$D\to P \ell^+\ell^-$ decays assisted by QCD light-cone sum rules

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Autori principali: Bansal, Anshika, Khodjamirian, Alexander, Mannel, Thomas
Natura: Preprint
Pubblicazione: 2025
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author Bansal, Anshika
Khodjamirian, Alexander
Mannel, Thomas
author_facet Bansal, Anshika
Khodjamirian, Alexander
Mannel, Thomas
contents We suggest a new method to analyse the rare $D_{(s)}\to P \ell^+\ell^-$ decays ($P=π,K$), combining QCD light-cone sum rules (LCSR) with hadronic dispersion relations. As our main study case, we consider the $D^+\toπ^+\ell^+\ell^-$ mode which attracts much of interest from the point of view of GIM cancellation and potential new sources of the FCNC $c\to u$ transitions. The hadronic amplitude of this decay is dominated by the combination of weak annihilation with the emission of a virtual photon. This $D^+\to π^+γ^*$ amplitude is calculated at spacelike photon virtualities, $-q^2 \gg Λ_{QCD}^2$, using LCSR with pion distribution amplitudes. The LCSR results are then fitted to the hadronic dispersion relation in the variable $q^2$. 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 $D^+\toπ^+\ell^+\ell^-$ 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 $D^+\to π^+γ^*$ transition, the contribution induced by the short distance $c\to u \ell^+\ell^-$ quark transition generated by the effective $O_9$ operator in Standard Model turns out to be practically invisible. To detect its effect, one readily needs a enhancement of the coefficient $C_9$ from non-standard effects by many orders of magnitude. We also establish new $U$-spin symmetry relations between the amplitudes of $D\to P \ell^+\ell^-$ decays and apply our method to the Cabibbo-favoured modes $D^+_s\toπ^+\ell^+\ell^-$ and $D^0\to\bar{K}^0\ell^+\ell^-$ which proceed via the same weak annihilation mechanism.
format Preprint
id arxiv_https___arxiv_org_abs_2505_21369
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle $D\to P \ell^+\ell^-$ decays assisted by QCD light-cone sum rules
Bansal, Anshika
Khodjamirian, Alexander
Mannel, Thomas
High Energy Physics - Phenomenology
High Energy Physics - Experiment
We suggest a new method to analyse the rare $D_{(s)}\to P \ell^+\ell^-$ decays ($P=π,K$), combining QCD light-cone sum rules (LCSR) with hadronic dispersion relations. As our main study case, we consider the $D^+\toπ^+\ell^+\ell^-$ mode which attracts much of interest from the point of view of GIM cancellation and potential new sources of the FCNC $c\to u$ transitions. The hadronic amplitude of this decay is dominated by the combination of weak annihilation with the emission of a virtual photon. This $D^+\to π^+γ^*$ amplitude is calculated at spacelike photon virtualities, $-q^2 \gg Λ_{QCD}^2$, using LCSR with pion distribution amplitudes. The LCSR results are then fitted to the hadronic dispersion relation in the variable $q^2$. 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 $D^+\toπ^+\ell^+\ell^-$ 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 $D^+\to π^+γ^*$ transition, the contribution induced by the short distance $c\to u \ell^+\ell^-$ quark transition generated by the effective $O_9$ operator in Standard Model turns out to be practically invisible. To detect its effect, one readily needs a enhancement of the coefficient $C_9$ from non-standard effects by many orders of magnitude. We also establish new $U$-spin symmetry relations between the amplitudes of $D\to P \ell^+\ell^-$ decays and apply our method to the Cabibbo-favoured modes $D^+_s\toπ^+\ell^+\ell^-$ and $D^0\to\bar{K}^0\ell^+\ell^-$ which proceed via the same weak annihilation mechanism.
title $D\to P \ell^+\ell^-$ decays assisted by QCD light-cone sum rules
topic High Energy Physics - Phenomenology
High Energy Physics - Experiment
url https://arxiv.org/abs/2505.21369