Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory

We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-beta decays with a state-of-the-art beyond mean-field covariant density functional theory. The dynamic effects of particle-number and angular-momentum conservations as well as quadrupole shape fluctuations are taken into account with projections and generator coordinate method for both initial and final nuclei. The full relativistic transition operator is adopted to calculate the NMEs. The present systematic studies show that in most of the cases there is a much better agreement with the previous non-relativistic calculation based on the Gogny force than in the case of the nucleus $^{150}$Nd found in Song et al. [Phys. Rev. C 90, 054309 (2014)]. In particular, we find that the total NMEs can be well approximated by the pure axial-vector coupling term with a considerable reduction of the computational effort.Comment: 9 pages with 7 figures and 3 table

Heavy-to-light scalar form factors from Muskhelishvili-Omn\`es dispersion relations

By solving the Muskhelishvili-Omn\`es integral equations, the scalar form factors of the semileptonic heavy meson decays $D\to\pi \bar \ell \nu_\ell$, $D\to \bar{K} \bar \ell \nu_\ell$, $\bar{B}\to \pi \ell \bar\nu_\ell$ and $\bar{B}_s\to K \ell \bar\nu_\ell$ are simultaneously studied. As input, we employ unitarized heavy meson-Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omn\`es matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to $q^2=0$ as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at $q^2=0$, we obtain $|V_{cd}|=0.244\pm 0.022$, $|V_{cs}|=0.945\pm 0.041$ and $|V_{ub}|=(4.3\pm 0.7)\times10^{-3}$ for the involved Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at $q^2=0$: $|f_+^{D\to\eta}(0)|=0.01\pm 0.05$, $|f_+^{D_s\to K}(0)|=0.50 \pm 0.08$, $|f_+^{D_s\to\eta}(0)|=0.73\pm 0.03$ and $|f_+^{\bar{B}\to\eta}(0)|=0.82 \pm 0.08$, which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the $q^2-$regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupled-channel chiral approach.Comment: includes further discussions and references; matches the accepted versio

Triaxially deformed relativistic point-coupling model for Λ\Lambda hypernuclei: a quantitative analysis of hyperon impurity effect on nuclear collective properties

The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_\Lambda$Li. Many more data on low-lying states of $\Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $\Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $\Lambda$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $\Lambda$ hyperon is injected into the lowest positive-parity ($\Lambda_s$) and negative-parity ($\Lambda_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $\Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(\beta, \gamma)$ deformation plane. We also calculate the PESs for the $\Lambda$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_{\Lambda}$Mg and $^{31}_{\Lambda}$Si as examples, we analyse the impurity effects of $\Lambda_s$ and $\Lambda_p$ on the low-lying states of the core nuclei...Comment: 15 pages with 18 figures and 1 table (version to be published in Physical Review C

Gap Equations and Electroweak Symmetry Breaking

Recently a new dynamical symmetry breaking model of electroweak interactions was proposed based on interacting fermions. Two fermions of different SU(2) representations form a symmetry breaking condensate and generate the lepton and quark masses. The weak gauge bosons get their usual standard model masses from a gauge invariant Lagrangian of a composite doublet scalar field. The new fermion fields become massive by condensation. In this note the gap equations are given in the linearized (mean field) approximation and the conditions for symmetry breaking and mass generation are presented. Perturbative unitarity constrains the self-couplings and the masses of the new fermions, a raw spectrum is given.Comment: 10 pages, 4 figure

Chaos, Determinacy and Fractals in Active-Sterile Neutrino Oscillations in the Early Universe

The possibility of light sterile neutrinos allows for the resonant production of lepton number in the early universe through matter-affected neutrino mixing. For a given a mixing of the active and sterile neutrino states it has been found that the lepton number generation process is chaotic and strongly oscillatory. We undertake a new study of this process' sensitivity to initial conditions through the quantum rate equations. We confirm the chaoticity of the process in this solution, and moreover find that the resultant lepton number and the sign of the asymmetry produces a fractal in the parameter space of mass, mixing angle and initial baryon number. This has implications for future searches for sterile neutrinos, where arbitrary high sensitivity could not be determinate in forecasting the lepton number of the universe.Comment: 6 pages, 3 figure

Impurity effect of Lambda hyperon on collective excitations of atomic nuclei

Taking the ground state rotational band in $^{24}$Mg as an example, we investigate the impurity effect of $\Lambda$ hyperon on collective excitations of atomic nuclei in the framework of non-relativistic energy density functional theory. To this end, we take into account correlations related to the restoration of broken symmetries and fluctuations of collective variables by solving the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom. The parameters of the collective Hamiltonian are determined with constrained mean-field calculations for triaxial shapes using the SGII Skyrme force. We compare the low-spin spectrum for $^{24}$Mg with the spectrum for the same nucleus inside $^{25}_{\Lambda}$Mg. It is found that the $\Lambda$ hyperon stretches the ground state band and reduces the $B(E2:2^+_1 \rightarrow 0^+_1)$ value by $\sim 9$, mainly by softening the potential energy surface towards the spherical shape, even though the shrinkage effect on the average proton radius is only $\sim0.5$.Comment: 16 pages, 5 figures, and 1 tabl

In-plane thermal conductivity of large single crystals of Sm-substituted (Y1−x_{1-x}Smx_{x})Ba2_{2}Cu3_{3}O7−δ_{7-\delta}

We have investigated the in-plane thermal conductivity $\kappa_{ab}(T,H)$ of large single crystals of optimally oxygen-doped (Y$_{1-x}$,Sm$_{x}$)Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ ($x$=0, 0.1, 0.2 and 1.0) and YBa$_{2}$(Cu$_{1-y}$Zn$_{y}$)$_{3}$O$_{7-\delta}$($y$=0.0071) as functions of temperature and magnetic field (along the c axis). For comparison, the temperature dependence of $\kappa_{ab}$ for as-grown crystals with the corresponding compositions are presented. The nonlinear field dependence of $\kappa_{ab}$ for all crystals was observed at relatively low fields near a half of $T_{c}$. We make fits of the $\kappa(H)$ data to an electron contribution model, providing both the mean free path of quasiparticles $\ell_{0}$ and the electronic thermal conductivity $\kappa_{e}$, in the absence of field. The local lattice distortion due to the Sm substitution for Y suppresses both the phonon and electron contributions. On the other hand, the light Zn doping into the CuO $_{2}$ planes affects solely the electron component below $T_{c}$, resulting in a substantial decrease in $\ell_{0}$ .Comment: 7 pages,4 figures,1 tabl