- Open Access
Implications of flavor symmetries for baryon number violation
Phys. Rev. D 113, 055021 – Published 12 March, 2026
DOI: https://doi.org/10.1103/dlq2-9yl8
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) standard model effective field theory (SMEFT) operators across several flavor-symmetry assumptions and analyze the resulting phenomenology. Interestingly, in certain flavor scenarios the nontrivial 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.
Physics Subject Headings (PhySH)
Article Text
References (103)
- G. D’Ambrosio, G. F. Giudice, G. Isidori, and A. Strumia, Minimal flavor violation: An effective field theory approach, Nucl. Phys. B645, 155 (2002).
- R. S. Chivukula and H. Georgi, Composite technicolor standard model, Phys. Lett. B 188, 99 (1987).
- V. Cirigliano, B. Grinstein, G. Isidori, and M. B. Wise, Minimal flavor violation in the lepton sector, Nucl. Phys. B728, 121 (2005).
- S. Davidson and F. Palorini, Various definitions of minimal flavour violation for leptons, Phys. Lett. B 642, 72 (2006).
- R. Alonso, G. Isidori, L. Merlo, L. A. Munoz, and E. Nardi, Minimal flavour violation extensions of the seesaw, J. High Energy Phys. 06 (2011) 037.
- M. B. Gavela, T. Hambye, D. Hernandez, and P. Hernandez, Minimal flavour seesaw models, J. High Energy Phys. 09 (2009) 038.
- P. Minkowski, at a rate of one out of muon decays?, Phys. Lett. 67B, 421 (1977).
- R. N. Mohapatra and G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation, Phys. Rev. D 23, 165 (1981).
- R. Foot, H. Lew, X. G. He, and G. C. Joshi, Seesaw neutrino masses induced by a triplet of leptons, Z. Phys. C 44, 441 (1989).
- S. Davidson and S. Descotes-Genon, Minimal flavour violation for leptoquarks, J. High Energy Phys. 11 (2010) 073.
- E. Nikolidakis and C. Smith, Minimal flavor violation, seesaw, and R-parity, Phys. Rev. D 77, 015021 (2008).
- C. Smith, Proton stability from a fourth family, Phys. Rev. D 85, 036005 (2012).
- A. Helset and A. Kobach, Baryon number, lepton number, and operator dimension in the SMEFT with flavor symmetries, Phys. Lett. B 800, 135132 (2020).
- S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
- F. Wilczek and A. Zee, Operator analysis of nucleon decay, Phys. Rev. Lett. 43, 1571 (1979).
- L. F. Abbott and M. B. Wise, The effective Hamiltonian for nucleon decay, Phys. Rev. D 22, 2208 (1980).
- S. Weinberg, Varieties of baryon and lepton nonconservation, Phys. Rev. D 22, 1694 (1980).
- A. Takenaka et al. (Super-Kamiokande Collaboration), Search for proton decay via and with an enlarged fiducial volume in Super-Kamiokande I-IV, Phys. Rev. D 102, 112011 (2020).
- K. Abe et al. (Super-Kamiokande Collaboration), Search for nucleon decay via and in Super-Kamiokande, Phys. Rev. Lett. 113, 121802 (2014).
- R. Matsumoto et al. (Super-Kamiokande Collaboration), Search for proton decay via in 0.37 megaton-years exposure of Super-Kamiokande, Phys. Rev. D 106, 072003 (2022).
- K. Abe et al. (Hyper-Kamiokande Collaboration), Hyper-Kamiokande design report, arXiv:1805.04163.
- B. Abi et al. (DUNE Collaboration), Deep underground neutrino experiment (DUNE), far detector technical design report, volume II: DUNE physics, arXiv:2002.03005.
- B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085.
- W. Buchmuller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B268, 621 (1986).
- A. B. Beneito, I, J. Gargalionis, J. Herrero-Garcia, A. Santamaria, and M. A. Schmidt, An EFT approach to baryon number violation: Lower limits on the new physics scale and correlations between nucleon decay modes, J. High Energy Phys. 07 (2024) 004.
- A. Hayrapetyan et al. (CMS Collaboration), Search for baryon number violation in top quark production and decay using proton-proton collisions at , Phys. Rev. Lett. 132, 241802 (2024).
