2025/10/28 by Donini, Andrea, González, Marcela, Hirsch, Martin +1
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)
paper · doi:10.48550/arxiv.2510.24835
Lepton number violating meson decays, such as M1- → M2+ℓ1-ℓ2-, provide constraints on d=9 ΔL = 2 operators. RGE-improved bounds on the Wilson coefficients of these operators have been presented in the literature, taking into account perturbative 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 ⟨ M2 | \cal Oh | M1 ⟩. These diagrams, usually overlooked under the assumption that ⟨ M2 | \cal Oh | M1 ⟩ ∼ ⟨ M2 | Jq3 q4 | 0 ⟩ × ⟨ 0 |Jq1 q2 | M1 ⟩ ≫ ⟨ M2 | Jq3 q2 × Jq1 q4 | M1 ⟩, can give indeed a significant contribution to the matrix element. Including these connected diagrams is but the first step towards a full non-perturbative 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/Nc expansion of the QCD non-perturbative 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.