An EFT approach to baryon number violation: lower limits on the new physics scale and correlations between nucleon decay modes

TL;DR

The study addresses baryon-number violation by casting nucleon-decay phenomenology in a bottom-up EFT framework that spans SMEFT at high scales, LEFT at intermediate scales, and BχPT at hadronic scales. It analyzes dimension-$6$ $| riangle B|=1$ operators with $| riangle(B-L)|=0$ and dimension-$7$ operators with $| riangle(B-L)|=2$, including one-loop RG running and threshold matching, to translate UV Wilson coefficients into hadronic decay rates. Lower bounds on operator scales are extracted from current nucleon-decay limits, with RG running strengthening these bounds (roughly 60–130% for dim-6 and 20–30% for dim-7), and a set of κ matrices is provided to efficiently relate SMEFT WCs to decay widths across channels. The results reveal strong correlations among decay modes, rule out flat directions in the WC parameter space, and are complemented by a simplified UV model illustrating how specific operator structures map to observable decays. Together, the framework and data offer a practical roadmap for interpreting future proton-decay signals and constraining UV completions like GUTs.

Abstract

Baryon number is an accidental symmetry of the Standard Model at the Lagrangian level. Its violation is arguably one of the most compelling phenomena predicted by physics beyond the Standard Model. Furthermore, there is a large experimental effort to search for it including the Hyper-K, DUNE, JUNO, and THEIA experiments. Therefore, an agnostic, model-independent, analysis of baryon number violation using the power of Effective Field Theory is very timely. In particular, in this work we study the contribution of dimension six and seven effective operators to $|Δ(B-L)|=0, \, 2$ nucleon decays taking into account the effects of Renormalisation Group Evolution. We obtain lower limits on the energy scale of each operator and study the correlations between different decay modes. We find that for some operators the effect of running is very significant.

Figures (13)

• Figure 1: Limits on the UV scale $\Lambda/\sqrt{c}$ for each of the dimension-6 $\Delta (B-L)=0$ SMEFT operators without (with) RG effects in dark (light) blue. The numerical are given in Tab. \ref{['tab:general-limits-d6']}.
• Figure 2: The figure is analogous to Fig. \ref{['fig:stacked6']} but for the dimension-7 $|\Delta (B-L)|=2$ SMEFT operators, with the values provided in Tab. \ref{['tab:general-limits-d7']}. The expression bounded in this case is $\Lambda / \sqrt[3]{c}$.
• Figure 3: Running of the three SM gauge couplings alongside the lower limits on the UV scale for three different values of the WCs $c$ in blue (green) for the least (most) constraining operators, i.e. $\mathcal{O}_{duql,2111}$ ($\mathcal{O}_{qque,1111}$).
• Figure 4: Allowed parameter space of the dimensionless WCs $c_{duue,1111}$ and $c_{qque,1111}$ at the UV scale using the current limits on $p \to \pi^0 e^{+}$Super-Kamiokande:2020wjk and $p \to \eta^0 e^{+}$Super-Kamiokande:2017gev. Inner (outer) regions are obtained by setting $\Lambda=10^{14} \, (10^{15})$ GeV. Dashed lines indicate the effect of including the RGEs, leading always to a shrinking in the available parameter space. The hatched region corresponds to the non-perturbative regime for the WCs.
• Figure 5: The figure is analogous to Fig. \ref{['fig:flatdirections6']} but for $c_{\bar{l} dud \tilde{H},1111}$ and $c_{\bar{l}d qq \tilde{H},1111}$, where the relevant current limits are in this case on $n \to \pi^0\nu$Super-Kamiokande:2013rwg and $n \to \eta^0 \nu$McGrew:1999nd. Inner (outer) regions are obtained by setting $\Lambda=10^{10} \, (2 \cdot 10^{10})$ GeV.