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Leading large $N_{c}$ contributions to lepton number violating meson decays

Andrea Donini^1,*, Marcela González ^2,†, Martin Hirsch^1,‡, and Nicolás A. Neill ^3,§

¹Instituto de Física Corpuscular—CSIC—Universitat de València, Parc Científic-UV, c/Catedrático José Beltrán, 2, E-46980 Paterna (València), Spain
²Instituto de Física y Astronomía, Universidad de Valparaíso, Avenida Gran Bretaña 1111, Valparaíso, Chile
³Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, 8580745 Santiago, Chile

^*Contact author: donini@ific.uv.es
^†Contact author: marcela.gonzalezpi@uv.cl
^‡Contact author: mahirsch@ific.uv.es
^§Contact author: nclsneill@gmail.com

Phys. Rev. D 113, 075004 – Published 3 April, 2026

DOI: https://doi.org/10.1103/pwtl-6xkv

Abstract

Lepton number violating meson decays, such as $M_{1}^{-} \to M_{2}^{+} ℓ_{1}^{-} ℓ_{2}^{-}$ , provide constraints on $d = 9$ $Δ L = 2$ operators. Renormalization group equation (RGE)-improved bounds on the Wilson coefficients of these operators have been presented in the literature, taking into account perturbative quantum chromodynamics (QCD) one-loop corrections and the corresponding operator mixing. Here, we present for the first time the contribution of connected diagrams to the hadronic matrix elements $⟨ M_{2} | O_{h} | M_{1} ⟩$ . These diagrams, usually overlooked under the assumption that $⟨ M_{2} | O_{h} | M_{1} ⟩ \sim ⟨ M_{2} | J_{q_{3} q_{4}} | 0 ⟩ \times ⟨ 0 | J_{q_{1} q_{2}} | M_{1} ⟩ ≫ ⟨ M_{2} | J_{q_{3} q_{2}} \times J_{q_{1} q_{4}} | M_{1} ⟩$ , can give indeed a significant contribution to the matrix element. Including these connected diagrams is but the first step toward a full nonperturbative computation of the long-range QCD effects in these operators, that should be performed using lattice field theory techniques. However, connected diagrams represent the leading order in the $1 / N_{c}$ expansion of the QCD nonperturbative effects and thus our work can be understood as a realistic, first approximation to a complete calculation of the long-range part of the matrix elements.

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Phys. Rev. D 113, 075004– Published 3 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 12 November 2025
Accepted 27 February 2026

DOI: https://doi.org/10.1103/pwtl-6xkv

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Leading large $N_{c}$ contributions to lepton number violating meson decays

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Leading large Nc contributions to lepton number violating meson decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (78)

Leading large $N_{c}$ contributions to lepton number violating meson decays