Double beta decay a problem of particle, nuclear and atomic physics
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1 Workshop on Fundamental symmetries: from nuclei and neutrinos to the universe Trento, Italy, June 25-29, 2007 Double beta decay a problem of particle, nuclear and atomic physics Fedor Šimkovic Comenius University, Bratislava 6/27/2007 Fedor Simkovic 1
2 6/27/2007 Fedor Simkovic 2
3 OUTLINE Some particle physics aspects (neutrino mass mech. of the 0νββ-decay) Some nuclear physics aspects (0νββ-decay NME s) Some atomic physics aspects (double electron capture) Something exotic (bosonic neutrino) 6/27/2007 Fedor Simkovic 3
4 Some particle physics aspects 6/27/2007 Fedor Simkovic 4
5 Neutrino properties (60 years after discovery of ν) we know 3 families of light (V-A) neutrinos: ν e, ν µ, ν τ 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 ν mass scale? (cosmolology, 0νββ-decay, 3 H, 187 Rh) Are ν their own antiparticle? (Majorana ν) or not (Dirac ν) Is there a CP violation in the neutrino sector? (leptogenesis) Are neutrinos stable? What is the magnetic moment of ν??? 6/27/2007 Fedor Simkovic 5
6 Observation of ν oscillations changed the world (of physics) Solar neutrinos Reactor neutrinos 1968 Atmospheric neutrinos 1957 Accelerator neutrinos 1998 SuperKamiokande 6/27/2007 Fedor Simkovic 6
7 Standard Model Lepton Universality Lepton Family Number Violation NEW PHYSICS massive neutrinos, SUSY... Total Lepton Number Violation 6/27/2007 Fedor Simkovic 7
8 Pontecorvo -Maki-Nakagawa-Sakata matrix Mixing of 3 light Neutrinos Flavor eigenstates Mass eigenstates Mass matrix 6/27/2007 Fedor Simkovic 8
9 Pontecorvo-Maki-Nakagawa-Sakata matrix Quark mixing Neutrino mixing Large off diagonal elements!! Instruction for an extension of SM? Disperity and challange for quark-lepton unified theories 6/27/2007 Fedor Simkovic 9
10 Neutrinos mass spectrum We need 3mass-eigenstates to explain 2 different m 2: : m 2 2 m 12 = m 2 sol ~ ev 2 : m 3 2 m 22 = m 2 atm ~ ev 2 Absolute mass scale of neutrinos 0νββ-decay Tritium decay Cosmology 6/27/2007 Fedor Simkovic 10
11 Mass spectrum and mixing Questions to the mass spectrum: Absolute mass scale Type of the mass hierarchy: Normal, Inverted U e3 =? We know only that it is smaller than other angles Some mysteries: Tiny masses Large mixing angles θ 13 =0 and θ 13 =45 0 means ν µ ν τ symmetry Dirac or Majorana?
12 Quark-Lepton Complementarity QLC- relations: H. Minakata, A.S. Phys. Rev. D70: (2004) [hep-ph/ ] θ l 12 + θ q 12 π/4 θ l 23 + θ q 23 π/4 θ 12 + θ C = 46.5 o +/- 1.3 o θ 23 + V cb = 43.9 o + 5.1/-3.6 o 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 6/27/2007 Fedor Simkovic 12
13 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 on Bi-maximal mixing fundamental level the flavor problem θ 13 has a role! U bm bm 23m m = U 23m U 12 m 12 As dominant structure? Zero order? Bi-maximal mixing maximal 2-3 mixing zero 1-3 mixing maximal 1-2 mixing no CP-violation Contradicts data at (5-6)s level 6/27/2007 Fedor Simkovic 13
14 ν-masses in flavor basis: Inverted hierarchy eµ eτ ee µµ µτ ττ 6/27/2007 Fedor Simkovic 14 Gozdz,Kaminski, F.Š, Faessler, Acta Phys. Pol. 37 (2006) 2203
15 ν-masses in flavor basis: Normal hierarchy eµ eτ ee µµ µτ ττ 6/27/2007 Fedor Simkovic 15 Gozdz,Kaminski, F.Š, Faessler, Acta Phys. Pol. 37 (2006) 2203
16 3 neutrino observables Present knowledge Near Future θ a θ ± 9 P(ν µ ν µ ) MINOS, CNGS θ s θ ± 3 P(ν e ν e ) SNO P(ν e ν e ) θ x θ 13 9 Reactor, P(ν µ ν e )LBL m 2 a (2.5 1 ) 10 3 ev 2 P(ν µ ν µ ) MINOS, CNGS sign( m a2 ) unknown LBL P(ν µ ν e ), P(ν µ ν e ) P(ν e ν e ) m s 2 (7.±2.) 10 5 ev 2 KamLAND sign( m s2 ) + (MSW) done P(ν µ ν e ), P(ν µ ν e ) δ unknown LBL Majorana unknown 0νββ! α 12 unknown 0νββ (if 0, π) α 23 unknown hopeless 6/27/2007 Fedor Simkovic 16 m ν Σm ν < 1 ev cosmology, 0νββ, β-decay
