Comprehensive investigation on baryon number violating nucleon decays involving an axion-like particle

TL;DR

The paper provides a comprehensive EFT treatment of baryon-number-violating nucleon decays to axion-like particles within aLEFT, revealing that the complete set of dim-8 operators—including the novel ${\bf 6}_{\tt L} \otimes {\bf 3}_{\tt R}$ irreps—contribute at leading chiral order and can mediate isospin-3/2 transitions. By performing chiral matching to the SU(3)$_L\times$SU(3)$_R$ framework and deriving explicit ALP-dependent decay amplitudes and widths for two- and three-body channels, the authors enable detailed predictions of kinematic distributions that help distinguish operator structures. They recast Super-Kamiokande data to place stringent bounds on inverse decay widths and translate these into lower bounds on the effective scales $\Lambda_{\rm eff}$ across ALP masses, significantly improving upon inclusive limits and offering mass-dependent constraints in the massless ALP limit. The results have practical implications for upcoming experiments (Hyper-Kamiokande, JUNO, DUNE) by highlighting which exotic decay channels and ALP-mass ranges are most promising to probe, and by providing a framework to interpret future data in terms of BNV aLEFT operators.

Abstract

In this study, we systematically investigate baryon number violating (BNV) nucleon decays into an axion-like particle (ALP), within a low energy effective field theory extended with an ALP, which is referred to as aLEFT. Unlike previous studies in the literature, we consider contributions to nucleon decays from a complete set of dimension-eight BNV aLEFT operators involving light $u,\,d,$ and $s$ quarks. We perform the chiral irreducible representation (irrep) decomposition of these interactions under the QCD chiral group $\rm SU(3)_{\tt L}\times SU(3)_{\tt R}$, and match them onto the recently developed chiral framework to obtain nucleon-level effective interactions among the ALP, octet baryons, and octet pseudoscalar mesons. Within this framework, we derive general expressions for the decay widths of nucleon two- and three-body decays involving an ALP. Subsequently, we analyze momentum distributions for three-body modes and find that operators belonging to the newly identified chiral irreps $\pmb{6}_{\tt L(R)}\times \pmb{3}_{\tt R(L)}$ exhibit markedly different behavior compared to that in the usual irreps $\pmb{8}_{\tt L(R)}\times \pmb{1}_{\tt R(L)}$ and $\pmb{3}_{\tt L(R)}\times \bar{\pmb{3}}_{\tt R(L)}$. In addition, we reanalyze experimental data collected by Super-Kamiokande and establish bounds on the inverse decay widths of these new modes by properly accounting for experimental efficiencies and Cherenkov threshold effects because of the lack of direct constraints on those exotic decay modes. Our recasting constraints are several orders of magnitude more stringent than inclusive bounds used in the literature. Based on these improved bounds, we set conservative limits on associated effective scales across a broad range of ALP mass and predict stringent bounds on certain neutron and hyperon decays involving an ALP.

Figures (5)

• Figure 1: Diagrams for BNV octet baryon two-body (a) and nucleon three-body (b) decays involving an axion. The cyan blob (black square) represents the insertion of a BNV (usual) chiral vertex.
• Figure 2: Normalized momentum distributions for $p \to \ell^+ \pi^0 a$ and $n \to \ell^+ \pi^- a$ resulting from the insertion of various operators. All distributions are evaluated for three benchmark ALP masses: $m_a=\{0,~0.3,~0.5\}\,\rm GeV$. The vertical gray dashed lines indicate the Cherenkov thresholds: $121 \, \rm MeV$ for $\mu^+$ and $159 \, \rm MeV$ for $\pi^-$Heeck:2019kgr. $[{\cal O}^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^\pm \equiv [{\cal O}^{\tt SR,VL}_{\partial a eudu}]_{x1y1} \pm [{\cal O}^{\tt SR,VL}_{\partial a eduu}]_{xy11}$ correspond to operators associated with WCs $[C^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^\pm$, defined through the relationship $[C^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^+ [{\cal O}^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^+ + [C^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^- [{\cal O}^{\tt SR,VL}_{\partial a eudu}]_{x1y1}^- =[C^{\tt SR,VL}_{\partial a eudu}]_{x1y1} [{\cal O}^{\tt SR,VL}_{\partial a eudu}]_{x1y1} +[C^{\tt SR,VL}_{\partial a eduu}]_{xy11} [{\cal O}^{\tt SR,VL}_{\partial a eduu}]_{xy11}$.
• Figure 3: Same as \ref{['fig:p2pi']} but for the decay mode $p \to \ell^+ \eta a$ with $m_a=\{0,~0.1,~0.2\}\, \rm GeV$.
• Figure 4: New constraints on various proton decay channels as a function of the ALP mass $m_a$ obtained from our simulation based on Super-K experimental data. The plots for $p\to \ell^+ a$ are obtained by recasting the analysis in Super-Kamiokande:2015pys. The plots for $p\to \ell^+\pi^0 a$ are based on data provided in Fig. 4 of Super-Kamiokande:2016exg. The plots for $p\to \ell^+\eta a$ are based on the data provided in Fig. 5 of Super-Kamiokande:2024qbv, where the $\eta$ meson is reconstructed by the decay channel $\eta\to 2 \gamma$. The results for $p\to \nu(\bar{\nu})\pi^+ a$ and $p \to \mu^+ K^0 a$ are obtained by reanalyzing data provided in Fig. 3 of Super-Kamiokande:2013rwg and Fig. 6 of Super-Kamiokande:2022egr, respectively. The results are the same for the chirality-flipped operators with ${\tt L} \leftrightarrow {\tt R}$. The peaks or fluctuations observed in resulting constraints arise from the simplified statistical analysis and the neglect of nuclear effects.
• Figure 5: Constraints on the effective new physics scale associated with the dim-8 aLEFT operators as a function of the ALP mass $m_a$. We have set $\kappa_3=1$ in the numerical analysis, and the results for the operators belonging to the irreps $\pmb{3}_{\tt L(R)}\otimes \pmb{6}_{\tt R(L)}$ can be easily rescaled if $\kappa_3$ is found to differ from 1. The peaks observed in certain solid curves originate from the corresponding peaks in recasting bounds presented in \ref{['fig:newbound']}.