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Double Beta Decay: A Problem of Particle, Nuclear, and Atomic Physics

This article explores the particle physics, nuclear physics, and atomic physics aspects of double beta decay, as well as the possible oscillations of atoms and double electron capture. Results obtained in collaboration with various researchers are presented.

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Double Beta Decay: A Problem of Particle, Nuclear, and Atomic Physics

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  1.  0nbb-decay:  No | Yes  Double Beta Decay A problem of particle, nuclear and atomic physics Fedor Šimkovic JINR Dubna and Comenius University, Bratislava Erice Summer School on Nuclear Physics (Sept. 2009): “Neutrinos in Astro-, Particle and Nuclear Physics” Fedor Simkovic

  2. OUTLINE • Introduction • Particle physics aspects of the 0nbb-decay • Nuclear physics aspects of the 0nbb-decay • Oscillations of atoms and double electron capture • Outlook Presented results obtained in collaboration withAmand Faesler, Th. Gutsche, V. Rodin (Tuebingen U.), J. Engel (North Caroline U.), P. Vogel (Caltech), S. Kovalenko (Valparaiso U.), M. Krivoruchenko (ITEP Moscow), R. Dvornický (Comenius U.), S.M. Bilenky (JINR Dubna), A. Smirnov (ICTP Trieste), A.Dolgov (Bologna U), A. Barabash (ITEP Moscow) … Fedor Simkovic

  3. Neutrino properties(60 years after discovery of n) we know • 3 families of light (V-A) neutrinos: ne, nm, nt • neutrinos are massive: we know mass squared differences • relation between flavor eigenstates and mass eigenstates • (neutrino mixing) only partially known we do not know • Absolute n mass scale? (cosmolology, 0nbb-decay, 3H, 187Rh) • Is there a CP violation in the neutrino sector? (leptogenesis) • Are neutrinos stable? • What is the magnetic moment of n? • Are n their own antiparticle?(Majorana n) or not (Dirac n) ?? Fedor Simkovic

  4. Neutrino oscillations  Massive neutrinos Reactor neutrinos Solar neutrinos 1968 Atmospheric neutrinos Accelerator neutrinos 1957 Fedor Simkovic

  5. Standard Model Lepton Universality Lepton Family Number Violation NEW PHYSICS massive neutrinos, SUSY... Total Lepton Number Violation Fedor Simkovic

  6. Different types of Double Beta Decay Capture of bound e- and emission of e+ (EC/b+) Emission of two e-(b-b-) T(MeV): 76Ge(2.045), 82Se(3.005), 100Mo(3.033),130Te(2.533), 150Nd(3.367) T(MeV):78Kr(1.837), 106Cd (1.724) 124Xe(1.802), 130Ba(1.515), 136Ce(1.339) Double capture of bound e-(EC/EC) Emission of two e+(b+b+) T(MeV):78Kr(2.841), 106Cd (2.712) 124Xe(2.782), 130Ba(2.492), 136Ce(2.313) T(MeV):78Kr(0.838), 106Cd (0.738) 124Xe(1.024), 130Ba(0.534), 136Ce(0.362)  Disfavored by Coulomb repulsion  Fedor Simkovic

  7. bb-decay Observed for 10 isotopes: 48Ca, 76Ge, 82Se, 96Zr,100Mo. 116Cd. 128Te, 130Te, 150Nd, 238U, T1/2 ≈1018-1024 years 1967: 130Te,Kirsten et al, Takaoka et al,(geochemical) 1987:82Se, Moe et al. (direct observation) 2008:100Mo, NEMO 3 coll. ~ 300 00 events SMforbidden ,not observed yet: T1/2 ( 76Ge)>1025 years Fedor Simkovic

  8. Pairing Double Beta Decay Nuclei Double electron capture Emission of 2 electrons Nuclear systems with small DMAmight be also important(resonant enhancement) Signal from g- and X-rays Preferable nuclear systems with large DMA (E5) Fedor Simkovic

  9. 1937 Beginning of Majorana neutrino physics Ettore Majorana discoveres the possiility of existence of truly neutral fermions Charged fermion (electron) + electromagnetic field forbidden Neutral fermion (neutrino) + electromagnetic field allowed Majorana condition Symmetric Theory of Electron and Positron Nuovo Cim. 14 (1937) 171 Here is the beginning of Nonstandard Neutrino Properties