17 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
18 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 1/ years 1967: 130 Te, Kirsten et al, Takaoka et al, (geochemical) 1987: 82 Se, Moe et al. (direct observation) 2006: 100 Mo, NEMO 3 coll. ~ events SM forbidden,not observed yet: T 1/2 ( 76 Ge)>10 25 years 6/27/2007 Fedor Simkovic 18
19 Normal hierarchy Inverted hierarchy 6/27/2007 Fedor Simkovic years years Bilenky,Faessler, Gutsche, F.Š., PRD 72 (2005)
20 θ 13 and the cancellation 6/27/2007 Fedor Simkovic 20 Bilenky,Faessler, Gutsche, F.Š., PRD 72, (2005)
21 Familiar light masses Smallness of neutrino masses - Seesaw ν m ν Sterile neutrinos ν R fully sterile feels no gauge interaction of any sort. Singlets of the SM symmetry group weakly sterile does not feel SM gauge interactions Left-right symmetric models: N m D M R T. Yanagida, M. Gell-Mann, P. Ramond, R. Slansky SU(3) SU(2) L SU(R) R U(1) B-L If ν R exists then neutrino are naturaly massive mass is unprotected by symmetry, can be large at a scale of LNV 6/27/2007 Fedor Simkovic 21
22 Assumption M R»m D Eigenvalues and eigenvectors m 1 =m D2 /M R «m D m 2 M R ν 1 =ν L -m D /M R (ν R ) c ν 2 =ν R +m D /M R (ν L ) c Left-right symmetric models SO(10) Two-charged vector bosons Parameters See-saw scenario W 1± = cos ζ W L± + sin ζ W R ± W 2± = -sin ζ W L± + cos ζ W R ± ζ (superallowed β decay) M 1 =81 GeV, M 2 >715 GeV, (M 1 /M 2 ) 2 < large small small large 6/27/2007 Fedor Simkovic 22
23 quark level nucleon level Mechanisms 6/27/2007 Fedor Simkovic 23
24 Sterile neutrino in 0νββ-decay Beneš, Faesler, F.Š., Kovalenko, PRD 71 (2005) /27/2007 Fedor Simkovic 24
25 Some nuclear physics aspects 6/27/2007 Fedor Simkovic 25
26 2νββ-decay Nuclear Matrix Elements Deduced from measured T 1/2 2ν difference: by factor ~ 10 6/27/2007 Fedor Simkovic 26
27 0νββ decay Nuclear Matrix Elements Nuclear Matrix Elements Shell model QRPA NME s: which mechanism, which transition? It is a complex task 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 6/27/2007 Fedor Simkovic 27
28 Nuclear structure approaches H Ψ = Ε Ψ We can not solve the full problem in the complete Systematical study of the 0νββ-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) E. Caurier, E. Martinez-Pinedo, F. Nowacki, A. Poves, A. Zuker, Rev. Mod. Phys. 77, 427 (2005). QRPA, RQRPA: About 10 papers Other approaches: Shell Model Monte Carlo (1996), Operator Expansion Method ( )... 6/27/2007 Fedor Simkovic 28
29 Uncertainties in 0νββ decay NME? Bahcall, Murayama, Pena-Garay, Phys. Rev. D 70, (2004) Please no! Do not put different NME calculations at the same level (democratic approach) This suggest an uncertainty of NME as much as factor 5! Civitarese, Suhonen, NPA 729, 867 (2003) Is it really so bad?! 6/27/2007 Fedor Simkovic 29
30 Shell Model Define a valence space Derive an effective interaction H Ψ = Ε Ψ H eff Ψ eff = E Ψ eff Build and diagonalize Hamiltonian matrix (10 10 ) Transition operator < Ψ eff O eff Ψ eff > Some phenomenological input needed energy of states, systematics of B(E2) and GT transitions (quenching f.) 48 Ca 48 Ti 76 Ge 76 Se Small calculations 76 Se 42 in the valence 6 protons and 14 neutrons 6/27/2007 Fedor Simkovic 30
31 The QRPA-like approaches Particle number condition i) Uncorrelated BCS ground state Z=<BCS Z BCS> N=<BCS N BCS> QRPA, RQRPA ii) Correlated RPA ground state Z=<RPA Z RPA> N=<BCS N BCS> SRQRPA Pauli exclusion principle i) violated (QBA) [A,A + ] =<BCS [A,A + ] BCS> QRPA ii) Partially restored (RQBA) [A,A + ] =<RPA [A,A + ] RPA> RQRPA, SRQRPA Complex numerical procedure BCS and QRPA equations are coupled P. Beneš et al. 6/27/2007 Fedor Simkovic 31
