1. 6/3/2015Fedor Simkovic1 Neutrinoless Double-Beta Decay and Double-Electron capture Fedor Šimkovic JINR Dubna and Comenius University Bratislava) HEP2012, Valparaiso, January 3-9, 2012

2. 6/3/2015Fedor Simkovic2 OUTLINE Introduction 0  -decay (present status) - effective Majorana neutrino mass - nuclear matrix elements - distinguishing the 0  -decay mechanisms Resonant 0 -decay Conclusion

3. 6/3/2015Fedor Simkovic3 Amand Faessler, Vadim Rodin, Herbert Muether (University of Tuebingen) Sergey Kovalenko (University of Valparaiso) Mikhail Krivoruchenko (ITEP Moscow) Petr Vogel (Caltech, Pasadena) Walter Potzel (TU Muenchen) Dieter Frekers (University of Muenster) John Vergados (University of Ioannina) Serguey Petcov (SISSA Trieste) E. Lisi, G. Fogli, A. Rotunno (University of Bari) …

4. 6/3/2015Fedor Simkovic4 Flux on Earth of neutrinos from different sources as a function of energy Sources of neutrinos D. Vignaud and M. Spiro, Nucl. Phys.A 654 (1999) 350 The Sun is the most intense detected source with a flux on Earth of 6 10 10 /cm 2 s

5. 6/3/2015Fedor Simkovic5 Fundamental properties of neutrinos 3 families of light (V-A) neutrinos: e, ,  are massive: we know mass squared differences relation between flavor states and mass states (neutrino mixing) only partially known After 55 years we know No answer yet Is there a CP violation in sector? (leptogenesis) Are neutrinos stable? What is the magnetic moment of ? Sterile neutrinos? Statistical properties of ? Fermionic or partly bosonic? Like most people, physicists enjoy a good mystery. When you start investigating a mystery you rarely know where it is going Absolute mass scale from the  -decay. (cosmology, 3 H, 187 Rh ?) ’s are their own antiparticles – Majorana. Claim for evidence of the  -decay H.V. Klapdor-Kleingrothaus et al.,NIM A 522, 371 (2004); PLB 586, 198 (2004)

6. 6/3/2015Fedor Simkovic6 Lepton Universality Lepton Family Number Violation Total Lepton Number Violation NEW PHYSICS massive neutrinos, SUSY... Standard Model

7. 6/3/2015Fedor Simkovic7 Compelling evidence about new physics beyond the SM. Solar neutrinos Atmospheric neutrinos Accelerator neutrinos Reactor neutrinos 1968 1957

8. 6/3/2015Fedor Simkovic8 Mass matrix of light neutrinos Effective mass of Majorana neutrinos Flavor eigenstates Mass eigenstates  -decay Majorana condition Large off diagonal elements !

9. 6/3/2015Fedor Simkovic9 Neutrinoless Double-Beta Decay (A,Z)  (A,Z+2) + e - + e -

10. 6/3/2015Fedor Simkovic10 The double beta decay process can be observed due to nuclear pairing interaction that favors energetically the even-even nuclei over the odd-odd nuclei The NMEs for  -decay must be evaluated using tools of nuclear theory

11. 6/3/2015Fedor Simkovic11 An accurate knowledge of the nuclear matrix elements, which is not available at present, is however a pre-requisite for exploring neutrino properties. The answer to the question whether neutrinos are their own antiparticles is of central importance, not only to our understanding of neutrinos, but also to our understanding of the origin of mass. Absolute mass scale Normal or inverted Hierarchy of masses CP-violating phases

12. 6/3/2015Fedor Simkovic12 Inverted hierarchyNormal hierarchy Perspectives of the 0  -decay search sin 2  13 < 5 10 -2

13. 6/3/2015Fedor Simkovic13 Quark-Lepton Complemenarity Qualitatively correlation: 2-3 leptonic mixing is close to maximal because 2-3 quark mixing is small 1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large QLC- relations:  l   q 12   l   q 23   12  C = 46.5 o +/- 1.3 o  23  V cb = 43.9 o + 5.1 -3.6 o H. Minakata, A.S. Phys. Rev. D70: 073009 (2004)

14. 6/3/2015Fedor Simkovic14 θ 13 ≠ 0 : How Big or How Small? Convincing flavor theory has been lacking—it is at present impossible to predict fermion masses, flavor mixing angles and CP phases fundamental level  the flavor problem θ 13 has a role ! U bm = U 23 m U 12 m As dominant structure? Zero order? Bi-maximal mixing T2K: 0.03 < sin 2 2  13 < 0.34 (June 2011) DOOBLE CHOOZ: sin 2 2  13 =0.085±0.051 (9.11.2011)

