Nuclear matrix elements for $\lambda$ mechanism of $0\nu \beta \beta$ of ${}^{48}$Ca in nuclear shell-model: Closure versus nonclosure approach

Abstract

The $\lambda$ and $m_{\beta \beta }$ mechanisms of neutrinoless double beta decay ($0\nu \beta \beta$) occur with light neutrino exchange via $W_L-W_R$, and $W_L-W_L$ mediation, respectively. In the present study, we calculate the nuclear matrix elements (NMEs) for the $m_{\beta \beta }$ and $\lambda$ mechanisms of $0\nu \beta \beta$, which has origin in the left-right symmetric model with right-handed gauge boson at TeV scale. The NMEs are calculated for one of the $0\nu \beta \beta$ decaying isotope ${}^{48}$Ca in the interacting nuclear shell-model using the GXPF1A effective interaction of $pf$-shell. The NMEs are calculated in both closure and nonclosure approaches using four different methods: closure, running closure, running nonclosure, and mixed methods. All the NMEs are calculated incorporating the effects of the finite size of nucleons and the revisited higher order terms such as isoscalar and weak magnetism terms of the nucleon currents. Inclusion of the short-range nature of nucleon-nucleon interaction in Miller-Spencer, CD-Bonn, and AV18 parametrizations is also taken care of. The comparative dependence of the running closure and running nonclosure NMEs with the spin-parity of the allowed states of intermediate nucleus ${}^{48}$Sc, the coupled spin-parity of the two initial decaying neutrons and the final two protons, the cutoff excitation energy of ${}^{48}$Sc, the cutoff number of states of ${}^{48}$Sc are also examined. Results show that there are about 2-20\% enhancements in different types of total NMEs, calculated in the nonclosure approach as compared to the closure approach. The significant enhancements are found in the $M_{qGT}$ and $M_{qT}$ type NMEs for the inclusion of the higher-order terms of the nucleon currents.

arXiv comment13 pages, 6 figures, to be submitted in PHYSICAL REV. C

References in corpus (30)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Theory of neutrinoless double beta decay
• Neutrino-less Double Beta Decay and Particle Physics
• An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• Additional Nucleon Current Contributions to Neutrinoless Double Beta Decay
• Erratum: Assessment of uncertainties in QRPA $0\nu \beta \beta$-decay nuclear matrix elements [Nucl. Phys. A 766, 107 (2006)]
• The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
• Double Beta Decay
• Neutrinoless Double Beta Decay and Physics Beyond the Standard Model
• Limits on the neutrino mass from neutrinoless double-$\beta$ decay
• A renormalized approach to neutrinoless double-beta decay
• Uncertainties in nuclear transition matrix elements for neutrinoless $\beta \beta$ decay within the PHFB model
• Neutrinoless $\beta \beta$ decay mediated by the exchange of light and heavy neutrinos: The role of nuclear structure correlations
• Large-scale shell-model analysis of the neutrinoless $\beta \beta$ decay of ${}^{48}$Ca
• Shell Model Analysis of the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay
• Neutrinoless double beta decay matrix elements in light nuclei
• Neutrinoless double beta decay of 48Ca in the shell model: Closure versus nonclosure approximation
• The light neutrino exchange mechanism of the $0\nu \beta \beta$-decay with left- and right-handed leptonic and hadronic currents revisited
• Shell-model calculations of two-neutrino double-beta decay rates of ${}^{48}$Ca with GXPF1A interaction
• Nuclear Structure Aspects of Neutrinoless Double Beta Decay
• Accurate shell-model nuclear matrix elements for neutrinoless double-beta decay
• Comparison between Variational Monte Carlo and Shell Model Calculations of Neutrinoless Double Beta Decay Matrix Elements in Light Nuclei
• Shell model study on the possibility of using an effective field theory for disentangling several contributions to the neutrinoless double-beta decay
• The $\lambda$ mechanism of the $0\nu \beta \beta$-decay

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