Left-Right Symmetry and Leading Contributions to Neutrinoless Double Beta Decay

We study the impact of the mixing (LR mixing) between the standard model $W$ boson and its hypothetical, heavier right-handed parter $W_R$ on the neutrinoless double beta decay ($0\nu \beta \beta$ decay) rate. Our study is done in the minimal left-right symmetric model assuming a type-II dominance scenario with charge conjugation as the left-right symmetry. We then show that the $0\nu \beta \beta$ decay rate may be dominated by the contribution proportional to this LR mixing, which at the hadronic level induces the leading-order contribution to the interaction between two pions and two charged leptons. The resulting long-range pion exchange contribution can significantly enhance the decay rate compared to previously considered short-range contributions. Finally, we find that even if future cosmological experiments rule out the inverted hierarchy for neutrino masses, there are still good prospects for a positive signal in the next generation of $0\nu \beta \beta$ decay experiments.

Figure 1

Feynman diagrams in the minimal LRSM contributing to the $0\nu \beta \beta$ decay. Panels (a) corresponds to the RR amplitude, panel (b) denotes the contribution from the exchange of the doubly charged scalar, panel (c) denotes the contribution from the exchange of the SM $W$ boson and heavy neutrinos, while panel (d) corresponds to the LR amplitude.

Figure 2

Effective Majorana mass as a function of the lightest neutrino mass. The central values of the mixing angles and the Dirac $CP$-violating phase in $V_L$ are quoted from Ref. [54], and the Majorana phases are marginalized. The allowed regions with $\tan \beta =0$ and $\tan \beta \le 0.5$ are depicted in darker and lighter colors. Red (green) dots denote the NH (IH) of neutrino mass ordering. Gray and orange lines represent the current and expected limits from the KamLAND-Zen Collaboration [7] and future ton-scale experiment [9, 10], respectively. The lightest heavy neutrino mass is also given in the upper horizontal axis.

Figure 3

Effective Majorana mass as a function of the sum of light neutrino masses. The red and green regions as well as gray and the orange lines have the same meaning as in Fig. 2. The current constraint from cosmological experiments [15] is depicted in the gray region.