Nucleon decays into three leptons: contact contributions

TL;DR

This work develops a robust LEFT-based framework to study baryon-number-violating nucleon decays into three leptons via dimension-9 contact operators. It constructs a complete dim-9 operator basis, performs spurion-driven chiral perturbation theory matching to obtain hadronic four-fermion interactions, and computes the corresponding decay widths and momentum distributions, expressing results in terms of WC combinations. Using existing experimental limits, the authors derive stringent lower bounds on the effective operator scales (typically several hundred TeV) and discuss potential improvements from future detectors like Hyper-K and JUNO. A UV-complete leptoquark model is analyzed to illustrate the connection between high-scale new physics and the LEFT operators, including RG running and interference effects among operators. Overall, the work provides a comprehensive theoretical toolkit to guide searches for exotic BNV nucleon decays in upcoming neutrino experiments and to constrain UV theories that generate such high-dimensional operators.

Abstract

Baryon number violating (BNV) nucleon decays into three leptons provide a unique probe of BNV interactions beyond the conventional two-body modes involving a single lepton and a light meson. In a previous work [Nucleon decays into three leptons: noncontact contributions, arXiv:2512.02692.], two of us analyzed the noncontact contributions to these decays arising from dimension-6 (dim-6) operators within the low-energy effective field theory (LEFT), and found that they are severely suppressed due to stringent constraints on these dim-6 operators. In this work, we continue this endeavor by systematically investigating the contact contributions originating from dim-9 LEFT operators. We construct a complete basis of dim-9 operators relevant to these processes, and subsequently match them onto chiral perturbation theory to calculate their decay widths. By employing existing experimental data, we derive stringent constraints on the relevant operators. In addition, we present the analysis of an ultraviolet-complete model to demonstrate its connection with our theoretical framework, thereby facilitating further studies of these exotic nucleon decays in upcoming neutrino experiments with large fiducial masses.

Figures (7)

• Figure 1: Normalized double-momenta distributions of the processes $p\to e^+e^+e^-$ (top row), $p\to e^+e^+\mu^-$ (second row), $p\to \mu^+\mu^+e^-$ (third row), and $p\to \mu^+\mu^+\mu^-$ (bottom row).
• Figure 2: Constraints on the effective scales of the LEFT dim-9 operators from proton decays into three charged leptons. The red and green bars indicate operators belonging to the chiral irreps ${\bar{\pmb{3}}_{ {\tt L} ( {\tt R} )}\otimes\pmb{3}_{ {\tt R} ( {\tt L} )}}/{\pmb{8}_{ {\tt L} ( {\tt R} )}\otimes\pmb{1}_{ {\tt R} ( {\tt L} )}}$ and ${\pmb{6}_{ {\tt L} ( {\tt R} )}\otimes\pmb{3}_{ {\tt R} ( {\tt L} )}}$, respectively. Here, the superscript $\chi$ denotes either ${\tt L}$ or ${\tt R}$, and the flavor indices $xy$ correspond to $e\mu$ or $\mu e$.
• Figure 3: Same as \ref{['fig:cons_WCs1']} but for the operators involving neutrino fields. The expected JUNO sensitivities for $n\to\hat{\nu}\hat{\nu}\hat{\nu}$ are denoted by light red and light green bars. Here, $\chi= {\tt L} , {\tt R}$, and the neutrino flavor indices $x,y=e,\mu,\tau$.
• Figure 4: Constraints in the planes of pairs of WCs from proton decay modes $p \to e^+ e^+ e^-$ (top left), $p \to e^+ e^+ \mu^-$ (top right), $p \to \mu^+ \mu^+ e^-$ (bottom left), and $p \to \mu^+ \mu^+ \mu^-$ (bottom right).
• Figure 5: The diagram that induces dim-10 SMEFT BNV interactions.