We introduce the formalism to describe heavy-ion Double-Charge-Exchange (DCE) processes in the eikonal approximation. We focus on the low-momentum-transfer limit -- corresponding to the differential cross section at $θ=0^\circ$ -- and, for the first time, we show that it is possible to factorize the DCE cross-section in terms of reaction and nuclear parts. Whereas in the $θ\neq0^\circ$ case the nuclear part is a convolution of the beam and target nuclear matrix elements (NMEs), for $θ=0^\circ$ we demonstrate - for the first time- that the transition matrix elements can be written as the sum of Double-Gamow-Teller (DGT) and Double Fermi (DF) type parts, and that they can both be further factorized in terms of target and projectile NMEs. By making use of the Interacting Boson Model (IBM) formalism, we also show that the DGT and total parts of the neutrinoless double-beta decay NMEs are in linear correlation with DCE-DGT NMEs. This confirms the hypothesis of a linear correlation between them, as introduced in [Phys.\ Rev.\ Lett.\ {\bf 120}, 142502 (2018)]. The possibility of a Two-Step Factorization (TSF) of the very forward differential DCE-cross-section and the emergence of DGT and DF types for the DCE nuclear matrix elements, combined with a linear correlation between DCE-DGT and 0$νββ$ NMEs, opens the possibility of placing an upper limit on neutrinoless double-beta decay NMEs in terms of the DCE experimental data at $θ=0^\circ$.
Nuclear matrix elements (NMEs) for neutrinoless double beta decays (DBDs) are required for studying neutrino physics beyond the standard model by DBD. The experimental spin-dipole (SD) giant resonance energy and the SD strength are shown for the first time to be closely related to the DBD-NME, and are used for studying the spin-isospin correlation and the quenching of the axial-vector coupling. So they are used to help the theoretical model calculation of the DBD-NME.
We report on the calculation of the neutrinoless double-beta decay nuclear matrix element for 76Ge within the framework of the realistic shell model. The effective shell-model Hamiltonian and the two-body transition operator describing the decay are derived by way of many-body perturbation theory. Particular attention is focused on the role played by the so-called Pauli blocking effect in the derivation of the effective operator.
Benchmark comparisons between many-body methods are performed to assess the ingredients necessary for an accurate calculation of neutrinoless double beta decay matrix elements. Shell model and variational Monte Carlo (VMC) calculations are carried out for $A=10$ and $12$ nuclei. Different variational wavefunctions are used to evaluate the uncertainties in the {\it ab initio} calculations, finding fairly small differences between the VMC double beta decay matrix elements. For shell model calculations, the role of model space truncation, radial wavefunction choices, and short-range correlation a…
Neutrinoless double beta decay can significantly help to shed light on the issue of non-zero neutrino mass, as observation of this lepton number violating process would imply neutrinos are Majorana particles. However, the underlying interaction does not have to be as simple as the standard neutrino mass mechanism. The entire variety of neutrinoless double beta decay mechanisms can be approached effectively. In this work we focus on a theoretical description of short-range effective contributions to neutrinoless double beta decay, which are equivalent to 9-dimensional effective operators incorp…
We study the general phenomenology of neutrinoless double beta decay in seesaw models. In particular, we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the Majorana masses of light neutrinos. For this purpose, we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties. We then discuss what can be inferred on the seesaw model parameters in the different mass regimes and clarify how the contribution of the light neutrinos should always be taken in…
Neutrinoless double beta decay is a hypothetical radioactive process which, if observed, would prove the neutrino to be a Majorana fermion: a particle that is its own antiparticle. In this lecture mini-series I discuss the physics of Majorana fermions and the connection between the nature of neutrino mass and neutrinoless double beta decay. We review Dirac and Majorana spinors, discuss methods of distinguishing between Majorana and Dirac fermions, and derive in outline the connection between neutrino mass and double beta decay rates. We conclude by briefly summarizing the experimental landscap…
Addendum to: QRPA uncertainties and their correlations in the analysis of neutrinoless double beta decay
在以前的文章[Phys. Rev. D 79，053001（2009）]中，我们在准粒子无规相位近似（QRPA）中估计了与无中微子双β衰变（0 nu β β）的核矩阵元（NME）相关的不确定性。这种估计包括最近对NME的独立计算，因此仍然可以提供核模型不确定性的公平代表。在这种情况下，我们比较了Ge-76中0 nu β β衰变的声明与最近在Ge-136和其他核中的负结果，并推断了在90% C. L.时允许或排除的寿命范围。我们还强调了一些问题，应加以解决，以适当地比较和结合来自不同的0 nu β β衰变候选核的结果。
We quantify the extent to which future experiments will test the existence of neutrinoless double-beta decay mediated by light neutrinos with inverted-ordered masses. While it remains difficult to compare measurements performed with different isotopes, we find that future searches will fully test the inverted ordering scenario, as a global, multi-isotope endeavor. They will also test other possible mechanisms driving the decay, including a large uncharted region of the allowed parameter space assuming that neutrino masses follow the normal ordering.
