We develop the formalism for calculating the decay rate of neutrinoless double beta decay to the 2^+ excited states within L-R symmetric model. We consider the effects from induced hadronic currents up to NLO. The QRPA method in a spherical basis is adopted for the nuclear many-body calculation and the corresponding nuclear matrix elements are given. Also, the phase space factors are obtained with numerical electron wave functions. Our results suggest that the nuclear matrix elements are nucleus dependent and they are generally smaller than that of the decay to the ground states. And finally, we give a naive analysis of how current experiment data constrains the L-R symmetric model.

Partial decay widths of various decay channels of the X(1835) are evaluated in the P0 quark model, assuming that the X(1835) is a NN bound state with the quantum number assignment I(J) = 0(0). It is found that the decays to the ρρ, ωω and πa0(1450) states dominate over other channels, and that the product branching fractions Br(J/ψ → γX)Br(X → ππη) and Br(J/ψ → γX)Br(X → ππη) are in the same order. We suggest that the X(1835) may be searched in the πa0(1450) channel.

In this paper, we present the first beyond closure calculation for the neutrinoless double-beta decay of Ge-76 to the first 2(+) states of Se-76 within the two nucleon mechanism. The isospin symmetry restored quasiparticle random-phase approximation method with the charge-dependent-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the nuclear matrix elements and estimate the uncertainties from our nuclear many-body calculations. We find g(pp) plays an important role for the calculations, and if quenching is included, suppression for the transition matrix element M-lambda is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hartree-Fock-Bogolyubov results with the closure approximation.

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ($0\nu\beta\beta$) of $^{76}$Ge to the first $2^+$ states of $^{76}$Se. The isospin symmetry restored Quasi-particle random phase approximation (QRPA) method with the CD-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the two nucleon mechanism nuclear matrix elements, and estimate the uncertainties from the nuclear many-body calculations. We find $g_{pp}$ plays an important role for the calculations and if quenching is included, suppression for the transition matrix element $M_{\lambda}$ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hatree-Fock-Boglyubov results with the closure approximation.

(1) The classical way to determine the electron anti-neutrino mass is the single Beta Decay of Tritium [H-3 -> He-3 + e(-) + nu(c)(e)] (Particle Physics Booklet, 2014; Aker et al., 2019). This special decay is favored by the small Q-value Q = 18.5737 +/- 0.00025 keV (Aker et al., 2019). Presently KATRIN (Aker et al., 2019) yields an upper limit of 1.1 eV (90% CL) for the neutrino mass the best result. (2) Electron capture of a bound electron [Ho-67(163) + bound electron -> Dy-66(163) + nu(e)] distributes the Q-value of the decay between the energy (rest-mass plus kinetic energy) of the emitted neutrino and the excitation of the daughter atom. The maximum excitation of the daughter atom is the Q-value minus the neutrino rest mass. Thus the difference of the energies of the Q-value and the upper end of the deexcitation spectrum of the daughter atom is the neutrino mass. (3) The neutrinoless Double Beta Decay requires, that the neutrino is a Majorana particle, thus identical with the anti-particle. A good example is the decay: [Ge-76(32) -> Se-76(34) + 2e(-)]. The signal for the neutrinoless Double Beta decay is the sum of the energies of the two emitted electrons for the Ge-76 decay at a value of 2038 keV. The strength of this peak is proportional to the neutrino mass squared. (4) If Cosmology can reliably describe the galaxy formation, the average distances of the galaxies depending on the sum of the masses of the three neutrinos yield a value for the sum of the three masses. Larger neutrino masses favor an early formation of galaxies and thus a larger average distance of the galaxies. Smaller neutrino masses favor due to the pressure of the lighter neutrinos a later formation of galaxies and thus yield a smaller average distance of the galaxies. The present contribution reviews the status of these approaches for the neutrino masses. (C) 2020 Published by Elsevier B.V.

The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are presented. Rotational spectra of even-even nuclei are described by the quantum algebra SUq(2). The two parameter formula given by the algebra is equivalent to an expan- sion in terms of powers of j(j + 1), similar to the expansion given by the Variable Moment of Inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values. The same formalism is found to give very good results for superdeformed nuclear bands, which are closer to the classical SU(2) limit, as well as for rotational bands of diatomic molecules, in which a partial summation of the Dunham expansion for rotation-vibration spectra is achieved. Vibrational spectra of diatomic molecules can be described by the q-deformed anhannonic oscillator, having the symmetry Uq(2)>Oq(2). An alternative de- scription is obtained in terms of the quantum algebra SUq(1,1). In both cases the energy formula obtained is equivalent to an expansion in terms of powers of (v+½) , where ν is the vibrational quantum number, while in the classical ST(1,1) case only the first two powers appear. In all cases the improved description of the empirical data is obtained with q being a phase (and not a real number). Further applications of quantum algebraic symmetries in nuclei and molecules are discussed.

