In superpotential Neutrino-Neutralino mixing matrix (see-saw structure) Radiative corrections to neutrino mass Gozdz, Kaminski, Šimkovic, PRD 70 (2004)

Fedor Simkovic27 Gluino/neutralino exchange R-parity breaking SUSY mechanism of the 0  - decay quark-level diagrams exchange of squarks, neutralinos and gluinos d+d → u + u + e - + e -  ‘ 111

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.

Dominance of Neutralino Exchange Faessler, Gutsche, Kovalenko, Simkovic Phys. Rev. D77 (2008) Amand Faessler, Tuebingen

5/2/2015Fedor Simkovic31 Squark mixing SUSY mechanism Mixing between scalar Super-partners of the left- and right- handed fermions

Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino Amand Faessler, Tuebingen i = different nuclei, e.g. 76 Ge, 100 Mo, 130 Te; |    and our matrix element for g A = 1.25 Due to ratios only minimal changes for g A =1.00

Two leading non-interfering Mechanisms: Quenched g A ; Light Majorana and Heavy R Neutrino Amand Faessler, Tuebingen i = different nuclei, e.g. 76 Ge, 100 Mo, 130 Te; |    and quenched g A = 1.00 Due to ratios only minimal changes for g A =1.00

Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino Amand Faessler, Tuebingen Three different transitions needed, e.g. 76 Ge, 100 Mo, 130 Te, to determine the three parameters.

Neutrino Mass from   Experiment Klapdor et al. 76 Ge  Mod. Phys. Lett. A21,1547(2006) ;  T(1/2; 0  ) = ( ) x years; 6  Matrix Elements: QRPA Tuebingen = 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

T-T ) Summary T-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