- P. del Amo Sanchez et al. (BABAR Collaboration), Searches for the baryon- and lepton-number violating decays , , and , Phys. Rev. D 83, 091101 (2011).
- R. Aaij et al. (LHCb Collaboration), Search for the baryon- and lepton-number violating decays and , Phys. Rev. D 108, 012021 (2023).
- W.-S. Hou, M. Nagashima, and A. Soddu, Baryon number violation involving higher generations, Phys. Rev. D 72, 095001 (2005).
- M. Beneke, G. Finauri, and A. A. Petrov, Indirect constraints on third generation baryon number violation, J. High Energy Phys. 09 (2024) 090.
- A. Crivellin and M. Hoferichter, Rescattering effects in nucleon-to-meson form factors and application to tau-lepton-induced proton decay, Phys. Lett. B 845, 138169 (2023).
- H. Gisbert, A. Rodríguez-Sánchez, and L. Vale Silva, Constraints on baryon-number-violating top-quark operators in standard model effective field theory, Phys. Rev. D 112, 015026 (2025).
- J. Heeck and D. Watkins, Baryon number violation involving tau leptons, J. High Energy Phys. 07 (2024) 170.
- Z. Dong, G. Durieux, J.-M. Gerard, T. Han, and F. Maltoni, Baryon number violation at the LHC: The top option, Phys. Rev. D 85, 016006 (2012).
- W. J. Marciano, Tau physics: A theoretical perspective, Nucl. Phys. B, Proc. Suppl. 40, 3 (1995).
- M. Thomas Arun, S. M, and R. Pal, RG evolution and effect of intermediate new-physics on four-fermion operators, arXiv:2511.06106.
- R. Barbieri, G. Isidori, J. Jones-Perez, P. Lodone, and D. M. Straub, and minimal flavour violation in supersymmetry, Eur. Phys. J. C 71, 1725 (2011).
- G. Isidori and D. M. Straub, Minimal flavour violation and beyond, Eur. Phys. J. C 72, 2103 (2012).
- R. Barbieri, D. Buttazzo, F. Sala, and D. M. Straub, Flavour physics from an approximate symmetry, J. High Energy Phys. 07 (2012) 181.
- L. Allwicher, C. Cornella, G. Isidori, and B. A. Stefanek, New physics in the third generation. A comprehensive SMEFT analysis and future prospects, J. High Energy Phys. 03 (2024) 049.
- A. Greljo, A. Palavrić, and A. E. Thomsen, Adding flavor to the SMEFT, J. High Energy Phys. 10 (2022) 010.
- A. Greljo and A. Palavrić, Leading directions in the SMEFT, J. High Energy Phys. 09 (2023) 009.
- A. Greljo, A. Palavrić, and A. Smolkovič, Leading directions in the SMEFT: Renormalization effects, Phys. Rev. D 109, 075033 (2024).
- I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, NuFit-6.0: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 12 (2024) 216.
- R. Alonso, H.-M. Chang, E. E. Jenkins, A. V. Manohar, and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734, 302 (2014).
- A. B. I Beneito, J. Gargalionis, J. Herrero-Garcia, and M. A. Schmidt, Squeezing proton decay and neutrino masses: Upper bounds on standard model extensions, J. High Energy Phys. 10 (2025) 083.
- I. Dorsner, S. Fajfer, and N. Kosnik, Heavy and light scalar leptoquarks in proton decay, Phys. Rev. D 86, 015013 (2012).
- P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rep. 441, 191 (2007).
- E. E. Jenkins, A. V. Manohar, and P. Stoffer, Low-energy effective field theory below the electroweak scale: Operators and matching, J. High Energy Phys. 03 (2018) 016.
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- M. Claudson, M. B. Wise, and L. J. Hall, Chiral Lagrangian for deep mine physics, Nucl. Phys. B195, 297 (1982).
- J.-S. Yoo, Y. Aoki, P. Boyle, T. Izubuchi, A. Soni, and S. Syritsyn, Proton decay matrix elements on the lattice at physical pion mass, Phys. Rev. D 105, 074501 (2022).
- Y. Aoki, T. Izubuchi, E. Shintani, and A. Soni, Improved lattice computation of proton decay matrix elements, Phys. Rev. D 96, 014506 (2017).
