Distinguishing the neutrinoless double beta decay mechanisms

Many new neutrinoless double beta decay (0nbb) experiments are planned or in preparation. If the 0nbb-decay will be detected, the key issue will be what is the dominant mechanism of this process. By measuring only transitions to the ground state one can not distinguish among many of the 0nbb-decay mechanisms (the light and heavy Majorana neutrino exchange mechanisms, the trilinear R-parity breaking mechanisms etc.). We show that if the ratio of the 0nbb-decay half-lifes for transitions to the 0^+ first excited and ground states is determined both theoretically and experimentally, it might be possible to determine, which 0nbb-decay mechanisms is dominant. For that purpose the corresponding nuclear matrix elements have to be evaluated with high reliability. The present work is giving strong motivations for experimental studies of the 0nbb-decay transitions to the first excited 0^+ states of the final nuclei.Comment: 9 pages, 2 figures, Talk at the School `Neutrinos in Astro, Particle and Nuclear Physics', Erice, September 18-26, 2001,to appear in Prog.Part.Nucl.Phys. 48 (2002

Double Beta Decay

We review the recent developments in the field of nuclear double beta decay, which is presently an important topic in both nuclear and particle physics. The mechanism of lepton number violation within the neutrinoless double beta decay is discussed in context of the problem of neutrino mixing and the R-parity violating supersymmetric extensions of the Standard model. The problem of reliable determination of the nuclear matrix elements governing both two-neutrino and neutrinoless modes of the double beta decay is addressed. The validity of different approximation schemes in the considered nuclear structure studies is analyzed and the role of the Pauli exclusion principle for a correct treatment of nuclear matrix elements is emphasized. The constraints on different lepton number violating parameters like effective electron neutrino mass, effective right-handed weak interaction parameters, effective Majoron coupling constant and R-parity violating SUSY parameters are derived from the best presently available experimental limits on the half life of neutrinoless mode of this process.Comment: 32 pages, RevTex, 6 postscript figure

Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino Mass

The atomic pair 163 Holmium and 163 Dysprosium seems due to the small Q value of about 2.3 to 2.8 keV the best case to determine the neutrino mass by electron capture. The bolometer spectrum measures the full deexcitation energy of Dysprosium by X rays, by Auger electrons and by the recoil of Holmium. The spectrum has an upper energy limit given by the Q value minus the neutrino mass. Till now this spectrum has been calculated allowing in Dysprosium excitations with 3s1/2, 3p1/2, 4s1/2, 4p1/2, 5s1/2, 5p1/2 one-holes only. Robertson calculated recently also the spectrum with two electron hole excitations in Dy. He took the probability for the excitation for the second electron hole from work of Carlson and Nestor for Z=54 Xenon. He claims, that the bolometer spectrum with two holes is "not well enough understood to permit a sensitive determination of the neutrino mass in this way." The purpose of the present work is to determine the theoretical bolometer spectrum with two hole excitations more reliably directly in holmium and dysprosium. In addition it will be shown, that the two-hole excitations do not complicate more the determination of the neutrino mass compared to the situation with one-hole states only. At the Q value the highest one-hole resonance is dominant. Under the assumption of a Lorentzian line shape one has to fit after inclusion of the experimental spectral function of the detector four quantities to the data: (1) The neutrino mass, (2) the energy distance of the dominant resonance to the Q value, (3) the line witdth and (4) the strength of the resonance. Compared to Robertson this work includes major improvements and it shows, that a determination of the neutrino mass is difficult but not impossible.Comment: 10 pages and 5 figure

Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime

We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to connected diagrams, allows us to reach high ($\sim 10$) orders of the weak-coupling expansion for the self-energy of the two-dimensional Hubbard model. Access to high orders reveals a non-trivial analytic structure of the self-energy and enables its controlled reconstruction with arbitrary momentum resolution in the nonperturbative regime of essentially strong correlations, which has recently been reached with ultracold atoms in optical lattices.Comment: 5 pages, 4 figures, published versio

Neutrinoless Double Beta Decay of 134Xe

In view of recent great progress achieved in the experimental study of the neutrinoless double beta decay (0nbb-decay) of 134Xe we discuss theoretical aspects of this process. The light and heavy Majorana neutrino exchange as well as the trilinear R-parity breaking contributions to 0nbb-decay are considered. We show that the sensitivity of the studied process to the signal of lepton number violation is only by factor 2-3 weaker in comparison with the 0nbb-decay of 136Xe. The current limits on effective neutrino mass (light and heavy) and trilinear R-parity violating parameter lambda'_111 deduced from lower limits on the 0nbb-decay half-lifes of various nuclei are reviewed and perspectives of the experimental verification of recently announced evidence of the 0nbb-decay of 76Ge are discussed.Comment: 5 pages, RevTe

