Neutrinoless double beta decay and neutrino physics

TL;DR

The paper analyzes how neutrinoless double beta decay (0νββ) probes the Majorana nature of neutrinos and lepton-number violation, focusing on the standard light Majorana exchange mechanism and the experimental landscape. It reviews the origin of neutrino masses via the dimension-5 Weinberg operator and seesaw realizations, and explains how the PMNS matrix with Majorana phases governs the effective mass $⟨m_{ee}⟩$ that controls 0νββ rates: $\Gamma^{0\nu} = \sum_x G_x(Q,Z)\,|{\cal M}_x(A,Z)\,\eta_x|^2$ and $⟨m_{ee}⟩ = |\sum_i U_{ei}^2 m_i|$. The analysis highlights how mass ordering (NH vs IH), CP-violating Majorana phases, and possible cancellations shape the expected half-lives and the sensitivity required to test IH and QD scenarios, including the nonzero minimal IH bound $⟨m_{ee}⟩^{\rm inv}_{\rm min}$ and the conditions under which $⟨m_{ee}⟩$ can vanish in NH. It also discusses how light sterile neutrinos and exotic extensions can dramatically modify $⟨m_{ee}⟩$, potentially preventing cancellations and shifting predictions, while emphasizing the role of nuclear matrix elements and the experimental program in constraining or revealing the underlying neutrino physics. Overall, the work underscores the complementarity of 0νββ with direct mass measurements and cosmology, the importance of NMEs, and the potential to test flavor models and lepton-number violation in the coming decade.

Abstract

The connection of neutrino physics with neutrinoless double beta decay is reviewed. After presenting the current status of the PMNS matrix and the theoretical background of neutrino mass and lepton mixing, we will summarize the various implications of neutrino physics for double beta decay. The influence of light sterile neutrinos and other exotic modifications of the three neutrino picture is also discussed.

Figures (10)

• Figure 1: Left: quark level "lobster" diagram for neutrinoless double beta decay in case of light Majorana neutrino exchange. Right: geometrical visualization of the effective mass.
• Figure 2: Effective mass against the smallest neutrino mass for the $3\sigma$ ranges (top) and best-fit values (bottom) of the oscillation parameters. The green and red shaded areas are the general $3\sigma$ ranges, while the blue shaded areas can only be realized if the CP phases take non-trivial values. $(\pm,\pm)$ denote different CP conserving situations, corresponding to signs of $m_2$ and $m_3$, relative to positive $m_1$. Prospective future values of $\Sigma$ and $m_\beta$ are also given.
• Figure 3: Effective mass against sum of masses $\Sigma$ and kinematic neutrino mass $m_\beta$ for the $3\sigma$ ranges of the oscillation parameters. The green and red shaded areas are the general $3\sigma$ ranges, while the blue shaded areas can only be realized if the CP phases take non-trivial values. Prospective future values of $\Sigma$ and $m_\beta$ are also given.
• Figure 4: The main properties of the effective mass as function of the smallest neutrino mass. Here $m_0$ denotes the common mass for quasi-degenerate neutrinos and $t_{12} = \tan \theta_{12}$. We indicate the relevant formulae and the three important regimes: hierarchical, cancellation and quasi-degeneracy. See Lindner:2005kr.
• Figure 5: Nuclear matrix element compilation for 0$\nu\beta\beta$, different isotopes and calculational approaches.