- Y. Aoki, P. Boyle, P. Cooney, L. Del Debbio, R. Kenway, C. M. Maynard et al. (RBC-UKQCD Collaboration), Proton lifetime bounds from chirally symmetric lattice QCD, Phys. Rev. D 78, 054505 (2008).
- G. S. Bali, S. Collins, W. Söldner, and S. Weishäupl (RQCD Collaboration), Leading order mesonic and baryonic SU(3) low energy constants from lattice QCD, Phys. Rev. D 105, 054516 (2022).
- A. Celis, J. Fuentes-Martin, A. Vicente, and J. Virto, dsixtools: The standard model effective field theory toolkit, Eur. Phys. J. C 77, 405 (2017).
- J. Fuentes-Martin, P. Ruiz-Femenia, A. Vicente, and J. Virto, dsixtools 2.0: The effective field theory toolkit, Eur. Phys. J. C 81, 167 (2021).
- M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. B 94, 61 (1980).
- T. P. Cheng and L.-F. Li, Neutrino masses, mixings and oscillations in models of electroweak interactions, Phys. Rev. D 22, 2860 (1980).
- D. Wyler and L. Wolfenstein, Massless neutrinos in left-right symmetric models, Nucl. Phys. B218, 205 (1983).
- Recent Developments in Gauge Theories. Proceedings, Nato Advanced Study Institute, Cargese, France, 1979, edited by G. ’t Hooft, C. Itzykson, A. Jaffe, H. Lehmann, P. K. Mitter, I. M. Singer et al. (1980), Vol. 59, 10.1007/978-1-4684-7571-5.
- J. C. Helo, M. Hirsch, and T. Ota, Proton decay at one loop, Phys. Rev. D 99, 095021 (2019).
- J. Gargalionis, J. Herrero-García, and M. A. Schmidt, Model-independent estimates for loop-induced baryon-number-violating nucleon decays, J. High Energy Phys. 06 (2024) 182.
- J. de Blas, J. C. Criado, M. Perez-Victoria, and J. Santiago, Effective description of general extensions of the standard model: The complete tree-level dictionary, J. High Energy Phys. 03 (2018) 109.
- I. Doršner, S. Fajfer, A. Greljo, J. F. Kamenik, and N. Košnik, Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rep. 641, 1 (2016).
- A. Palavrić, Discrete leptonic flavor symmetries: UV mediators and phenomenology, Phys. Rev. D 110, 115025 (2024).
- A. Moreno-Sánchez and A. Palavrić, Leptonic flavor from modular : UV mediators and SMEFT realizations, Phys. Rev. D 112, 075002 (2025).
- R. Bartocci, A. Biekötter, and T. Hurth, A global analysis of the SMEFT under the minimal MFV assumption, J. High Energy Phys. 05 (2024) 074.
- L. Allwicher, M. McCullough, and S. Renner, New physics at Tera-Z: Precision renormalised, J. High Energy Phys. 02 (2025) 164.
- J. ter Hoeve, L. Mantani, J. Rojo, A. N. Rossia, and E. Vryonidou, Connecting scales: RGE effects in the SMEFT at the LHC and future colliders, J. High Energy Phys. 06 (2025) 125.
- M. Papucci, J. T. Ruderman, and A. Weiler, Natural SUSY endures, J. High Energy Phys. 09 (2012) 035.
- G. Larsen, Y. Nomura, and H. L. L. Roberts, Supersymmetry with light stops, J. High Energy Phys. 06 (2012) 032.
- R. Barbieri, D. Buttazzo, F. Sala, D. M. Straub, and A. Tesi, A 125 GeV composite Higgs boson versus flavour and electroweak precision tests, J. High Energy Phys. 05 (2013) 069.
- O. Matsedonskyi, On flavour and naturalness of composite Higgs models, J. High Energy Phys. 02 (2015) 154.
- G. Panico and A. Pomarol, Flavor hierarchies from dynamical scales, J. High Energy Phys. 07 (2016) 097.
- L. Allwicher, G. Isidori, and A. E. Thomsen, Stability of the Higgs sector in a flavor-inspired multi-scale model, J. High Energy Phys. 01 (2021) 191.
