D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules
Abstract We suggest a new method to analyse the rare D (s) → Pℓ + 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 cancella...
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| Format: | Article |
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SpringerOpen
2025-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2025)026 |
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| author | Anshika Bansal Alexander Khodjamirian Thomas Mannel |
| author_facet | Anshika Bansal Alexander Khodjamirian Thomas Mannel |
| author_sort | Anshika Bansal |
| collection | DOAJ |
| description | Abstract We suggest a new method to analyse the rare D (s) → Pℓ + 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, −q 2 ≫ Λ QCD 2 $$ {\Lambda}_{\textrm{QCD}}^2 $$ , 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 + → 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 → uℓ + ℓ − 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 an 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 → Pℓ + ℓ − decays and apply our method to the Cabibbo-favoured modes D s + → π + ℓ + ℓ − $$ {D}_s^{+}\to {\pi}^{+}{\ell}^{+}{\ell}^{-} $$ and D 0 → K ¯ 0 ℓ + ℓ − $$ {D}^0\to {\overline{K}}^0{\ell}^{+}{\ell}^{-} $$ which proceed via the same weak annihilation mechanism. |
| format | Article |
| id | doaj-art-d4a337fad06447d89bb9b44e4d6d9483 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d4a337fad06447d89bb9b44e4d6d94832025-08-20T03:42:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025815910.1007/JHEP08(2025)026D → Pℓ + ℓ − decays assisted by QCD light-cone sum rulesAnshika Bansal0Alexander Khodjamirian1Thomas Mannel2Center for Particle Physics Siegen (CPPS), Theoretische Physik 1, Universität SiegenCenter for Particle Physics Siegen (CPPS), Theoretische Physik 1, Universität SiegenCenter for Particle Physics Siegen (CPPS), Theoretische Physik 1, Universität SiegenAbstract We suggest a new method to analyse the rare D (s) → Pℓ + 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, −q 2 ≫ Λ QCD 2 $$ {\Lambda}_{\textrm{QCD}}^2 $$ , 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 + → 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 → uℓ + ℓ − 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 an 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 → Pℓ + ℓ − decays and apply our method to the Cabibbo-favoured modes D s + → π + ℓ + ℓ − $$ {D}_s^{+}\to {\pi}^{+}{\ell}^{+}{\ell}^{-} $$ and D 0 → K ¯ 0 ℓ + ℓ − $$ {D}^0\to {\overline{K}}^0{\ell}^{+}{\ell}^{-} $$ which proceed via the same weak annihilation mechanism.https://doi.org/10.1007/JHEP08(2025)026Charm Flavour ViolationSemi-Leptonic Decays |
| spellingShingle | Anshika Bansal Alexander Khodjamirian Thomas Mannel D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules Journal of High Energy Physics Charm Flavour Violation Semi-Leptonic Decays |
| title | D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules |
| title_full | D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules |
| title_fullStr | D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules |
| title_full_unstemmed | D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules |
| title_short | D → Pℓ + ℓ − decays assisted by QCD light-cone sum rules |
| title_sort | d pl l decays assisted by qcd light cone sum rules |
| topic | Charm Flavour Violation Semi-Leptonic Decays |
| url | https://doi.org/10.1007/JHEP08(2025)026 |
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