Squeezing Proton Decay and Neutrino Masses: Upper Bounds on Standard Model Extensions

TL;DR

This work develops a unified EFT framework to bound minimal UV extensions of the SM that violate baryon and lepton number by introducing linear SM extensions (LSMEs) and embedding them into XSMEFT. By analyzing their contributions to the dimension-5 Weinberg operator and to baryon-number-violating operators up to dimension 7, the authors derive upper bounds on the intermediate scale $M$ from neutrino-mass data and prospective nucleon-decay signals (e.g., Hyper-K). A genuineness filter and flavour antisymmetry considerations ensure the identified operators provide the leading contributions, yielding robust, model-independent bounds. The results reveal a two-cluster structure in the UV scales: around $10^{7}$ TeV for Δ(B−L)=2 and around $10^{12}$ TeV for Δ(B−L)=0, guiding UV model classification and informing which multiplets could be probed by future experiments. The framework offers a practical, semi-analytic map to organize UV completions that simultaneously address neutrino masses and baryon-number violation, with potential connections to GUTs and testable implications for upcoming experiments.

Abstract

Baryon and lepton number are excellent low-energy symmetries of the Standard Model (SM) that tightly constrain the form of its extensions. In this paper we investigate the possibility that these accidental symmetries are violated in the deep UV, in such a way that one multiplet necessary for their violation lives at an intermediate energy scale $M$ above the electroweak scale. We write down the simplest effective operators containing each multiplet that may couple linearly to the SM at the renormalisable level and estimate the dominant contribution of the underlying UV model to the pertinent operators in the SMEFT: the dimension-5 Weinberg operator and the baryon-number-violating operators up to dimension 7. Our results are upper bounds on the scale $M$ for each multiplet--operator pair, derived from neutrino-oscillation data as well as prospective nucleon-decay searches. We also analyse the possibility that both processes are simultaneously explained within a natural UV model. In addition, we advocate that our framework provides a convenient and digestible way of organising the space of UV models that violate these symmetries.

Figures (14)

• Figure 1: (Left) An illustration of the tower of EFTs we use in our analysis. The full theory describing the violation of baryon and lepton number lives above the scale $\Lambda$, while the intermediate scale $M$ characterises one of the LSMEs participating in the neutrino-mass or nucleon-decay mechanism. (Right) Quantum numbers of the 48 LSMEs analysed in this work under the Lorentz and gauge group $G_{\rm SM} =\left(\rm{SU}(3)_C, \, \rm{SU}(2)_L, U(1)_Y \right)$. Each particle $X$ is assumed to exist within the $X$SMEFT regime, while the unknown UV theory lives above $\Lambda$.
• Figure 2: Tree-level completion of operator $\Xi (L^\dagger \bar{d}^\dagger) (QQ) H^\dagger$. See the main text for details.
• Figure 3: Upper limits on the mass of new scalars (top), vectors (middle) and fermions (bottom) that couple linearly to the SM, obtained from reproducing neutrino masses (in blue) and a hypothetical signal from nucleon decay (in orange).
• Figure 4: Two-dimensional plane $(M_{\Delta L=2},$$M_{\Delta B=1})$ obtained under the assumption $M\sim \Lambda$. We use different colours to denote each LSME according to their category in Tab. \ref{['tab:generalclassification']}, and we use different markers to denote their Lorentz transformation. Note that several LSMEs share common points in the plot. See the main text for further details.
• Figure 5: Ratio of $\Lambda_{\Delta L=2}$ and $\Lambda_{\Delta B=1}$ for each LSME. For readiness, we highlight different ratios of UV scales with green bands. See main text for details.