NOW 2006 Conca Specchiulla September 9 16 2006

NOW 2006 Conca Specchiulla, September 9 -16, 2006 Recent developments in Double Beta Decay Fedor Šimkovic Comenius University, Bratislava 12/12/2021 Fedor Simkovic 1

OUTLINE • Introduction NO, n-masses, mn • From NO to 0 nbb-decay CP-phases, q 13, sterile n • Bosonic n and 2 nbb-decay • Conclusions 12/12/2021 Fedor Simkovic 2

Standard Model Lepton Universality Lepton Family Number Violation 12/12/2021 NEW PHYSICS massive neutrinos, SUSY. . . Total Lepton Number Violation Fedor Simkovic !!! Perspectives are opened !!! 3

Neutrino oscillations Massive neutrinos Reactor neutrinos Solar neutrinos 1968 Atmospheric neutrinos 1957 12/12/2021 Fedor Simkovic Accelerator neutrinos 4

Mixing of 3 light Neutrinos Pontecorvo -Maki-Nakagawa-Sakata matrix Flavor eigenstates Mass eigenstates mbb= S Uei mi ? ? ? q 13, CPphases, hierarchy, absolute mass scale ? ? ? 12/12/2021 Fedor Simkovic Mass matrix 5

n-masses in flavor basis: Inverted hierarchy em et ee mm 12/12/2021 mt tt Fedor Simkovic Gozdz, Kaminski, F. Š, Faessler, Acta Phys. Pol. 37 (2006) 2203 6

n-masses in flavor basis: Normal hierarchy em et mt tt ee mm 12/12/2021 Fedor Simkovic Gozdz, Kaminski, F. Š, Faessler, Acta Phys. Pol. 37 (2006) 2203 7

n Majorana transitional magnetic moment n-oscillations n magnetic moment n-e scattering g → nn 12/12/2021 Fedor Simkovic 8

Transitional magnetic moment of Majorana n m 0=m 1/2=150 Ge. V, A 0=100 Ge. V tan b=19 Normal hierarchy Inverted hierarchy R-parity violation SUSY, masses generated via lepton-slepton loops 12/12/2021 Fedor Simkovic Gozdz, Kaminski, F. Š, Faessler, hep-ph/0606077, to be published in PRD 9

n-oscillations 0 nbb-decay 12/12/2021 Fedor Simkovic 10

Double Beta Decay Observed for 10 isotopes: 48 Ca, 76 Ge, 82 Se, 96 Zr, 100 Mo. 116 Cd. 128 Te, 130 Te, 150 Nd, 238 U, T 18 24 1/2 ≈10 -10 years SM forbidden , not observed yet: T 1/2 ( 76 Ge)>1025 years 12/12/2021 Fedor Simkovic 11

Bilenky, Faessler, Gutsche, F. Š. , PRD 72, 053015 (2005) Goals for 0 nbb-experiments 12 12/12/2021 Normal hierarchy Inverted hierarchy 1029 -1030 years Fedor Simkovic 1027 -1028 years

q 13 and the cancellation 12/12/2021 Fedor Simkovic Bilenky, Faessler, Gutsche, F. Š. , PRD 72, 053015 (2005) 13

Perspectives of the 0 nbb-search 12/12/2021 Fedor Simkovic 14

0 nbb-decay NME 12/12/2021 Fedor Simkovic 15

NME-Nuclear structure approaches HY=EY We can not solve the full problem in the complete Systematical study of the 0 nbb-decay NME Projected mean field (Vampir) ●Tomoda, Faessler, Schmid, Grummer, PLB 157, 4 (1985) Shell model: ●Haxton, Stephensson, Prog. Part. Nucl. Phys. 12, 409(1984) ●Caurier, Nowacki, Poves, Retamosa, PRL 77, 1954 (1996) QRPA, RQRPA: About 10 papers 1987→ 2006 Other approaches: Shell Model Monte Carlo (1996), Operator Expansion Method (1988 -1994). . . 12/12/2021 Fedor Simkovic 16

QRPA 2 nbb-decay NME H = H 0 + gph Hph + gpp Hpp 21 lev. 12/12/2021 Fedor Simkovic Collapse of the QRPA 17 21 l. m. s. 12 l. m. c

Neutrinoless Double Beta Decay Nuclear Matrix Elements Recommended 0 nbb-decay NME (April 2005) Light Majorana Neutrino Exchange Mechanism 12/12/2021 V. Rodin, A. Faessler, F. Š. , P. Vogel, NPA 766 (2006) 107 Fedor Simkovic 18

Shell Model Define a valence space Derive an effective interaction H Y = E Y → Heff Yeff = E Yeff Build and diagonalize Hamiltonian matrix (1011) Transition operator < Yeff | Oeff | Yeff> ·Some phenomenological input needed energy of states, systematics of B(E 2) and GT transitions (quenching f. ) 48 Ca → 48 Ti Small calculations 12/12/2021 76 Ge 76 Se Fedor Simkovic → 76 Se 42 in the valence 19 6 protons and 14 neutrons

