Relation between the 2νββ2\nu\beta\beta and 0νββ0\nu\beta\beta nuclear matrix elements

A formal relation between the GT part of the nuclear matrix elements M^0\nu}_{GT} of $0\nu\beta\beta$ decay and the closure matrix elements $M^{2\nu}_{cl}$ of $2\nu\beta\beta$ decay is established. This relation is based on the integral representation of these quantities in terms of their dependence on the distance $r$ between the two nucleons undergoing transformation. We also discuss the difficulties in determining the correct values of the closure $2\nu\beta\beta$ decay matrix elements.Comment: Talk at the MEDEX'11 workshop, Prague, June 201

Relation between the 0νββ and 2νββ nuclear matrix elements reexamined

We show that the dominant Gamow-Teller part, M^(0ν)_(GT), of the nuclear matrix element governing the neutrinoless ββ decay is related to the matrix element M^(2ν)_(cl) governing the allowed two-neutrino ββ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance r between the pair of neutrons that are transformed into a pair of protons in the ββ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when A and Z is changed; while M^(0ν)_(GT) changes slowly and smoothly, M^(2ν) has pronounced shell effects. We also discuss the possibility of phenomenological determination of the M^(2ν)_(cl) and from them of the M^(0ν)_(GT)values from the experimental study of the β^± strength functions

Muon capture rates: Evaluation within the quasiparticle random phase approximation

The quasiparticle random phase approximation is used in evaluation of the total muon capture rates for final nuclei participating in double-β decay. Several variants of the method are used, depending on the size of the single-particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic results in rates that are in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant g_A. Its standard value g_A = 1.27 seems to be adequate

Pion dominance in RPV SUSY induced neutrinoless double beta decay

At the quark level there are basically two types of contributions of R-parity violating SUSY (RPV SUSY) to neutrinoless double beta decay: the short-range contribution involving only heavy virtual superpartners and the long-range one with the virtual squark and neutrino. Hadronization of the effective operators, corresponding to these two types of contributions, may in general involve virtual pions in addition to the close on-mass-shell nucleons. It is known that the short-range contribution is dominated by the pion exchange. In the present paper we show that this is also true for the long-range RPV SUSY contribution and, therefore, the RPV SUSY contributes to the neutrinoless double beta decay dominantly via charged pion exchange between the decaying nucleons.Comment: 7 pages, 1 figure. Minor corrections, several comments and references adde

Majorana neutrino magnetic moments

The presence of trilinear R-parity violating interactions in the MSSM lagrangian leads to existence of quark-squark and lepton-slepton loops which generate mass of the neutrino. By introducing interaction with an external photon the magnetic moment is obtained. We derive bounds on that quantity being around one order of magnitude stronger than those present in the literature.Comment: I've decided to move the collection of my papers to arXiv for easier access. Proceedings of the Nuclear Physics Workshop in Kazimierz Dolny, Poland, 200

0νββ and 2νββ nuclear matrix elements evaluated in closure approximation, neutrino potentials and SU(4) symmetry

The intimate relation between the Gamow-Teller part of the matrix element M^(0ν)_(GT) and the 2νββ closure matrix element M^(2ν)_(cl) is explained and explored. If the corresponding radial dependence C^(2ν)_(cl)(r) would be known, M^(0ν) corresponding to any mechanism responsible for the 0νββ decay can be obtained as a simple integral. However, the M^(2ν)_(cl) values, and therefore also the functions C^(2ν)_(cl)(r), sensitively depend not only on the properties of the first few 1^+ states but also of higher-lying 1^+ states in the intermediate odd-odd nuclei. We show that the β^− and β^+ amplitudes of such states typically have opposite relative signs, and their contributions reduce severally the M^(2ν)_(cl) values. We suggest that demanding that M^(2ν)_(cl) = 0 is a sensible alternative way, within the QRPA method, of determining the amount of renormalization of isoscalar particle-particle interaction strength g^(T=0)_(pp). Using such prescription, the matrix elements M^(0ν) are evaluated; their values are not very different (≤ 20%) from the usual QRPA values when g^(T=0)_(pp) is related to the known 2νββ half-lives. We note that vanishing values of M^(2ν)_(cl) are signs of a partial restoration of the spin-isospin SU(4) symmetry

Neutrino mass in GUT constrained supersymmetry with R-parity violation in light of neutrino oscillations

The neutrino masses are generated in grand unified theory (GUT) constrained supersymmetric model with R-parity violation. The neutrinos acquire masses via tree-level neutrino-neutralino mixing as well as via one-loop radiative corrections. The theoretical mass matrix is compared with the phenomenological one, which is reconstructed by using neutrino oscillation and neutrinoless double beta decay data. This procedure allows to obtain significantly stronger constraints on R-parity breaking parameters than those existing in the literature. The implication of normal and inverted neutrino mass hierarchy on the sneutrino expectation values, lepton-Higgs bilinear and trilinear R-parity breaking couplings is also discussed