- J. Fuentes-Martín and P. Stangl, Third-family quark-lepton unification with a fundamental composite Higgs, Phys. Lett. B 811, 135953 (2020).
- J. Fuentes-Martin, G. Isidori, J. M. Lizana, N. Selimovic, and B. A. Stefanek, Flavor hierarchies, flavor anomalies, and Higgs mass from a warped extra dimension, Phys. Lett. B 834, 137382 (2022).
- J. Fuentes-Martín and J. M. Lizana, Deconstructing flavor anomalously, J. High Energy Phys. 07 (2024) 117.
- A. Greljo and B. A. Stefanek, Third family quark–lepton unification at the TeV scale, Phys. Lett. B 782, 131 (2018).
- R. Barbieri and G. Isidori, Minimal flavour deconstruction, J. High Energy Phys. 05 (2024) 033.
- R. Barbieri, Phenomenology of minimal flavour deconstruction at the lowest new scale, arXiv:2409.08657.
- M. Bordone, C. Cornella, J. Fuentes-Martin, and G. Isidori, A three-site gauge model for flavor hierarchies and flavor anomalies, Phys. Lett. B 779, 317 (2018).
- J. Davighi and B. A. Stefanek, Deconstructed hypercharge: A natural model of flavour, J. High Energy Phys. 11 (2023) 100.
- J. Davighi and G. Isidori, Non-universal gauge interactions addressing the inescapable link between Higgs and flavour, J. High Energy Phys. 07 (2023) 147.
- S. Covone, J. Davighi, G. Isidori, and M. Pesut, Flavour deconstructing the composite Higgs, J. High Energy Phys. 01 (2025) 041.
- J. M. Lizana, A common origin of the Higgs boson and the flavor hierarchies, J. High Energy Phys. 05 (2025) 176.
- M. Fernández Navarro and S. F. King, Tri-hypercharge: A separate gauged weak hypercharge for each fermion family as the origin of flavour, J. High Energy Phys. 08 (2023) 020.
- M. Fernández Navarro, S. F. King, and A. Vicente, Minimal complete tri-hypercharge theories of flavour, J. High Energy Phys. 07 (2024) 147.
- M. Fernández Navarro, S. F. King, and A. Vicente, Natural neutrino mass hierarchy in a theory of gauge flavour deconstruction, J. High Energy Phys. 02 (2026) 046.
- G. Isidori, P. Paradisi, A. Sainaghi, and N. Selimovic, Anarchic neutrinos from flavor deconstruction: Phenomenology of the lepton sector, J. High Energy Phys. 02 (2026) 146.
- A. Greljo, A. Palavrić, and B. A. Stefanek, Minimal flavor protection for TeV-scale new physics, arXiv:2512.04159.
- R. M. Fonseca, Thesym2int program: Going from symmetries to interactions, J. Phys. Conf. Ser. 873, 012045 (2017).
- R. M. Fonseca, Enumerating the operators of an effective field theory, Phys. Rev. D 101, 035040 (2020).
- A. M. Baldini et al. (MEG Collaboration), Search for the lepton flavour violating decay with the full dataset of the MEG experiment, Eur. Phys. J. C 76, 434 (2016).
- A. M. Baldini et al. (MEG II Collaboration), The design of the MEG II experiment, Eur. Phys. J. C 78, 380 (2018).
- U. Bellgardt et al. (SINDRUM Collaboration), Search for the decay , Nucl. Phys. B299, 1 (1988).
- A. Blondel et al., Research proposal for an experiment to search for the decay , arXiv:1301.6113.
- M. Raidal and A. Santamaria, Muon electron conversion in nuclei versus : An effective field theory point of view, Phys. Lett. B 421, 250 (1998).
- L. Calibbi, X. Marcano, and J. Roy, lepton flavour violation as a probe for new physics at future colliders, Eur. Phys. J. C 81, 1054 (2021).
- W. H. Bertl et al. (SINDRUM II Collaboration), A search for muon to electron conversion in muonic gold, Eur. Phys. J. C 47, 337 (2006).
- L. Bartoszek et al. (Mu2e Collaboration), Mu2e technical design report, arXiv:1501.05241.
- Y. Fujii (COMET Collaboration), A search for a muon to electron conversion in COMET, J. Instrum. 18, C10010 (2023).