Baryon-number-violating nucleon decays in SMEFT extended with a light scalar

New light particles have received considerable attention in recent years. Baryon-number-violating (BNV) nucleon decays involving such light particles are able to provide stringent constraints. They exhibit distinctive experimental signatures that merit thorough investigation. We systematically investigate BNV nucleon decay with a light scalar in an effective field theory framework. Within this framework, we set stringent bounds on BNV operators using available experimental data and predict the occurrence of several BNV three-body nucleon decays. We further study contributions to dinucleon to dilepton transitions in a nucleus mediated by the scalar, which complements single nucleon decay. Finally, we provide three ultraviolet-complete models that can generate different subsets of BNV operators in leading order. Our theoretical framework will facilitate experimental searches for those exotic nucleon decays.

💡 Research Summary

The paper presents a comprehensive study of baryon-number‑violating (BNV) nucleon decays in the presence of a light scalar particle φ, using an effective‑field‑theory (EFT) approach that bridges the electroweak (EW) scale down to the GeV scale relevant for nucleon decay. The authors first extend the Standard Model EFT (SMEFT) by a singlet scalar φ, calling the resulting framework φ‑SMEFT. At dimension‑7, operators with Δ(B–L)=0 appear, while at dimension‑8 operators with Δ(B+L)=0 arise. Table I lists all such operators, constructed by inserting φ into the known dim‑6 and dim‑7 BNV SMEFT operators.

Below the EW scale the heavy W, Z, Higgs and top are integrated out, yielding a low‑energy EFT (φ‑LEFT) that respects only QCD × QED. The leading BNV operators now appear at dimension‑7. The authors perform tree‑level matching of φ‑SMEFT onto φ‑LEFT, carefully distinguishing the up‑type and down‑type quark flavor bases. The matching coefficients involve the CKM matrix and, for the dim‑8 operators, the Higgs vacuum expectation value v≈246 GeV. The results are summarized in Table II.

To compute nucleon‑decay matrix elements, the paper employs baryon chiral perturbation theory (ChPT). The scalar φ and the lepton fields are introduced as spurions, and the low‑energy constants c₁ and c₂ (often denoted α and β) are taken from recent lattice QCD determinations (c₁≈−0.01257 GeV³, c₂≈0.01269 GeV³). Expanding the chiral Lagrangian yields contact interactions between a baryon, a meson, a lepton and φ, as well as the usual SM baryon‑meson couplings. Explicit expressions for two‑body decays (p→ℓ⁺φ) and three‑body decays (n→ν̄π⁰φ, n→ν̄π⁻φ, etc.) are derived, both in the massless‑φ limit (Appendix A) and for arbitrary φ mass. The momentum distribution of the visible SM particle encodes the φ mass and the chiral structure of the underlying operator.

Using existing experimental data, the authors set limits on the Wilson coefficients. Super‑Kamiokande searches for p→e⁺φ and p→μ⁺φ are re‑interpreted to constrain the relevant dim‑7 and dim‑8 operators across the full kinematically allowed φ‑mass range. The SNO limits on invisible neutron decay constrain operators involving first‑generation quarks. The analysis includes both single‑operator limits and two‑operator fits, illustrating the complementarity of different decay channels.

When φ is heavier than the nucleon, the paper studies long‑distance contributions to dinucleon decay (NN→ℓℓ′) mediated by t‑channel φ exchange. These ΔB=2 processes provide additional bounds, especially for parameter regions where the two‑body nucleon decay is kinematically forbidden. The authors compute the relevant nuclear matrix elements (Appendix B) and compare the resulting constraints with those from single‑nucleon decay.

Finally, three ultraviolet‑complete models are constructed that generate the effective operators at tree level: (i) a lepto‑quark model producing Δ(B–L)=0 dim‑7 operators, (ii) a vector‑like quark model yielding the same Δ(B–L)=0 structures but with different gauge quantum numbers, and (iii) a second lepto‑quark model that generates Δ(B+L)=0 dim‑8 operators. Each model is mapped onto the φ‑SMEFT operator basis, showing how the Wilson coefficients relate to the masses and couplings of the heavy mediators.

In conclusion, the work provides a systematic EFT framework for BNV nucleon decays involving a light scalar, derives robust experimental limits, predicts several exotic three‑body decay modes, and supplies concrete UV completions. The results are directly applicable to upcoming large‑volume detectors such as JUNO, Hyper‑K, DUNE, THEIA and ESSνSB, guiding future searches for exotic BNV signatures.