32 QRPA 2νββ-decay NME H=H 0 + g ph H ph + g pp H pp 21 lev. 12 lev. Collapse of the QRPA 21 l.m.s. 12 l.m.c 6/27/2007 Fedor Simkovic 32 Only BCT group
33 The 0νββ-decay NME: g pp fixed to 2νββ-decay Each point: (3 basis sets) x (3 forces) = 9 values By adjusting of g pp to 2νββ-decay half-life the dependence of the 0νββ-decay NME on other things that are not a priori fixed is essentially removed Rodin, Faessler, Šimkovic,Vogel, Phys. Rev. C 68, (2003) 6/27/2007 Fedor Simkovic 33
34 Neutrinoless Double Beta Decay Nuclear Matrix Elements Light Majorana Neutrino Exchange Mechanism QRPA, RQRPA: V.Rodin, A. Faessler, F. Š., P. Vogel, NPA 766 (2006) 107 shell model: E. Caurier, E. Martinez-Pinedo, F. Nowacki, A. Poves, A. Zuker, Rev. Mod. Phys. 77, 427 (2005). 6/27/2007 Fedor Simkovic 34
35 Code error found in the treatment of s.r.c. Main conclusions remain unchanged 6/27/2007 Fedor Simkovic 35
36 Φιξινγ οφ γ ππ It is not possible to describe simultaneously both β + /EC and β decays: move with g pp in opposite directions only one free parameter and two physical quantities the role of overlap factor ignored g A =1.25 (A,Z) (A,Z+1) (A,Z+1) (A,Z+2) But the lowest 1 + state is not the only responsible for double beta decay 6/27/2007 Fedor Simkovic 36
37 The importance of transition through higher-lying states of (A,Z+1) nucleus Rodin,Faessler, Šimkovic, Vogel, nucl-th/ /27/2007 Fedor Simkovic 37
38 Two-nucleon short range correlations: 6/27/2007 Fedor Simkovic 38
39 0νββ-decay NME with UCOM s.r.c. Korteleinen, Civitarese, Suhonen, Toivanen, nucl-th/ Feldmeier et al.: UCOM corelations introduce correlations by means of a unitary transformation with respect to the relative coordinate of all pairs UCOM correlations: determined by two-body energy minimization V UCOM and V bare are phase shift equivalent 6/27/2007 Fedor Simkovic 39
40 Comparison of UCOM and Spencer-Miller (Jastrow) s.r.c. UCOM 6/27/2007 Fedor Simkovic 40
41 Two-body correlated wave function Numerical solution of Bethe-Goldstone equation H. Muether et al. Collaboration with A. Faessler (Tuebingen) 6/27/2007 Fedor Simkovic 41
42 Finite nucleon size (formfactors) versus short range correlations. Neutrino potential: I(r)/r 6/27/2007 Fedor Simkovic 42
43 Finite nucleon size (formfactor) do thesamejobass.r.c.!! 6/27/2007 Fedor Simkovic 43
44 Our results: Code improved and corrected Jyvaskyla group: Changed of the formalism to our (new code), but no tensor term Spencer-Miller s.r.c NME up 50% Given for r 0 =1.1 fm! 10 level model space, g pp =1.00 6/27/2007 Fedor Simkovic 44
45 Is there a convergence of QRPA-like results? We hope that everbody agrees that one can not put all calculated 0νββ-decay NME s at the same level There is no factor 5! Which formalism? Quark model approach of Khadkikhar Jyvaskyla group [NPA 643, 207 (1998); NPA 729, 867 (2003)...] s.r.c. not considered, formfactor cutoff unknown, M 0ν = 3.33 (3.05 for r 0 =1.1 fm) Our approach based on formfactors and inclusion of higher order of nucleon current without s.r.c. and h.o.t. nucleon current M 0ν = 7.16 (6.57 for r 0 =1.1 fm) Strong contradiction! factor > 2! Which s.r.c.? Spencer-Miller (Jastrow function), Co Jastrow-like, UCOM, or something else? 6/27/2007 Fedor Simkovic 45
46 Nuclear deformation? Exp. I (nuclear reorientation method) Exp.II (based on measured E2 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 0νββ-decay NME spherical symetry was assumed The effect of deformation on NME has to be considered 6/27/2007 Fedor Simkovic 46
47 New Suppression Mechanism of the DBD NME The suppression of the NME depends on relative deformation of initial and final nuclei Šimkovic, Pacearescu, Faessler. NPA 733 (2004) 321 Systematic study of the deformation effect on the 2νββ-decay NME within deformed QRPA Alvarez,Sarriguren, Moya,Pacearescu, Faessler, Šimkovic, Phys. Rev. C 70 (2004) 321 6/27/2007 Fedor Simkovic 47