  10. Mass matrix of light neutrinos Flavor eigenstates Mass eigenstates 0nbb-decay Majorana condition Effective mass of Majorana neutrinos Fedor Simkovic

  11. Pontecorvo- Maki-Nakagawa-Sakata matrix Quark mixing (small mixing angles) Neutrino mixing (large mixing angles) q12≈34o,q23≈45o,q13≈0o, Large off diagonal elements ! ! Instruction for an extension of SM? Fedor Simkovic n mass hierarchy

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

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

  14. Heidelberg-Moscow Experiment LNGS (completed 2003)(Two different results) 2) Analysis of the 76Ge experiment in Gran Sasso 1990-2003 (71.7 kg yr) H.V. Klapdor-Kleingrothaus et al., NIM A 522, 371 (2004); PLB 586, 198 (2004) 1) 0n T1/2> 1.9 1025 years <mbb> < 0.34 eV H-M collaborations, PRL 83 (1999) 41 • Data reanalyzed with • improved summing • Peak visible at 2030 keV • Effect reclaimed with4.2s • T1/2= (0.69 - 4.18) 1025 years • 0.23 eV |mbb| 0.57 eV 0n Fedor Simkovic

  15. Running Double Beta Decay experiments Gran Sasso CUORICINO (stopped) 130Te40.7 kg Qbb = 2529 keV T1/2 > 3.0 1024 years |mbb|| < 0.42 eV 100Mo (6.914 kg) T1/2 > 5.8 1023 years Qbb = 3034 keV |mbb| < 0.98 eV NEMO 3 82Se (0.932 kg) T1/2 > 2.1 1023 years Qbb = 2995 keV|mbb| < 1.7 eV Fréjus Underground Laboratory : 4800 m.w.e. Fedor Simkovic

  16. 1934 First double beta decay calculation Fermi, Z. Physik 88 (1934) 161 Fermi 4-fermion contact interaction, Lagrangian of interaction (in analogy with electrodynamics): GF = Fermi coupling constant = (1.16637±0.000001) 10-5 GeV-2 1935 Q-value about 10 MeV T1/2 ≈ 1017 years Eugene Wigner Maria-Goeppert Mayer

  17. The 0nbb-decay is a particle physics problem Fedor Simkovic

  18. Mechanisms of the 0nbb-decay We know that n are Massive particles !! • Neutrino mass mechanisms • nmasses: see-saw – sterilen • R-parity breaking SUSY mechanisms • n masses: v.e.v + rad. cor. • Leptoquark exchange mechanisms • Extra dimensions ! SUSY particles are expected to be seen at LHC Fedor Simkovic

  19. Left-right symmetric models SO(10) Assumption MR» mD Eigenvalues and eigenvectors m1=mD2/MR«mD m2≈MR n1=nL-mD/MR (nR)c n2=nR+mD/MR (nL)c Dirac-Majorana mass term Lepton number is violated by two units! W1± = cos z WL±+ sin z WR± Two-charged vector bosons W2± = -sin z WL±+ cos z WR± -2 10-4z  3.3 10-3(superallowed b-decay) M1=81 GeV, M2>715 GeV, (M1/M2)2< 10-2 Parameters See-saw scenario + small large Fedor Simkovic small large

  20. Mechanisms (within LR-models) nucleon level quark level mbb Fedor Simkovic

  21. Neutrino mass spectrum and perspectives of the 0nbb-decay search What is the absolute mass scale of neutrinos: Limits from cosmology, tritium beta decay, neutrinoless double beta decay What are the Majorana CP phases? ... Inverted hierarchy Normal hierarchy Fedor Simkovic Bilenky, Faessler, F.Š., PRD 70 (2004) 033003

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

  23. Minimal Supersymmetric Standard Model R-parity non-conservation: neutralino is not Dark Matter candidate but 0nbb-decay possible R-parity: R=(-1)3B+L+2S Fedor Simkovic

  24. R-parity Breaking MSSM (neutralino is not dark matter candidate) R-parity breaking terms In superpotential Neutrino-Neutralino mixing matrix (see-saw structure) Radiative corrections to neutrino mass Gozdz, Kaminski, Šimkovic, PRD 70 (2004) 095005 Fedor Simkovic