15. 6/3/2015Fedor Simkovic15 T2K: 0.03(0.04) < sin 2 2  13 < 0.28(0.34) for NH(IH) 0.084 eV  i=1,2,3 =0.28 eV

16. 6/3/2015Fedor Simkovic16 DOOBLE CHOOZ: sin 2 2  13 =0.085±0.051 (9.11.2011)

17. Fedor Simkovic17 See-Saw mechanism Assumption M R » m D large small Left-right symmetric models SO(10) N  m ij 2  ij CP -------------------------------------- 2 1 1 0 3 2 31 65 15 10 As N increases, the formalism gets rapidly more complicated! Probability of Neutrino Oscillations N

18. Reactor neutrinos anomaly (January 2011) Double Chooz re-evaluated reactor antineutrino flux (PRD 83, 073006 (2011)) previous procedure used a phenomenological model based 30 effective beta branches new analysis used detailed knowledge of the decays of 10,000 + fission products New calculations results in flux increase of 3.5% in reactor antineutrinos sin 2 (2  new ) ~ 0.14  m new 2 > 1.5 eV 2

19. 6/3/2015Fedor Simkovic19 Reactor neutrinos anomaly and  -decay

20. 6/3/2015Fedor Simkovic20 If (or when) the  decay is observed two theoretical problems must be resolved 1)What is the mechanism of the decay, i.e., what kind of virtual particle is exchanged between the affected nucleons (quarks). 2) How to relate the observed decay rate to the fundamental parameters, i.e., what is the value of the corresponding nuclear matrix elements. S.R. Elliott, P. Vogel, Ann.Rev.Nucl.Part.Sci. 52, 115 (2002)

21. 6/3/2015Fedor Simkovic21 In double beta decay two neutrons bound in the ground state of an initial even-even nucleus are simultaneously transformed into two protons that are bound in the ground state or excited (0 +, 2 + ) states of the final nucleus It is necessary to evaluate, with a sufficient accuracy, wave functions of both nuclei, and evaluate the matrix element of the  -decay operator connecting them This can not be done exactly, some approximation and/or truncation is always needed. Moreover, there is no other analogues observable that can be used to judge directly the quality of the result. The  -decay NME

22. 6/3/2015Fedor Simkovic22 Many-body Hamiltonian Start with the many-body Hamiltonian Introduce a mean-field U to yield basis The mean field determines the shell structure In effect, nuclear-structure calculations rely on perturbation theory 0s N=0 0d1s N=2 0f1p N=4 1p N=1 Residual interaction The success of any nuclear structure calculation depends on the choice of the mean-field basis and the residual interaction!

23. 6/3/2015Fedor Simkovic23 Bahcall, Murayama, Pena-Garay, Phys. Rev. D 70, 033012 (2004) Uncertainties in 0nbb-decay NME? This suggest an uncertainty of NME as much as factor 5 !!! Is it really so bad?! The  -decay NMEs from literature - 2004 (mostly QRPA-like)

24. 24 The  -decay NMEs (Status:2012) Nuclear structure approaches Large Scale Shell Model: Caurier, Menendez, Nowacki, Poves, PRL 100, 052503 (2008). (Renormalized) QRPA: Šimkovic, Faessler, Müther, Rodin, Stauf, PRC 79, 055501 (2009). Interacting Boson Model: Barea, Iachello, PRC 79, 044301 (2009). Projected Hartree-Fock-Bogoliubov: Rath, Chandra, et al. PRC 82, 064310 (2010). g A =1.25, Jastrow s.r.c., r 0 =1.20 fm Differences: i) mean field; ii) residual interaction; iii) size of the model space iv) many-body approximation Energy Dendity Functional appr.: Rodrígez, Martínez-Pinedo, arXiv:1008.5260 [nucl-th].

25. 6/3/2015Fedor Simkovic25 Half-life T 1/2 for m  = 50 meV

26. 6/3/2015Fedor Simkovic26 0  -decay and 2  -decay NMEs F.Š., R. Hodák, A. Faessler, P. Vogel, PRC 83, 015502 (2011)

27. 6/3/2015Fedor Simkovic27  -decay: (A,Z)  (A,Z+2)+e - +e - + e +  e Differencies among 2  -decay NMEs: up to factor 10 Why the spread of the 2  NMEs is large and of the  NMEs is small? Are both type of NMEs related? --

28. 6/3/2015Fedor Simkovic28 The cross sections of (t, 3 He) and (d, 2 He) reactions give B(GT ± ) for   and  , product of the amplitudes (B(GT) 1/2 ) entering the numerator of M 2 GT Closure 2  -decay NME SSD hypothesis Grewe, …Frekers at al, PRC 78, 044301 (2008)