Using partially restored isospin symmetry, we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay - the decay to the first 2(+)excited states. Employing the realistic CD-Bonn nuclear force, we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton-neutron particle-particle interactions. The dependence on the different nuclear matrix elements is observed, and the results are explained. We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies. Finally, we present our results for the half-lives of this decay mode for different nuclei.

The neutrinoless muon-to-electron conversion in nuclei is studied by using the renormalized quasiparticle random-phase approximation (RQRPA). This generalization of RPA is more reliable for the extremely small (μ-,e-) transition matrix elements than the ordinary QRPA because it restores the Pauli principle to a large extent. We apply the method to a set of nuclei throughout the periodic table, but we specifically investigate the 48Ti and 208Pb nuclei which are currently used as stopping targets at the PSI μ-e conversion experiments with the SINDRUM II spectrometer.

A workable basis of quark configurations $s^3$, $s^2p$ and $sp^2$ at light front has been constructed to describe the high-$Q^2$ behavior of transition form factors and helicity amplitudes in the electroproduction of the lightest nucleon resonances, $N_{1/2^-}(1535)$ and $N_{1/2^+}(1440)$. High-quality data of the CLAS Collaboration are described in the framework of a model which takes into account mixing of the quark configurations and the hadron-molecular states. The model allows for a rough estimate of the quark core weight in the wave function of the resonance in a comparison with high momentum transfer data on resonance electroproduction.

There are three different methods used to search the neutrino mass: - The electron antineutrino mass can probably best be determined by the Triton decay. - The neutrinoless Double Beta Decay yields information, if the neutrino is a Dirac or a Majorana particle. It can also determine the Majorana neutrino mass. - Electron capture of an atomic bound electron by a proton in a nucleus bound electron plus proton to neutron plus electron-neutrino can give the mass of the electron neutrino. This contribution summarizes our theoretical work on the possibility to determine the electron neutrino mass by electron capture. One expects the largest influence of the neutrino mass on this decay for a small Q = 2.8 keV for electron capture in Holmium. The energy of the Q value is distributed to the emitted neutrino and the excitation of the Dy atom. Thus the energy difference between the Q value and the upper end of the deexcitation spectrum is the electron neutrino mass. The excitation spectrum of Dy is calculate by one-, two- and three-electron hole excitations, and by the shake-off process. The electron wave functions are calculated selfconsistently by the Dirac-Hartree-Fock approach for the bound and the continuum states. To extract the neutrino mass from the spectrum one must adjust simultaneously the neutrino mass, the Q value, the position, the relative strength and the width of the highest resonance. This fit is only possible, if the background is reduced relative to the present situation. In case of a drastically reduced background a fit of the Q-value and the neutrino mass only seems also to be possible. The analysis presented here shows, that the determination of the electron neutrino mass by electron capture is difficult, but seems not to be impossible.

An improved formalism of the two-neutrino double-beta decay ($2\nu\beta\beta$-decay) rate is presented, which takes into account the dependence of energy denominators on lepton energies via the Taylor expansion. Till now, only the leading term in this expansion has been considered. The revised $2\nu\beta\beta$-decay rate and differential characteristics depend on additional phase-space factors weighted by the ratios of $2\nu\beta\beta$-decay nuclear matrix elements with different powers of the energy denominator. For nuclei of experimental interest all phase-space factors are calculated by using exact Dirac wave functions with finite nuclear size and electron screening. For isotopes with measured $2\nu\beta\beta$-decay half-life the involved nuclear matrix elements are determined within the quasiparticle random phase approximation with partial isospin restoration. The importance of correction terms to the $2\nu\beta\beta$-decay rate due to Taylor expansion is established and the modification of shape of single and summed electron energy distributions is discussed. It is found that the improved calculation of the $2\nu\beta\beta$-decay predicts slightly suppressed $2\nu\beta\beta$-decay background to the neutrinoless double-beta decay signal. Further, a novel approach to determine the value of effective weak-coupling constant in nuclear medium $g^{\rm eff}_{\rm A}$ is proposed.