  25. gluino/neutralino exchange R-parity breaking SUSY mechanism of the 0nbb-decay quark-level diagrams d+d → u + u + e- + e- exchange of squarks, neutralinos and gluinos (l’111)2 mechanism 1987 R. Mohapatra, J.D. Vergados Fedor Simkovic

  26. Hadron-level diagrams Faessler, Kovalenko, F.Š. PRL 78 (1998) 183 Wodecki, Kaminski, F.Š., PRD 60 (1999) 11507 Fedor Simkovic

  27. Limit on R-parity breaking parameter ´111 Faessler, F.Š , Kovalenko, PRD 58 (1998) 115004 Fedor Simkovic

  28. Squark mixing SUSY mechanism Mixing betweenscalarsuperpartners of the left- and right-handed fermions A. Faessler, Th. Gutsche, S. Kovalenko, F.Š., PRD 77 (2008) 113012 Hirsch, Klapdor-Kleingrothaus, Kovalenko PLB 372 (1996) 181 L R Fedor Simkovic

  29. Effective SUSY n-e Lagrangian Neutrino vertex Hirsch,Klapdor-Kleingrothaus, Kovalenko PLB 372 (1996) 181 R-parity violating SUSY vertex Paes, Hirsch,Klapdor-Kleingrothaus, PLB 459 (1999) 450 LN-violating parameter Fedor Simkovic

  30. Limits on R-breaking parameters A. Faessler, Th. Gutsche, S. Kovalenko, F.Š., PRD 77 (2008) 113012 Pion mode Fedor Simkovic

  31. The double b-decay is a nuclear physics problem It is a complex task Models • Medium and heavy open shell nuclei with a complicated nuclear structure • The construction of complete set of the states of the intermediate nucleus is needed • Many-body problem  approximations needed • Nuclear structure input has to be fixed QRPA-like LSSM IBM Projected HFB Operator expansion Fedor Simkovic

  32. 2nbb-decay nuclear matrix elements Deduced from measured T1/22n Differencies in NME: byfactor ~ 10 Fedor Simkovic

  33. Shell Model • Define a valence space • Derive an effective interactionH Y = E Y→ HeffYeff = E Yeff • Build and diagonalize Hamiltonian matrix (1010) • Transition operator < Yeff| Oeff | Yeff> • Some phenomenological input needed energy of states, systematics of B(E2) and GT transitions (quenching f.) 48Ca → 48Ti 76Ge → 76Se 76Se42 in the valence 6 protons and 14 neutrons Small calculations Fedor Simkovic

  34. QRPA 2nbb-decay NME Mean field Residual interaction H=H0 + gphHph + gpp Hpp 21 lev. 12 lev. Collapse of the QRPA 21 l.m.s. 12 l.m.c Fedor Simkovic Only Bratislava-Tuebingen group

  35. The 0nbb-decay NME (light n exchange mech.) T NME= sum of Fermi, Gamow-Teller and tensor contributions The 0nbb-decay half-life Neutrino potential (about 1/r12) Induced pseudoscalar coupling (pion exchange) Form-factors: finite nucleon size Jp = 0+,1+,2+... 0-,1-,2-... Jastrow f. s.r.c. Fedor Simkovic

  36. The 0nbb-decay NMEs from literature (mostly QRPA-like) • absolute n mass scale • CP violating Majorana phases Uncertainties in 0nbb-decay NME? This suggest an uncertainty of NME as much as factor 5 !!! Is it really so bad?! Bahcall, Murayama, Pena-Garay, Phys. Rev. D 70, 033012 (2004) Fedor Simkovic

  37. The 0nbb-decay NME: gpp fixed to 2nbb-decay Each point: (3 basis sets) x (3 forces) = 9 values By adjusting of gpp to 2nbb-decay half-life the dependence of the 0nbb-decay NME on other things that are not a priori fixed is essentially removed Rodin, Faessler, F.Š,Vogel, Phys. Rev. C 68, 044302 (2003) Fedor Simkovic

  38. The 0nbb-decay NMEs (2009) Nobody is perfect: LSSM (small m.s., negative parity states) PHFB (GT force neglected) IBM (Hamiltonian truncated) (R)QRPA (g.s. correlations not accurate enough) Fedor Simkovic