29. 6/3/2015Fedor Simkovic29 Neutrino potential A connection between closure 2  and 0  GT NMEs Going to relative coordinates: r- relative distance of two nucleons Neutrino potential prefer short distances F.Š., R. Hodák, A. Faessler, P. Vogel, PRC 83, 015502 (2011)

30. 6/3/2015Fedor Simkovic30 Closure 2  GT NME The only non-zero contribution from J  =1 + =

31. 6/3/2015Fedor Simkovic31 M 0 GT depends weakly on g A /g pp and QRPA approach unlike M 2 GT NucleonNuclear physics NucleonNuclear physics 76 Ge Different QRPA-like approchesDependence on axial-vector coupling

32. 6/3/2015Fedor Simkovic32 Co-existence of few mechanisms of the 0  -decay It may happen that in year 201? (or 2???) the 0  -decay will be detected for 2-3 or more isotopes … F.Š., J.D. Vergados, A. Faessler, PRD 82, 113015 (2010) A. Faessler, G. Fogli, E. Lisi, A. Rotunno, F. Š., Phys. Rev. D 83, 113015 (2011) A. Faessler, A. Meroni, S.T. Petcov, F. Š., J.D. Vergados, Phys. Rev. D 83, 113003 (2011)

33. 6/3/2015Fedor Simkovic33 Dominance of light mass mechanism of the 0  -decay Faessler, Fogli, Lisi, Rodin, Rotunno, F.Š., PRD 79, 053001 (2009) H.V. Klapdor, I. Krivosheina, Mod. Phys. Lett. A 21, 1547 (2006)

34. 6/3/2015Fedor Simkovic34 There exist heavy Majorana neutral leptons N i (singlet of SU(2)xU(1) group) Effective interaction for processes with virtual N i at electroweak scale After spontaneous violation of the electroweak symmetry the left-handed Majorana mass term is generated Neutrino mixing Probing the see-saw mechanism Inverted hierarchy N

35. 6/3/2015Fedor Simkovic35 Probe of the see-saw mechanism Inverted hierarchy Bilenky, Faessler, Potzel, F.Š, Eur. Phys. J. C 71 (2011) 1754

36. 6/3/2015Fedor Simkovic36 gluino/neutralino exchange R-parity breaking SUSY mechanism of the  decay exchange of squarks, neutralinos and gluinos d+d → u + u + e - + e -  ’ 111 ) 2 mechanism

37. 6/3/2015Fedor Simkovic37 Squark mixing SUSY mechanism Mixing between scalar superpartners of the left- and right-handed fermions LR A. Faessler, Th. Gutsche, S. Kovalenko, F.Š., PRD 77, 113012 (2008) M. Hirsch, H.V. Klapdor-Kleingrothaus, S. Kovalenko PLB 372 (1996) 181

38. 6/3/2015Fedor Simkovic38 Co-existence of 2, 3 or more interferring mechanisms of 0  -decay ξ Te < 1.2 ξ Mo < 2.6 It is well-known that there exist many mechanisms that may contribute to the 0  Let consider 3 mechanisms: i) light -mass mechanism, ii) heavy -mass mechanism, iii) R-parity breaking SUSY mechanism with gluino exchange and CP conservation We introduce Claim of evidence: Klapdor-Kleingrothaus, Krivosheina, Mod. Phys. A 21, 1547 (2009) ξ=0, non-observation (T 2 →∞) ξ=1, solution for single active mech. is reproduced

39. 6/3/2015Fedor Simkovic39 2 active mechanisms of the  -decay: Light and heavy -mass mechanism CP-conservation assumed Non-observation for 130 Te ● Single solution for light -mass mech. 4 sets of two linear eq.2 different solutions Non-observation of the 0  -decay for some isotopes might be in agreement with non- zero m  ● F.Š., J.D. Vergados, A. Faessler, PRD 82, 113015 (2010)

40. 6/3/2015Fedor Simkovic40 Two non-interfering mechanisms of the 0  -decay (light LH and heavy RH neutrino exchange) A.Faessler, A. Meroni, S.T. Petcov, F. Š., J.D. Vergados, Phys. Rev. D 83, 113003 (2011) Half-life: Set of equations: Solutions:

41. 6/3/2015Fedor Simkovic41 The positivity condition: Very narrow ranges! Two non-interfering mechanisms of the 0  -decay (light LH and heavy RH neutrino exchange)

42. 6/3/2015Fedor Simkovic42 Neutrinoless Double-Electron Capture F.Š., M. Krivoruchenko, Phys.Part.Nucl.Lett. 6 (2009) 485  M. Krivoruchenko, F.Š., D. Frekers, A. Faessler, Nucl. Phys. A 859, 140171 (2011) F.Š., Krivoruchenko, Faessler, PPNP 66, 446 (2011) Eliseev, et al., F.Š, M. Krivoruchenko, PRL 106, 052504 (2011)

