Neutrinoless double beta decays of hyperons in covariant chiral perturbation theory

TL;DR

This work analyzes neutrinoless double beta decays of spin-1/2 hyperons within covariant SU(3) baryon chiral perturbation theory, augmented by a ΔL=2 operator tied to Majorana neutrino mass. The long-range contribution from light Majorana exchange appears at one loop and is renormalized using dimensional regularization and the extended-on-mass-shell scheme to preserve chiral power counting. The authors compute differential decay rates and branching ratios for all kinematically allowed hyperon channels, finding them exceedingly small—more than 20 orders of magnitude below current experimental bounds—while showing that the leading effect is actually governed by short-range counterterms required by renormalization. They propose neutrinoless transition form factors, which can be accessed by lattice QCD to determine the short-range LNV LECs, thereby enabling a lattice-driven determination of the dominant contributions and providing robust benchmarks for future searches of lepton-number-violating signals in hyperon decays.

Abstract

Neutrinoless double beta ($0νββ$) decays of spin-1/2 hyperons are investigated in a covariant baryon chiral perturbation theory framework, extended by a $ΔL=2$ operator proportional to the Majorana neutrino mass, where $L$ denotes the lepton number. Within the light Majorana neutrino exchange mechanism, the decay amplitudes are found to emerge at the one-loop level, representing the long-range contribution. The extended-on-mass-shell scheme is employed to renormalize the one-loop amplitudes and restore consistent chiral power counting. Consequently, the differential decay rates for all accessible hyperon $0νββ$ channels are predicted and the corresponding branching ratios are more than 20 orders of magnitude smaller than the current experimental upper bounds. Interestingly, it is found that the leading contribution to hyperon $0νββ$ decay is actually from short-range counterterm operators, as required by the renormalization argument. Neutrinoless transition form factors are proposed to determine this leading contribution through future lattice QCD simulations.

Figures (7)

• Figure 1: Kinematics of hyperon $0\nu\beta\beta$ decays.
• Figure 2: Mass mechanism of hyperon $0\nu\beta\beta$ decays.
• Figure 3: One-loop Feynman diagrams contributing to the $0\nu \beta\beta$ decay of hyperons. The thick solid, thin solid and dashed lines represent baryons, leptons and pions, in order. The teal box denotes the LNV vertex with $\Delta L= 2$, while the gray filled circles stand for charged-current vertices from the SM. The crossed diagrams are not shown explicitly.
• Figure 4: Normalized differential decay distributions $\mathrm{d}\Gamma/\mathrm{d}\sqrt{s} \times (1/m_{\ell\ell}^2)$ for the LNV hyperon decay channels: $\Sigma^- \to p\, \ell^- \ell^-$ (top left), $\Sigma^- \to \Sigma^+\, \ell^- \ell^-$ (top right), $\Xi^- \to p\, \ell^- \ell^-$ (bottom left), and $\Xi^- \to \Sigma^+\, \ell^- \ell^-$ (bottom right). The blue solid and red dashed curves correspond to electronic and muonic modes, respectively. For comparison, the green dashed curve shows the decay rate in the massless lepton limit.
• Figure 5: Dependence of the LNV hyperon decay branching ratios, obtained from the one-loop amplitudes in the EOMS scheme with the renormalization scale $\mu=m$, on the effective Majorana mass $m_{\ell\ell}$. The insets compare the upper limits from HyperCP (left) HyperCP:2005sby and BESIII (right) BESIII:2020iwkBESIII:2025ylz. A zoomed-in view of the gray band, which covers $0 \leq m_{\ell\ell} \leq 400$ meV, is provided in figure \ref{['fig:Br']}.