D→ P ℓ⁺ℓ^- decays assisted by QCD light-cone sum rules

2025/05/27 by Anshika Bansal, Bansal, Anshika, Alexander Khodjamirian +3
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2505.21369

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We suggest a new method to analyse the rare D_(s)→ P ℓ⁺ℓ^- decays (P=π,K), combining QCD light-cone sum rules (LCSR) with hadronic dispersion relations. As our main study case, we consider the D⁺→π⁺ℓ⁺ℓ^- mode which attracts much of interest from the point of view of GIM cancellation and potential new sources of the FCNC c→ u transitions. The hadronic amplitude of this decay is dominated by the combination of weak annihilation with the emission of a virtual photon. This D⁺→ π⁺γ^* amplitude is calculated at spacelike photon virtualities, -q² ≫ Λ_QCD², using LCSR with pion distribution amplitudes. The LCSR results are then fitted to the hadronic dispersion relation in the variable q². The fit allows us to determine relative phases of the ρ-,ω- and ϕ-meson terms and to estimate the contributions of heavier hadronic states. The latter are parameterized in two different ways: first, with a z-expansion and second, using a model with excited vector-meson resonances. The resulting D⁺→π⁺ℓ⁺ℓ^- width obtained from the LCSR-assisted dispersion relation is not much smaller than the current upper bound measured by LHCb collaboration. In comparison with our result for the dominant D⁺→ π⁺γ^* transition, the contribution induced by the short distance c→ u ℓ⁺ℓ^- quark transition generated by the effective O₉ operator in Standard Model turns out to be practically invisible. To detect its effect, one readily needs a enhancement of the coefficient C₉ from non-standard effects by many orders of magnitude. We also establish new U-spin symmetry relations between the amplitudes of D→ P ℓ⁺ℓ^- decays and apply our method to the Cabibbo-favoured modes D⁺_s→π⁺ℓ⁺ℓ^- and D⁰→K⁰ℓ⁺ℓ^- which proceed via the same weak annihilation mechanism.

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