43. 6/3/2015Fedor Simkovic43 J. Bernabeu, A. DeRujula, C. Jarlskog, Nucl. Phys. B 223, 15 (1983) Neutrinoless double electron capture (resonance transitions) (A,Z)→(A,Z-2) *HH’ Atom mixing amplitude  Decay rate Pertubation theory Sujkowski, Wycech, PRC 70, 052501 (2004)

44. 6/3/2015Fedor Simkovic44 Oscillations of atoms In analogy with oscillations of n-anti{n} (baryon number violation) Oscillation of atoms (lepton number violation) F.Š., M. Krivoruchenko, Phys.Part.Nucl.Lett. 6 (2009) 485

45. OSCILLATIONS BETWEEN TWO STABLE ATOMS  = 0 &  M i - M f )/2. Transition probability: The exposure time of atoms in double-beta decay experiments (months and years) is greater than 1/  by many orders of magnitude. Typically V = 10 -30 MeV, and so with no chances to observe the effect. 1/2

46. OSCILLATIONS & RESONANT TRANSITIONS BETWEEN GROUND-STATE AND EXCITED ATOMS To the lowest order in V: where Breit-Wigner factor i = (A,Z) f = (A,Z - 2)** UNITARY LIMIT: M A,Z = M** A,Z-2

47. Decay width of the parent atom: Calculations: 1. Mass difference  Coulomb energy of electron holes. 2. Decay width   widths of the excited electron shells, Auger & radiative transitions. 3. V  L T violating potential, electron w.f. & NME. LIKELY RESONANT 0  TRANSITIONS The process of the 0νεε has been revisited. New 0νεε transitions with parity violation to ground and excited states of final atom/nucleus were found. Selection rules for the 0νεε transitions were established. The explicit form of corresponding NMEs was derived. Assuming an effective Majorana neutrino mass of 1 eV, some half-lives has been predicted to be as low as 10 22 years in the unitary limit. M. Krivoruchenko, F.Š., D. Frekers, A. Faessler, Nucl. Phys. A 859, 140171 (2011)

48. Decays are dominated by 1.radiative transitions with the emission of X-rays, 2.the emission of Auger electrons. X-rays are dominant in the decays of atoms with Z > 35. The width of a two-hole state  is represented by are taken from: J. L. Campbell and T. Papp, At. Data and Nuclear Data Tables, 77 (2001) 1. DECAY WIDTHS OF TWO-ELECTRON HOLES electron shell nuclear de-excitation

49. 6/3/2015Fedor Simkovic49 152 Gd  152 Sm (Eliseev, et al., F.Š, M. Krivoruchenko, PRL 106, 052504 (2011)) (F.Š., Krivoruchenko, Faessler, PPNP 66, 446 (2011) Improved Q-value measurements Klaus Blaum (MPI Heidelberg) Remeasured Q-value: 112 Sn, 74 Se, 136 Ce, 96 Ru, 152 Gd, 162 Er, 168 Yb, 106 Cd, 156 Dy need to be remeasured: 124 Xe, 130 Ba, 180 W, 184 Os, 190 Pt

50. 6/3/2015Fedor Simkovic50 0  experiment in Bratislava Frekers, Puppe, Thies, Povinec, F.Š., Staníček, Sýkora, NPA 860, 1 (2011) Muenster and Bratislava groups T 1/2 > 4.3 10 19 years 74 Se

51. 6/3/2015Fedor Simkovic51 TGV experiment in Modane underground laboratory 10 g of 106 Cd T 1/2 2  ( 106 Cd) > 3.6 10 20 y T 1/2 0  ( 106 Cd) > 1.1 10 20 y TGV Coll., Rukhadze et al., NPA 852, 197 (2011) New level 2737 keV (J  

52. 6/3/2015Fedor Simkovic52 e - + e - + (A,Z)  (A,Z-2) ** (A,Z)  (A,Z+2) + e - + e - Summary  -decay background can be a problem Uncertainty in NMEs factor ~2, 3 0 +  0 +,2 + transitions Large Q-value 76 Ge, 82 Se, 100 Mo, 130 Te, 136 Xe … Many exp. in construction, potential for observation in the case of inverted hierarchy (2020)  -decay strongly suppressed NMEs need to be calculated 0 +  0 +,0 -, 1 +, 1 - transitions Small Q-value Q-value needs to be measured at least with 100 eV accuracy 152 Gd, looking for additional small experiments yet Perturbation theoryBreit-Wigner form

53. 6/3/2015Fedor Simkovic53 We have to communicate more with neutrinos. We have no end of fun with neutrino physics. Neutrino physics is Babylonian Mathematics is Egyptian