The Neutrinoless Double Beta Decay, Physics beyond the Standard Model and the Neutrino Mass – INSPIRE-HEP

is shown. the neutrino must be identicaql with the antineutrino (Majorana neutrino) and helicity must not be a good quantum number. this means the neutrino must be a massive Majorana particle. transform into proton pairs with the same angular momenta. The different contributions for the angular momenta to the total , used in the shell model calculations cite{Poves1,Poves3,Poves2}. The Ikeda Sum Rule (ISR) cite{Ikeda} is exhausted by 50%. The second bar from the left includes in addition the Se nucleus in ref. ~cite{Poves3} for the shell model. The ISR is exhausted by 66%. The third bar from the left includes both missing spin-orbit partners amounting in total to 6 single-particle levels. The ISR is fulfilled by 100%. This leads to the increase in the neutrinoless matrix element from 1.12 to 4.07. The right bar represents the QRPA result with 9 single-particle levels . The matrix element gets only slightly increased to 4.27. The spin-orbit partners are essential to fulfill the Ikeda Sum Rule (ISR). Neutron pairs with different angular momenta contributing to the neutrinoless double beta decay transition matrix elements for Se calculated from a HFB wave function with angular momentum and proton and neutron particle number projection before variation. The Fermi, the Gamow-Teller and the total contribution including the tensor part as defined in eq.~( correspond to the minima of the projected HFB total energy. The results for the transition matrix elements are qualitatively and almost quantitatively the same for the experimental deformation from the Coulomb reorientation effect: and also for different forces. The angular momenta of the neutron pairs are in the PHFB approach with axial symmetry, real coefficients and no parity mixing restricted to , which change into two protons are are coming from the left and are characterized by the two down quarks d in the two neutrons, which change into two up quarks u in two protons in the final nucleus. The vector bosons (Color online) Transition matrix elements of the neutrinoless double beta decay for the different approaches: QRPA~cite{Rod05, Ana}, the SM cite{Poves1, Poves2, Poves3}, the projected HFB method~cite{Rath3}, the projected HFB with the Generator Coordinate Method (GCM) with deformations cite{Martinez} (GCM-PNAMP) and the IBM2 cite{Iachello}. The error bars of the filled circles for the QRPA are calculated as the highest and the lowest values for three different single-particle basis sets, two forces (Bonn CD and Argonne V18) two different axial charges and two different treatments of short range correlations (Jastrow-like~cite{Miller} and the Unitary Correlator Operator Method (UCOM)~cite{Feld}). The radius parameter is as in this whole work fm. The triangle with the tip up are the SM results cite{Poves1, Poves2, Poves3}. The triangle with the tip down represent the transition matrix element of the Interacting Boson Model 2 (IBM2) cite{Iachello}. The squares have been calculated by Pradfulla Rath and coworkers cite {Rath3} with the correction of the factor 2 from December 2010 included, with which all previous results of Rath et al. have to be multiplied cite{Rath1,Rath2,Rath3}. The star (GCM-PNAMP) is a projected HFB calculation with the Gogny force cite{Gogny} by Rodriguez and Martinez-Pinedo cite{Martinez} allowing for different deformations with the Generator Coordinate Method (GCM). Source.

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Last Modified: April 18, 2016 @ 6:07 am