The electron neutrino mass can be determined by electron capture. One expects the largest influence of the neutrino mass on this decay for a small Q value of Q = 2.8 keV for Ho-163(67) + e -> Dy-163(66) + nu The energy of the Q value is distributed to the emitted neutrino and the excitation of the Dy atom. Thus the energy difference between the Q value and the upper end of the deexcitation spectrum is the electron neutrino mass. The electron wave functions are calculated selfconsistently by the Dirac-Hartree-Fock approach for the bound and the continuum states. To extract the neutrino mass from the spectrum is only possible, if the background is reduced relative to the present situation. The analysis presented here shows, that the determination of the electron neutrino mass by electron capture is difficult, but seems not to be impossible.

KATRIN plans to determine the electron anti-neutrino mass in the Tritium decay. Electron capture in Ho-163 can measure the electron neutrino mass supported by the small decay energy Q = 2.8 keV(67)(163)Ho/mium + electron -> (163)(66) Dysprosium + v. The decay energy of 2.8 keV is used to emit a neutrino and to excite the Dy atom. The neutrino mass is then given by the difference between the Q value and the upper end of the Dy deexcitation spectrum. The Dirac-Hartree-Fock approach is used for the bound and the continuum states in Holmium and in Dysprosium. The present background must be reduced by at least two orders to extract the neutrino mass from the spectrum. The present work discuses the one- and the two-hole excitations in Dy. The two-hole states are excited by shake-up of an electron into a free bound state and the shake-off into the continuum. The shake-off contribution can practically be neglected. It seems not to influence the neutrino mass determination.

In this work, with restored isospin symmetry, we evaluated the neutrinoless double beta decay nuclear matrix elements for $^{76}$Ge, $^{82}$Se, $^{130}$Te, $^{136}$Xe and $^{150}$Nd for both the light and heavy neutrino mass mechanisms using the deformed QRPA approach with realistic forces. We give detailed decompositions of the nuclear matrix elements over different intermediate states and nucleon pairs, and discuss how these decompositions are affected by the model space truncations. Compared to the spherical calculations, our results show reductions from $30\%$ to about $60\%$ of the nuclear matrix elements for the calculated isotopes mainly due to the presence of BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon forces with corresponding Short-Range-Correlations (src) shows, that the choice of the NN force gives roughly $20\%$ deviations for light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism.

The lightest nucleon resonances are described at light front as mixed states of the 3q cluster (“quark core”) possessing a definite value of the inner orbital momentum L = 0,1 and a hadron molecular state, N+σ or Λ+K. Helicity amplitudes of the resonance electroproduction off the proton are calculated at large Q2 up to 12 GeV2 and compared to the last CLAS data. At this basis we have estimated the probability of quark core in lightest nucleon resonances and predicted the high Q2 behaviour of the resonance electrocoupling.

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. In electron capture, e.g., Ho-163(67) + e(-) -> Dy-167(66)* + nu(e), one 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 excitation of Dy is described by one, two, and even three hole excitations limited by the Q value. These 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 (or more) electrons 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 Ho-163. The purpose of the present work is to give a more reliable description of "s" wave shake-off in electron capture on holmium. One uses the sudden approximation to calculate the spectrum of the decay of Dy-163(66)* after electron capture on Ho-163(67). 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. DeRujula and Lusignoli use screened nonrelativistic Coulomb wave functions for the Ho electrons 3s and 4s and calculate the Dy* states by first-order perturbation theory based on Ho. In the present approach the wave functions of Ho and Dy* are determined self-consistently with the antisymmetrized relativistic Dirac-Hartree-Fock approach. The relativistic continuum electron wave functions for the ionized Dy* are obtained in the corresponding self-consistent Dirac-Hartree-Fock potential. The result of this improved approach is that shake-off can hardly be seen in the bolometer spectrum after electron capture in Ho-163 and thus can probably not affect the determination of the electron neutrino mass.

We report progress, in last decade in description of heavy exotic resonances using phenomenological Lagrangians — of a hadronic molecular approach developed by the Tübingen–Beijing group. In particular, we present a comprehensive analysis of decays properties of exotic heavy mesons and baryons.

The determination of the absolute scale of the neutrino masses is one of the most challenging questions in particle physics. Different approaches are followed to achieve a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay and electron capture processes of suitable nuclides can provide necessary information on the electron neutrino mass value. In this talk we present the Electron Capture 163-Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following the electron capture process of 163-Ho. A high precision and high statistics spectrum will be measured by means of low temperature magnetic calorimeter arrays. We present preliminary results obtained with a first prototype of single channel detectors as well as the participating groups and their on-going developments.