Study of form factors and branching ratios for $D\rightarrow S,Al\bar{ν_{l}}$ with light-cone sum rules
Abstract: We systematically study the semileptonic decay process of D → S , Al νl (l = e, µ) by light-cone sum rules (LCSR) with chiral currents, calculate the form factors containing only the contribution of the leading twist light-cone distribution amplitudes (LCDAs). For scalar mesons a 0 (980) and a 0 (1450), we take them as q q states. For axial-vector meson, we study a 1 (1260)(1 3 p 1 ) and b 1 (1235)(1 1 p 1 ). Based on the results of these form factors, we further present the branching ratios of these semilepto… Show more
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 3 publications
References 30 publications
In the paper, we investigate the moments $$\langle \xi _{2;a_1}^{\Vert ;n}\rangle $$ ⟨ ξ 2 ; a 1 ‖ ; n ⟩ of the axial-vector $$a_1(1260)$$ a 1 ( 1260 ) -meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale $$\mu _0=1~{\mathrm{GeV}}$$ μ 0 = 1 GeV are $$\langle \xi _{2;a_1}^{\Vert ;2}\rangle |_{\mu _0} = 0.223 \pm 0.029$$ ⟨ ξ 2 ; a 1 ‖ ; 2 ⟩ | μ 0 = 0.223 ± 0.029 , $$\langle \xi _{2;a_1}^{\Vert ;4}\rangle |_{\mu _0} = 0.098 \pm 0.008$$ ⟨ ξ 2 ; a 1 ‖ ; 4 ⟩ | μ 0 = 0.098 ± 0.008 , $$\langle \xi _{2;a_1}^{\Vert ;6}\rangle |_{\mu _0} = 0.056 \pm 0.006$$ ⟨ ξ 2 ; a 1 ‖ ; 6 ⟩ | μ 0 = 0.056 ± 0.006 , $$\langle \xi _{2;a_1}^{\Vert ;8}\rangle |_{\mu _0} = 0.039 \pm 0.004$$ ⟨ ξ 2 ; a 1 ‖ ; 8 ⟩ | μ 0 = 0.039 ± 0.004 and $$\langle \xi _{2;a_1}^{\Vert ;10}\rangle |_{\mu _0} = 0.028 \pm 0.003$$ ⟨ ξ 2 ; a 1 ‖ ; 10 ⟩ | μ 0 = 0.028 ± 0.003 , respectively. We then construct a light-cone harmonic oscillator model for $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude $$\phi _{2;a_1}^{\Vert }(x,\mu )$$ ϕ 2 ; a 1 ‖ ( x , μ ) , whose model parameters are fitted by using the least squares method. As an application of $$\phi _{2;a_1}^{\Vert }(x,\mu )$$ ϕ 2 ; a 1 ‖ ( x , μ ) , we calculate the transition form factors (TFFs) of $$D\rightarrow a_1(1260)$$ D → a 1 ( 1260 ) in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point ($$q^2=0$$ q 2 = 0 ), we obtain $$ A(0) = 0.130_{ - 0.013}^{ + 0.015}$$ A ( 0 ) = 0 . 130 - 0.013 + 0.015 , $$V_1(0) = 1.898_{-0.121}^{+0.128}$$ V 1 ( 0 ) = 1 . 898 - 0.121 + 0.128 , $$V_2(0) = 0.228_{-0.021}^{ + 0.020}$$ V 2 ( 0 ) = 0 . 228 - 0.021 + 0.020 , and $$V_0(0) = 0.217_{ - 0.025}^{ + 0.023}$$ V 0 ( 0 ) = 0 . 217 - 0.025 + 0.023 . By applying the extrapolated TFFs to the semi-leptonic decay $$D^{0(+)} \rightarrow a_1^{-(0)}(1260)\ell ^+\nu _\ell $$ D 0 ( + ) → a 1 - ( 0 ) ( 1260 ) ℓ + ν ℓ , we obtain $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) e^+\nu _e) = (5.261_{-0.639}^{+0.745}) \times 10^{-5}$$ B ( D 0 → a 1 - ( 1260 ) e + ν e ) = ( 5 . 261 - 0.639 + 0.745 ) × 10 - 5 , $${\mathcal {B}}(D^+\rightarrow a_1^0(1260) e^+\nu _e) = (6.673_{-0.811}^{+0.947}) \times 10^{-5}$$ B ( D + → a 1 0 ( 1260 ) e + ν e ) = ( 6 . 