Implications of Flavor Symmetries for Baryon Number Violation

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.

💡 Research Summary

The paper investigates how flavor symmetries can dramatically affect the phenomenology of baryon-number‑violating (BNV) processes in the Standard Model Effective Field Theory (SMEFT). Starting from the observation that baryon number is an accidental symmetry of the SM, the authors note that any observation of proton decay would be a smoking‑gun signal of new physics, yet current limits from Super‑Kamiokande already push generic dimension‑six BNV operators to scales of order 10^16 GeV. To explore whether flavor structure can relax these bounds, the authors adopt an extended Minimal Flavor Violation (MFV) framework. In addition to the usual Yukawa spurions (Y_u, Y_d, Y_e), they introduce a symmetric spurion Υ_ν that encodes the breaking associated with Majorana neutrino masses generated by the dimension‑5 Weinberg operator. This spurion transforms as a 6 of the lepton‑flavor U(3)_ℓ and can be expressed in terms of the physical neutrino masses and the PMNS matrix.

Within this setup the four independent dimension‑six BNV operators of the SMEFT (QQQL, QQu e, u^c d^c ℓ, d^c d^c e) are systematically analyzed. For each operator the authors decompose the fermion bilinears under the full flavor group G_F = U(3)^5, identify the minimal set of spurion insertions needed to restore G_F invariance, and write down the leading flavor‑invariant structures. The key observation is that Υ_ν allows the construction of invariants that are suppressed not only by CKM elements (as in ordinary MFV) but also by factors of (Δm_ν / v)^2, where Δm_ν denotes the neutrino mass splittings. Consequently, in certain flavor configurations—particularly those where the BNV operator couples predominantly to third‑generation quarks and leptons—the effective proton‑decay amplitude can be reduced by many orders of magnitude. The authors estimate that the BNV scale Λ_B can be as low as a few TeV while still satisfying current proton‑lifetime limits, a dramatic relaxation compared with the generic 10^16 GeV bound.

The paper then turns to ultraviolet completions that generate the dimension‑six BNV operators at tree level. Four representative single‑particle mediators are discussed: (i) a scalar diquark S ∼ (3, 1, −1/3), (ii) a vector leptoquark V_μ ∼ (3, 1, 2/3), (iii) a color‑triplet fermion ψ ∼ (3, 2, 1/6), and (iv) mixed scalar‑leptoquark scenarios. For each case the authors write the renormalizable couplings to SM fermions, perform the matching onto the SMEFT operators, and relate the mediator mass M and coupling g to the effective scale Λ_B (typically Λ_B ≈ M / (g^2/16π^2) for loop‑induced scenarios). They point out that some UV completions also generate dimension‑5 or dimension‑7 operators, which can dominate in certain kinematic regimes, emphasizing the need to go beyond the leading EFT description when interpreting experimental data.

Beyond the extended MFV, the authors explore alternative flavor symmetries such as U(2) or a third‑generation‑only U(3) that preferentially couple new physics to the heavy families. In these reduced symmetry settings the suppression of BNV operators involving first‑generation quarks can be even stronger, while operators involving only third‑generation fields remain relatively unsuppressed. This opens a phenomenologically interesting window: proton decay constraints are weakened, but collider signatures involving top, bottom, and τ final states become the primary probes of BNV at the TeV scale.

In the concluding section the authors summarize that flavor symmetries—especially when augmented by the neutrino‑mass spurion—provide a natural mechanism to lower the BNV scale to experimentally accessible energies without conflicting with existing proton‑decay limits. They stress that upcoming experiments such as Hyper‑Kamiokande and DUNE will improve proton‑lifetime sensitivities by up to an order of magnitude, potentially testing the most optimistic flavor‑suppressed scenarios. Simultaneously, high‑energy colliders (LHC, future FCC) could directly produce the mediators identified in the UV completions, offering complementary discovery avenues. The work thus bridges EFT analyses, flavor model building, and concrete UV physics, delivering a comprehensive roadmap for future searches for baryon‑number violation.