$$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes
Abstract 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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-10555-y |
| _version_ | 1828774930952486912 |
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| author | Dan-Dan Hu Hai-Bing Fu Tao Zhong Zai-Hui Wu Xing-Gang Wu |
| author_facet | Dan-Dan Hu Hai-Bing Fu Tao Zhong Zai-Hui Wu Xing-Gang Wu |
| author_sort | Dan-Dan Hu |
| collection | DOAJ |
| description | Abstract 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 . |
| first_indexed | 2024-12-11T15:30:03Z |
| format | Article |
| id | doaj.art-4188cf546196424e8b1bc9a1640a64dc |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-12-11T15:30:03Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-4188cf546196424e8b1bc9a1640a64dc2022-12-22T01:00:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-07-0182711310.1140/epjc/s10052-022-10555-y$$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processesDan-Dan Hu0Hai-Bing Fu1Tao Zhong2Zai-Hui Wu3Xing-Gang Wu4Department of Physics, Guizhou Minzu UniversityDepartment of Physics, Guizhou Minzu UniversityDepartment of Physics, Guizhou Minzu UniversityDepartment of Physics, Guizhou Minzu UniversityDepartment of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing UniversityAbstract 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 .https://doi.org/10.1140/epjc/s10052-022-10555-y |
| spellingShingle | Dan-Dan Hu Hai-Bing Fu Tao Zhong Zai-Hui Wu Xing-Gang Wu $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes European Physical Journal C: Particles and Fields |
| title | $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes |
| title_full | $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes |
| title_fullStr | $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes |
| title_full_unstemmed | $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes |
| title_short | $$a_1(1260)$$ a 1 ( 1260 ) -meson longitudinal twist-2 distribution amplitude and the $$D\rightarrow a_1(1260)\ell ^+\nu _\ell $$ D → a 1 ( 1260 ) ℓ + ν ℓ decay processes |
| title_sort | a 1 1260 a 1 1260 meson longitudinal twist 2 distribution amplitude and the d rightarrow a 1 1260 ell nu ell d a 1 1260 l ν l decay processes |
| url | https://doi.org/10.1140/epjc/s10052-022-10555-y |
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