673 - 0.811 + 0.947 ) × 10 - 5 , $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) \mu ^+ \nu _\mu )=(4.732_{-0.590}^{+0.685}) \times 10^{-5}$$ B ( D 0 → a 1 - ( 1260 ) μ + ν μ ) = ( 4 . 732 - 0.590 + 0.685 ) × 10 - 5 , $${\mathcal {B}}(D^+ \rightarrow a_1^0(1260) \mu ^+ \nu _\mu )=(6.002_{-0.748}^{+0.796}) \times 10^{-5}$$ B ( D + → a 1 0 ( 1260 ) μ + ν μ ) = ( 6 . 002 - 0.748 + 0.796 ) × 10 - 5 .
In the paper, we investigate the moments $$\langle \xi _{2;a_1}^{\Vert ;n}\rangle $$ ⟨ ξ 2 ; a 1 ‖ ; n ⟩ of the axial-vector $$a_1(1260)$$ a 1 ( 1260 ) -meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale $$\mu _0=1~{\mathrm{GeV}}$$ μ 0 = 1 GeV are $$\langle \xi _{2;a_1}^{\Vert ;2}\rangle |_{\mu _0} = 0.223 \pm 0.029$$ ⟨ ξ 2 ; a 1 ‖ ; 2 ⟩ | μ 0 = 0.223 ± 0.029 , $$\langle \xi _{2;a_1}^{\Vert ;4}\rangle |_{\mu _0} = 0.098 \pm 0.008$$ ⟨ ξ 2 ; a 1 ‖ ; 4 ⟩ | μ 0 = 0.098 ± 0.008 , $$\langle \xi _{2;a_1}^{\Vert ;6}\rangle |_{\mu _0} = 0.056 \pm 0.006$$ ⟨ ξ 2 ; a 1 ‖ ; 6 ⟩ | μ 0 = 0.056 ± 0.006 , $$\langle \xi _{2;a_1}^{\Vert ;8}\rangle |_{\mu _0} = 0.039 \pm 0.004$$ ⟨ ξ 2 ; a 1 ‖ ; 8 ⟩ | μ 0 = 0.039 ± 0.004 and $$\langle \xi _{2;a_1}^{\Vert ;10}\rangle |_{\mu _0} = 0.028 \pm 0.003$$ ⟨ ξ 2 ; a 1 ‖ ; 10 ⟩ | μ 0 = 0.028 ± 0.003 , respectively. We then construct a light-cone harmonic oscillator model for $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude $$\phi _{2;a_1}^{\Vert }(x,\mu )$$ ϕ 2 ; a 1 ‖ ( x , μ ) , whose model parameters are fitted by using the least squares method. As an application of $$\phi _{2;a_1}^{\Vert }(x,\mu )$$ ϕ 2 ; a 1 ‖ ( x , μ ) , we calculate the transition form factors (TFFs) of $$D\rightarrow a_1(1260)$$ D → a 1 ( 1260 ) in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point ($$q^2=0$$ q 2 = 0 ), we obtain $$ A(0) = 0.130_{ - 0.013}^{ + 0.015}$$ A ( 0 ) = 0 . 130 - 0.013 + 0.015 , $$V_1(0) = 1.898_{-0.121}^{+0.128}$$ V 1 ( 0 ) = 1 . 898 - 0.121 + 0.128 , $$V_2(0) = 0.228_{-0.021}^{ + 0.020}$$ V 2 ( 0 ) = 0 . 228 - 0.021 + 0.020 , and $$V_0(0) = 0.217_{ - 0.025}^{ + 0.023}$$ V 0 ( 0 ) = 0 . 217 - 0.025 + 0.023 . By applying the extrapolated TFFs to the semi-leptonic decay $$D^{0(+)} \rightarrow a_1^{-(0)}(1260)\ell ^+\nu _\ell $$ D 0 ( + ) → a 1 - ( 0 ) ( 1260 ) ℓ + ν ℓ , we obtain $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) e^+\nu _e) = (5.261_{-0.639}^{+0.745}) \times 10^{-5}$$ B ( D 0 → a 1 - ( 1260 ) e + ν e ) = ( 5 . 261 - 0.639 + 0.745 ) × 10 - 5 , $${\mathcal {B}}(D^+\rightarrow a_1^0(1260) e^+\nu _e) = (6.673_{-0.811}^{+0.947}) \times 10^{-5}$$ B ( D + → a 1 0 ( 1260 ) e + ν e ) = ( 6 . 673 - 0.811 + 0.947 ) × 10 - 5 , $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) \mu ^+ \nu _\mu )=(4.732_{-0.590}^{+0.685}) \times 10^{-5}$$ B ( D 0 → a 1 - ( 1260 ) μ + ν μ ) = ( 4 . 732 - 0.590 + 0.685 ) × 10 - 5 , $${\mathcal {B}}(D^+ \rightarrow a_1^0(1260) \mu ^+ \nu _\mu )=(6.002_{-0.748}^{+0.796}) \times 10^{-5}$$ B ( D + → a 1 0 ( 1260 ) μ + ν μ ) = ( 6 . 002 - 0.748 + 0.796 ) × 10 - 5 .
