Longitudinal leading-twist distribution amplitude of the $^1P_1$-state $b_1(1235)$ meson and its implications on $B\to b_1(1235)\ell^+ν_\ell$ decays
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2025
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| _version_ | 1866917972689289216 |
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| author | Zeng, Long Wu, Xing-Gang Hu, Dan-Dan Fu, Hai-Bing Zhong, Tao |
| author_facet | Zeng, Long Wu, Xing-Gang Hu, Dan-Dan Fu, Hai-Bing Zhong, Tao |
| contents | In the paper, we derive the $ξ$-moments $\langleξ_{2;b_1}^{n;\|}\rangle$ of the longitudinal leading-twist distribution amplitude $ϕ_{2;b_1}^{\|}$ for $^1P_1$-state $b_1(1235)$-meson by using the QCD sum rules under the background field theory. Considering the contributions from the vacuum condensates up to dimension-six, its first two non-zero $ξ$-moments at the scale 1 GeV are $\langleξ_{2;b_1}^{1;\|}\rangle= -0.647^{+0.118}_{-0.113}$ and $\langleξ_{2;b_1}^{3;\|}\rangle = -0.328^{+0.055}_{-0.052}$, respectively. Using those moments, we then fix the Gegenbauer expansion series of $ϕ_{2;b_1}^{\|}$ and apply it to calculate $B\to b_1(1235)$ transition form factors (TFFs) that are derived by using the QCD light-cone sum rules. Those TFFs are then extrapolated to the physically allowable $q^2$-range via the simplified series expansion. As for the branching fractions, we obtain ${\cal B}(\bar B^0 \to b_1^+(1235)e^- \barν_e) = 2.179^{+0.553}_{-0.422}\times 10^{-4}$, ${\cal B}(B^0 \to b_1^-(1235)μ^+ν_μ) = 2.166^{+0.544}_{-0.415}\times 10^{-4}$, ${\cal B}(B^+ \to b_1^0(1235)e^+ν_e) = 2.353^{+0.597}_{-0.456}\times 10^{-4}$, and ${\cal B}(B^+ \to b_1^0(1235)μ^+ν_μ) = 2.339^{+0.587}_{-0.448}\times 10^{-4}$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Longitudinal leading-twist distribution amplitude of the $^1P_1$-state $b_1(1235)$ meson and its implications on $B\to b_1(1235)\ell^+ν_\ell$ decays Zeng, Long Wu, Xing-Gang Hu, Dan-Dan Fu, Hai-Bing Zhong, Tao High Energy Physics - Phenomenology In the paper, we derive the $ξ$-moments $\langleξ_{2;b_1}^{n;\|}\rangle$ of the longitudinal leading-twist distribution amplitude $ϕ_{2;b_1}^{\|}$ for $^1P_1$-state $b_1(1235)$-meson by using the QCD sum rules under the background field theory. Considering the contributions from the vacuum condensates up to dimension-six, its first two non-zero $ξ$-moments at the scale 1 GeV are $\langleξ_{2;b_1}^{1;\|}\rangle= -0.647^{+0.118}_{-0.113}$ and $\langleξ_{2;b_1}^{3;\|}\rangle = -0.328^{+0.055}_{-0.052}$, respectively. Using those moments, we then fix the Gegenbauer expansion series of $ϕ_{2;b_1}^{\|}$ and apply it to calculate $B\to b_1(1235)$ transition form factors (TFFs) that are derived by using the QCD light-cone sum rules. Those TFFs are then extrapolated to the physically allowable $q^2$-range via the simplified series expansion. As for the branching fractions, we obtain ${\cal B}(\bar B^0 \to b_1^+(1235)e^- \barν_e) = 2.179^{+0.553}_{-0.422}\times 10^{-4}$, ${\cal B}(B^0 \to b_1^-(1235)μ^+ν_μ) = 2.166^{+0.544}_{-0.415}\times 10^{-4}$, ${\cal B}(B^+ \to b_1^0(1235)e^+ν_e) = 2.353^{+0.597}_{-0.456}\times 10^{-4}$, and ${\cal B}(B^+ \to b_1^0(1235)μ^+ν_μ) = 2.339^{+0.587}_{-0.448}\times 10^{-4}$, respectively. |
| title | Longitudinal leading-twist distribution amplitude of the $^1P_1$-state $b_1(1235)$ meson and its implications on $B\to b_1(1235)\ell^+ν_\ell$ decays |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2501.06737 |