48 Estimation of the effect of the deformation on the 0νββ-decay NME s 6/27/2007 Fedor Simkovic 48
49 Some atomic physics aspects 6/27/2007 Fedor Simkovic 49
50 Different types of Double Beta Decay Emission of two e - (β β ) T(MeV): 76 Ge(2.045), 82 Se(3.005), 100 Mo(3.033), 130 Te(2.533), 150 Nd(3.367) Capture of bound e - and emission of e + (EC/β + ) T(MeV): 78 Kr(1.837), 106 Cd (1.724) 124 Xe(1.802), 130 Ba(1.515), 136 Ce(1.339) Double capture of bound e - (EC/EC) Emission of two e+ (β + β + ) T(MeV): 78 Kr(2.841), 106 Cd (2.712) 124 Xe(2.782), 130 Ba(2.492), 136 Ce(2.313) T(MeV): 78 Kr(0.838), 106 Cd (0.738) 124 Xe(1.024), 130 Ba(0.534), 136 Ce(0.362) Disfavored by Coulomb repulsion 6/27/2007 Fedor Simkovic 50
51 ECEC-γ decay e b + e b + (A,Z) (A,Z-2) + γ D.Frekers, hep-ex/ GERDA %: Q=0.433 MeV Γ r =100 ev Sujkowski, Wycech, PRC 70, (2004) T 1/2 0νγ = years (<m ββ >=1eV) 6/27/2007 Fedor Simkovic 51
52 Neutrinoless double electron capture Modes of the 0νECEC-decay: e b + e b + (A,Z) (A,Z-2) + γ + 2γ + e + e - + Μ Nuclear physics mechanisms: γ from the nucleus Theoretically, not well understood yet: which mechanism is important? which transition is important? in comparison with the 0νββ-decay disfavoured due: process in the 3-rd (4th) order in electroweak theory bound electron wave functions favoured due:? 6/27/2007 Fedor Simkovic 52
53 e b + e b + (A,Z) (A,Z-2) + γ + γ ECEC-γγ decay (preliminary) Advanteges: -bothe b in 0s 1/2 states (K-orbit) - large Q values prefarable -1/(m e (ε 0s + k 0 )) enhancement Disadvantages: - 2 γ s in final state (phase space) - additional el.-mag. interaction <m ββ >=1eV: T 0νγγ 1/2 ( 36 Ar) = years T 0νγγ 1/2 ( 106 Cd) = years T 0νγγ 1/2 ( 162 Er) = years Carefull study study (Merle, Lindner, Beneš, F.Š) in progress 6/27/2007 Fedor Simkovic 53
54 Something exotic: bosonic neutrinos ν I am fermionic! Can be. I am partially bosonic! Might be. I am bosonic! Excluded. Dolgov, Smirnov, F.Š, R. Dvornický, to be published in Nucl. Phys. B 6/27/2007 Fedor Simkovic 54
55 2νββ-decay: fermionic (f) or bosonic (b) ν Sign difference!!! Lepton energies!!! 6/27/2007 Fedor Simkovic 55
56 Higher states dominance ( 76 Ge, 82 Se, 130 Te, 136 Xe... ) Approximation in energy denominators e k + ν j =( E i -E f )/2 fermionic ν 0 + bosonic ν 0 +, 2 + fermionic ν 0 +, 2 + 6/27/2007 Fedor Simkovic 56
57 Looking for a signature of bosonic ν 2νββ decay half-lives ( g.s., , ) HSD NME needed SSD log ft EC, log ft β needed Normalized differential characteristics The single electron energy distribution The distribution of the total energy of two electrons Angular correlations of two electrons (free of NME and log ft) 6/27/2007 Fedor Simkovic 57
58 2νββ-decay of 76 Ge 0 + g.s. 0 + g.s. HSD bosonic fermionic 6/27/2007 Fedor Simkovic 58
59 Outlook Elliott, Vogel The 0νββ decay will be observed (up to 2020) Neutrino is Majorana particle (Schechter- Valle theorem) The dominant mechanism has to be determined, i.e., further study (differential characteristics, trans. to excited states, related phenomenology, NME, GUT models) The 0νββ decay will be not observed (up to 2020) Inverted hierarchy of neutrino masses excluded Stronger constraints on GUT, A challenge for next generation? If mass spectrum already determined Dirac neutrino (why small mass?) Schechter-Valle 6/27/2007 Fedor Simkovic 59
60 What is the nature of neutrinos? theory Only the 0νββ-decay can answer this fundamental question By product: Absolute ν mass scale CP Majorana phases 6/27/2007 Fedor Simkovic 60
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