0νββ0\nu\beta\beta nuclear matrix elements and the occupancy of individual orbits

The measured occupancies of valence orbits in $^{76}$Ge and $^{76}$Se are used as a guideline for modification of the effective mean field energies that results in better description of these quantities. With them, in combination with the selfconsitent renormalized quasiparticle random phase approximation (SRQRPA) method that ensures conservation of the mean particle number in the correlated ground state, we show that the resulting $0\nu\beta\beta$ nuclear matrix element for the $^{76}$Ge $\to$ $^{76}$Se transition is reduced by $\sim$25% compared to the previous QRPA value, and therefore the difference between the present approach and the interacting shell model predictions becomes correspondingly smaller. Analogous modification of the mean field energies for the A=82 system also results in a reduction of $0\nu\beta\beta$ matrix element for the $^{82}$Se $\to$ $^{82}$Kr transition, making it also closer to the shell model prediction.Comment: 9 pages, 6 figure

Neutrino Mass, Electron Capture and the Shake-off Contributions

Electron capture can determine the electron neutrino mass, while the beta decay of Tritium measures the electron antineutrino mass and the neutrinoless double beta decay observes the Majorana neutrino mass. Electron capture e. g. on 163Ho plus bound electron to 163Dy* plus neutrino can determine the electron neutrino mass from the upper end of the decay spectrum of the excited Dy*, which is given by the Q-Value minus the neutrino mass. The Dy* states decay by X-ray and Auger electron emissions. The total decay energy is measured in a bolometer. These excitations have been studied by Robertson and by Faessler et al.. In addition the daughter atom Dy can also be excited by moving in the capture process one electron into the continuum. The escape of these continuum electrons is automatically included in the experimental bolometer spectrum. Recently a method developed by Intemann and Pollock was used by DeRujula and Lusignoli for a rough estimate of this shake-off process for "s" wave electrons in capture on 163Ho. The purpose of the present work is to give a more reliable description of "s" wave shake-off in electron capture on Holmium. For that one needs very accurate atomic wave functions of Ho in its ground state and excited atomic wave functions of Dy* including a description of the continuum electrons. In the present approach the wave functions of Ho and Dy* are determined selfconsistently with the antisymmetrized relativistic Dirac-Hartree-Fock approach. The relativistic continuum electron wave functions for the ionized Dy* are obtained in the corresponding selfconsistent Dirac-Hartree-Fock-Potential. In this improved approach shake-off can hardly be seen after electron capture in 163Ho and thus can probably not affect the determination of the electron neutrino mass.Comment: 20 pages, 9 figure

Structure of the two-neutrino double-β\beta decay matrix elements within perturbation theory

The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-$\beta$ decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-$\beta$ decay matrix elements on the like-nucleon pairing, particle-particle T=0 and T=1, and particle-hole proton-neutron interactions is obtained. It is found that double-$\beta$ decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-$\beta$ decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting Delta Z = 2 nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.Comment: 12 pages, 4 figure

Two-neutrino double beta decay of 76Ge within deformed QRPA: A new suppression mechanism

The effect of deformation on the two-neutrino double decay (2nbb-decay) for ground state transition 76Ge -> 76Se is studied in the framework of the deformed QRPA with separable Gamow-Teller residual interaction. A new suppression mechanism of the 2nbb-decay matrix element based on the difference in deformations of the initial and final nuclei is included. An advantage of this suppression mechanism in comparison with that associated with ground state correlations is that it allows a simultaneous description of the single beta and the 2nbb-decay. By performing a detail calculation of the 2nbb-decay of 76Ge, it is found that the states of intermediate nucleus lying in the region of the Gamow-Teller resonance contribute significantly to the matrix element of this process.Comment: 33 pages, 12 figure

Neutrino masses from R-parity non-conserving loops

We present new formulae for the neutrino masses generated by R-parity violating interactions within minimal supersymmetric standard model. The importance of inclusion of CP phases in the neutrino mass matrix is discussed in detail.Comment: I've decided to move the collection of my papers to arXiv for easier access. Talk presented at the Cracow Epiphany Conference on Neutrinos and Dark Matter, 5-8.1.2006, Cracow, Polan