Hadronic three-body D decays mediated by scalar resonances
We study the quasi-two-body D → SP decays and the three-body D decays proceeding through intermediate scalar resonances, where S and P denote scalar and pseudoscalar mesons, respectively. Our main results are: (i) Certain external and internal W -emission diagrams with the emitted meson being a scalar meson are naïvely expected to vanish, but they actually receive contributions from vertex and hard spectator-scattering corrections beyond the factorization approximation. (ii) For light scalars with masses below or close to 1 GeV, it is more sensible to study three-body decays directly and compare with experiment as the two-body branching fractions are either unavailable or subject to large finite-width effects of the scalar meson. (iii) We consider the two-quark (scheme I) and four-quark (scheme II) descriptions of the light scalar mesons, and find the latter generally in better agreement with experiment. This is in line with recent BESIII measurements of semileptonic charm decays that prefer the tetraquark description of light scalars produced in charmed meson decays. (iv) The topological amplitude approach fails here as the D → SP decay branching fractions cannot be reliably inferred from the measurements of three-body decays, mainly because the decay rates cannot be factorized into the topological amplitude squared and the phase space factor. (v) The predicted rates for D 0 → f 0 P, a 0 P are generally smaller than experimental data by one order of magnitude, presumably implying the significance of W -exchange amplitudes. (vi) The W -annihilation amplitude is found to be very sizable in the SP sector with |A/T | SP ∼ 1/2, contrary to its suppression in the P P sector with |A/T | P P ∼ 0.18. (vii) Finite-width effects are very important for the very broad σ/f 0 (500) and κ/K * 0 (700) mesons. The experimental branching fractions B(D + → σπ + ) and B(D + → κ0 π + ) are thus corrected to be (3.8 ± 0.3) × 10 −3 and (6.7 +5.6 −4.5 )%, respectively.
Chiral dynamics and S-wave contributions in $\bar B^0/D^0 \to π^{\pm}η l^{\mp} ν$ decays
In this work, we analyze the semi-leptonic decays B0 /D 0 → (a 0 (980) ± → π ± η)l ∓ ν within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the a 0 (980), we use a scalar form factor to describe the final-state interaction between the πη mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the D 0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the B0 decay can be tested in future experiments.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
