Implications of Flavor Symmetries for Baryon Number Violation

TL;DR

The work examines how Standard-Model flavor symmetries constrain baryon-number violation (BNV) within the SMEFT, focusing on four dim-6 BNV operators and their interplay with lepton-number violation through neutrino masses. By promoting Yukawa couplings and a Weinberg-operator–originated spurion $oldsymbol{appa}_ u$ to spurions, the authors construct flavor-invariant structures, perform SMEFT-LEFT matching, and track RG evolution to hadronic scales to derive proton-decay bounds. They find that in extended MFV, most BNV operators can accommodate multi-TeV BNV scales when the LNV scale $ ext{Λ}_L$ is suitably large, though the operator $ ext{O}_{qqq ext{l}}$ remains highly constrained; radiative effects and operator mixing play a crucial role in connecting high-scale operators to low-energy observables. Beyond EFT, the study of UV completions via leptoquarks reveals how flavor representations can introduce additional neutrino-mass–driven suppressions or enhancements, and reduced flavor symmetries can yield even stronger or alternative suppression patterns, thereby shaping the prospects for proton-decay signals in current and future experiments.

Abstract

In the Standard Model, baryon number is an accidental symmetry, whose violation would constitute unambiguous evidence of new physics, with proton decay providing its most prominent experimental signature. At the same time, the peculiar structure of flavor can serve as a guiding principle for exploring possible new-physics effects. In this work, we present a systematic classification of dimension-six baryon-number-violating (BNV) SMEFT operators across several flavor-symmetry assumptions and analyze the resulting phenomenology. Interestingly, in certain flavor scenarios the non-trivial interplay with tiny neutrino masses leads to proton-decay constraints compatible with BNV scales in the multi-TeV range. Finally, we complement the EFT analysis by identifying one-particle UV completions of the BNV operators, revealing scenarios in which the leading-order EFT description may not fully account for their underlying dynamics.

Figures (3)

• Figure 1: Representative one-loop diagram contributing to two-body proton decay, $N \to M \ell$, where $N$ denotes a nucleon decaying into a pseudoscalar meson $M$ and a lepton $\ell$. The red blob indicates a BNV vertex involving fermions of heavier generations, generated via the spurion expansion of a generic dimension-six BNV operator. The dashed line corresponds to the exchange of a SM Higgs boson, which mediates the flavor-changing transition to light-generation fermions.
• Figure 2: Predicted proton lifetimes $\tau_p$ from the leading spurion expansion of baryon-number violating operators $\mathcal{O}_{qqq\ell}$, $\mathcal{O}_{duq\ell}$, $\mathcal{O}_{qque}$, and $\mathcal{O}_{duue}$ from Tab. \ref{['tab:dim6_BNV_SMEFT_Spurions']}. The dashed and dot-dashed curves represent current (Super-K) and projected (Hyper-K, DUNE) experimental sensitivities, respectively. For each operator, we vary $\Lambda_{{ \mathrm{L}}}$ across three benchmark values to map the allowed $\Lambda_{{ \mathrm{B}}}$ parameter space. The limiting decay channel for each case follows Tab. \ref{['tab:dim6bnvtablelim']}, with all lifetimes computed in the up-quark basis for concreteness.
• Figure 3: Ratio of the proton-decay channels $p \to \pi^0 \ell^+$ and $p \to K^+ \nu$ defined in Eq. \ref{['eq:ratio_r_def']} as a function of $\Lambda_{{ \mathrm{B}}}$ for the three spurion expansions relevant in the MFV framework (see Tab. \ref{['tab:dim6_BNV_SMEFT_Spurions']}). The predictions for $\mathcal{O}_{duue}$ and $\mathcal{O}_{qque}$ correspond to the muonic channel, while those for $\mathcal{O}_{duq\ell}$ correspond to the electron mode $p \to \pi^{0} e^{+}$. The horizontal dashed (dot--dashed) gray lines indicate the experimental values from Super-K for the electronic (muonic) channel; operator curves lying above (below) these lines are therefore more tightly constrained by $p \to \pi^{0}\ell^{+}$ ($p \to K^{+}\nu$), in agreement with Tab. \ref{['tab:dim6bnvtablelim']}. For $\mathcal{O}_{duue}$ and $\mathcal{O}_{qque}$, solid (dashed) segments denote the regions where $\Lambda_{{ \mathrm{L}}}$ is below (above) $10^{12}\,\mathrm{TeV}$, with the latter being the maximal scale compatible with a weakly-coupled regime of a UV seesaw origin of $\Upsilon_\nu$. The dashed portions remain phenomenologically viable, but observable proton decay in this regime would require $\Lambda_{{ \mathrm{L}}} >10^{12} \,\mathrm{TeV}$. All decay widths are computed in the up-quark basis; see the main text for details.