Comparison of M 0 n of Rodin et al. (RQRPA) and Nowacki et al. (SM, private comm. , preliminary 2004, 2006) SM results 0 nbb-decay Nucleus 2 nbb-decay Isotope T 1/2(th. )[y] T 1/2(exp. )[y] 48 Ca 3. 7 1019 4. 2 1019 76 Ge 1. 2 1021 1. 4 1021 82 Se 3. 4 1019 130 Te 1020 4. 136 Xe 6. 1020 9. 0 1019 6. 1 1020 8. 1 1020 Strasbourg group, Nowacki, IDEA meeting, Heidelberg, 2004 12/12/2021 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 130 Te 136 Xe RQRPA (2005) 2. 3 -2. 4 1. 9 -2. 1 0. 3 -0. 4 1. 1 -1. 2 -1. 4 1. 3 0. 6 -1. 0 SM (2004) 1. 6 1. 7 0. 4 0. 3 1. 9 2. 0 (1. 0) 1. 6 (0. 6) SM (2006) 1. 8 1. 7 1. 4 Except for 100 Mo the agreement between these very different calculations is reasonably good. Note that the SM calculations include the reduction Fedor Simkovic caused by the s. r. c. and 20 induced currents (30%).

Nuclear deformation Exp. I (nuclear reorientation method) Exp. II (based on measured E 2 trans. ) Theor. I (Rel. mean field theory) Theor. II (Microsc. -Macrosc. Model of Moeller and Nix) Till now, in the QRPA-like calculations of the 0 nbb-decay NME spherical symmetry was assumed The effect of deformation on NME has to be considered 12/12/2021 Fedor Simkovic 21

New Suppression Mechanism of the DBD NME The suppression of the NME depends on relative deformation of initial and final nuclei F. Š. , Pacearescu, Faessler. NPA 733 (2004) 321 Systematic study of the deformation effect on the 2 nbb-decay NME within deformed QRPA Alvarez, Sarriguren, Moya, Pacearescu, Faessler, F. Š. , 12/12/2021 Fedor Simkovic Phys. Rev. C 70 (2004) 321 22

Sterile neutrino in 0 nbb-decay 12/12/2021 Fedor Simkovic 23

Sterile neutrino in 0 nbb-decay 12/12/2021 Simkovic Beneš, Faesler, F. Š. , Fedor Kovalenko, PRD 71 (2005) 077901 24

Bosonic n in the 0 nbb-decay 12/12/2021 Fedor Simkovic 25

Since n´s have spin one half they are believed to obey Fermi statistics Bosonic n introduced: Ignatiev, Kuzmin, Yad. Fiz 46 (1987) 786 Bosonic n in 2 nbb-decay: Dolgov, Smirnov, PLB 621 (2005) 1 Motivations: Dark matter, BBN, supernova n For electrons and nucleons, a possible violation of statistics is strongly restricted by experiments. A consistent quantum field theory with of half-integer spin particles 12/12/2021 with any other statistics Fedor Simkovic 26 than the Fermi one is missing

2 nbb-decay: fermionic (f) or bosonic (b) n Sign difference!!! Lepton energies!!! 12/12/2021 Fedor Simkovic 27

bosonic 12/12/2021 fermionic Fedor Simkovic 28 Barabash, Dolgov, Dvornický, F. Š. , Smirnov, in preparation 2 nbb-decay of 100 Mo 0+g. s. → 0+g. s

Mixed statistics Definition: Commutators: Amplitude: Decay rate: 12/12/2021 Fedor Simkovic 29

12/12/2021 Large admixture of. Fedor bosonic n excluded: b 2 < 0. 75 Simkovic 30 Barabash, Dolgov, Dvornický, F. Š. , Smirnov, in preparation SSD free of log ft values

SSD free of log ft values 12/12/2021 HSD nuclei even more sensitive to admixture of bosonic n but calculation of M. E. needed Fedor Simkovic 31 Barabash, Dolgov, Dvornický, F. Š. , Smirnov, in preparation Sensitive to a small admixture of bosonic n

Outlook (NME) Moore’s law of 0 nbb-decay There will be a progress Shell model: increased computer power, larger m. s. , better effective interactios, new groups (T. Otsuka – Tokyo U. ) MCSM: unsolved problems? H. Nakada (NNR 05), Alhassid, Bertsch, Liu, Fang Projected mena field: New calculations are planed, Petrovici, Schmid QRPA: further progress expected → effects of deformation, overlap factor What is the dominant mechanism of the 0 nbb-decay? Elliott, Vogel, Ann. Rev. Nucl. Part. Sci. 52 (2002)115 Inverted hierarchy NME + PPP 12/12/2021 Fedor Simkovic There is still some time 32