  39. Fedor Simkovic

  40. r-dependence of the 0nbb-decay NME The radial dependence of M0n for the three indicated nuclei. The contributions summed over all components shown in the upper panel. The `pairing’ J = 0 and `broken pairs’ J  0 parts are shown separately below. Note that these two parts essentially cancel each other for r > 2-3 fm. This is a generic behavior. Hence the treatment of small values of r and large values of q are quite important. QRPA F.Š, Faessler, Rodin, Vogel, Engel PRC 77, 045503 (2008) Fedor Simkovic

  41. Large Scale Shell Model Menendez, Poves, Caurier, Nowacki, Arxive:0901.3760 [nucl-th] PHFB P.Rath, R. Chandra, K. Chaturverdi, P.Raina, J.G. Hirsch, to be published in PRC Nuclear physics Nucleon physics Fedor Simkovic

  42. A consistent approach forthe 0nbb-decay (pairing, s.r.c, g.s.c. calculated with the same NN potential- BonnCD, Argon) Two-nucleon short range correlations Neutrino potential:I(r)/r |Y>corr. = f(r12) |Y> Ocorr.(r12) = f(r12)O(r12)f(r12) Fedor Simkovic

  43. Neutrinoless double beta decay matrix elements F.Š.,Faessler, Muether, Rodin, Stauf, PRC 79, 055501 (2009) Fedor Simkovic

  44. Constraining the 0nbb-decay NME Proton, neutron removing transfer reaction 76Ge → 76Se John Schiffer, P.Grabmayr et al Kay et. Al, PRC 79, 021301 (2009) QRPA(A)≡ BCS (WS) QRPA(B)≡BCS (AWS) Suhonen, Civitarese, PLB 668, 277 (2008) Fedor Simkovic

  45. How can we take into account theoretically the constraint represented by the experimentally determined occupancies? The experiment fixesnjexp = <0+init| S cj,m+ cj,m |0+init>and the same for the final nucleus particle creation and annihilation operators In BCSnjBCS = vj2 x (2j+1)depends only on vj which in turn depends on the mean field eigenenergies In QRPA the ground state includes correlations and thus njQRPA = (2j+1)x[vj2 + (uj2-vj2)xj] xj = (2j+1)-1/2 <0+qrpa| [a+jaj]0 | 0+qrpa>depends on the quasiparticle content of the correlated ground state quasiparticle creation and annihilation operators Fedor Simkovic

  46. Initial and adjusted mean field levels While njexp and njBCSare constrained by Snj = N (or Z) the njQRPA are not constrained by that requirement. The particle number is not conserved, even on average. Thus the QRPA must be modified to remedy this  Selfconsistent Renormalized QRPA F.Š., A. Faessler, P. Vogel, PRC 79, 015502 (2009) Fedor Simkovic

  47. Constraining the 0nbb-decay NME charge-exchange reactions (t, 3He) (d, 2He) From D. Frekers, RIKEN 2008 lecture The cross sections give B(GT) for b+ and b-, product of the amplitudes (B(GT)1/2) gives the numerator of the M2n matrix element. Fedor Simkovic

  48. Staircase plot (running sum) of the contributions to the 2 decay (76Ge→76Se) adjusted mean field old Woods-Saxon potential Experiment(Frekers) Fedor Simkovic

  49. HSD, higher levels contribute to the decay 1+ SSD, 1+ level dominates in the decay (Abad et al., 1984, Ann. Fis. A 80, 9) 100Tc 0+ 100Mo Single State Dominance ( 100Mo, 106Cd,116Cd, 128Te …) Ei-Ef= -0.343 MeV Ei-Ef= -0.041 MeV Ei-Ef= 0.705 MeV Fedor Simkovic

  50. SSD – theoretical studies SSD common approx. Isotope f.s. T1/2(SSD)[y] T1/2(exp.)[y] 2nb-b- 100Mo0g.s.6.8 10186.8 1018 01 4.2 1020 6.1 1018 116Cd 0g.s. 1.1 1019 2.6 1019 128Te 0g.s. 1.1 1025 2.2 1024 EC/EC 106Cd 0g.s. >4.4 1021 >5.8 1017 130Ba 0g.s. 5.0 1022 4.0 1021 E1-Ei≈ 0 or neg.  sensitivity to lepton energies in energy denominators  SSD and HSDoffer different differential characteristics F.Š., Šmotlák, Semenov J. Phys. G, 27,2233, 2001 Domin, Kovalenko, F.Š., Semenov, NPA 753, 337 (2005) Fedor Simkovic

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