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Register a new userAssessment of uncertainties in QRPA $0 ubetabeta$-decay nuclear matrix elements
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The nuclear matrix elements $M^{0 u}$ of the neutrinoless double beta decay ($0 ubetabeta$) of most nuclei with known $2 ubetabeta$-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental $2 ubetabeta$-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. New results confirm that with such procedure the $M^{0 u}$ values become essentially independent on the size of the single-particle basis. Furthermore, the matrix elements are shown to be also rather stable with respect to the possible quenching of the axial vector strength parametrized by reducing the coupling constant $g_A$, as well as to the uncertainties of parameters describing the short range nucleon correlations. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. Furthermore, a discussion of other implicit and explicit parameters, inherent to the QRPA method, is presented. Comparison is made of the ways these factors are chosen by different authors. It is suggested that most of the spread among the published $0 ubetabeta$ decay nuclear matrix elements can be ascribed to these choices.
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This is an erratum to our previously published paper.
The nuclear matrix elements $M^{0 u}$ of the neutrinoless double beta decay ($0 ubetabeta$) are evaluated for $^{76}$Ge,$^{100}$Mo, $^{130}$Te, and $^{136}$Xe within the Renormalized Quasiparticle Random Phase Approximation (RQRPA) and the simple QRPA. Three sets of single particle level schemes are used, ranging in size from 9 to 23 orbits. When the strength of the particle-particle interaction is adjusted so that the $2 ubetabeta$ decay rate is correctly reproduced, the resulting $M^{0 u}$ values become essentially independent on the size of the basis, and on the form of different realistic nucleon-nucleon potentials. Thus, one of the main reasons for variability of the calculated $M^{0 u}$ within these methods is eliminated.
We examine the leading effects of two-body weak currents from chiral effective field theory on the matrix elements governing neutrinoless double-beta decay. In the closure approximation these effects are generated by the product of a one-body current with a two-body current, yielding both two- and three-body operators. When the three-body operators are considered without approximation, they quench matrix elements by about 10%, less than suggested by prior work, which neglected portions of the operators. The two-body operators, when treated in the standard way, can produce much larger quenching. In a consistent effective field theory, however, these large effects become divergent and must be renormalized by a contact operator, the coefficient of which we cannot determine at present.
The $lambda$ and $m_{betabeta}$ mechanisms of neutrinoless double beta decay ($0 ubetabeta$) 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 $m_{betabeta}$ and $lambda$ mechanisms of $0 ubetabeta$, 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 $0 ubetabeta$ 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.
Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first principles. The NME for 48Ca shows a good agreement among three different ab initio calculations starting from the same nuclear interaction constructed within the chiral EFT and the same decay operator. These studies open the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate goal is the computation of NMEs in many-body calculations with controllable approximations, using nuclear interactions and weak transition operators derived consistently from chiral EFT. We are expecting more progress towards this goal in the near future.
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