Semirelativistic study on the semileptonic decays of $B_q$ mesons to orbital excited heavy Tensors
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910370172502016 |
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| author | Ke, Wen-Yuan Pei, Su-Yan Wang, Tianhong Wang, Guo-Li |
| author_facet | Ke, Wen-Yuan Pei, Su-Yan Wang, Tianhong Wang, Guo-Li |
| contents | Based on the method of solving the complete Salpeter equation, we study the semileptonic decays of a $0^-$ heavy meson to $1P$, $2P$, or $3P$ heavy tensor mesons, $B_q \to (\bar c q)(nP) \ell^+ ν_\ell$ $(q=u,d,s,c;n=1,2,3)$. The obtained branching ratio of $\mathcal{B} (B \rightarrow D_2^{\star}(2460)\ell^{+} ν_{\ell})$ agrees with the experimental data. We predict $\mathcal{B}\left(B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}\right)$$=$$3.76\times 10^{-3}$ and $\mathcal{B}\left(B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}\right)$$=$$1.82\times 10^{-3}$. The branching ratios of decays to $2P$ and $3P$ final states are found to be very small. The ratios $\mathcal{R}(\bar{D}_{2}^{\star 0})=0.045$, $\mathcal{R}({D}_{s2}^{\star})=0.048$ and $\mathcal{R}(χ_{c2})=0.059$ are also obtained. This study focuses on the contribution of relativistic corrections. The wave function of the pseudoscalar includes non-relativistic $S$-wave and relativistic $P$-wave. While for a tensor, it contains non-relativistic $P$-wave and relativistic $P$, $D$ and $F$ waves in its wave function. We find the individual contributions of relativistic partial waves are significant in the decay $B \to D_2^{\star }(2460)\ell^{+} ν_{\ell}$, but the overall contribution of the relativistic effect is $24.4\%$, which is small due to cancellation. Similarly, for the decay $B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}$, the contribution of the relativistic effect is $28.8\%$. While for $B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}$, the individual contributions of relativistic partial waves and the overall relativistic correction are both small, the later of which is $22.1\%$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15748 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semirelativistic study on the semileptonic decays of $B_q$ mesons to orbital excited heavy Tensors Ke, Wen-Yuan Pei, Su-Yan Wang, Tianhong Wang, Guo-Li High Energy Physics - Phenomenology High Energy Physics - Experiment Based on the method of solving the complete Salpeter equation, we study the semileptonic decays of a $0^-$ heavy meson to $1P$, $2P$, or $3P$ heavy tensor mesons, $B_q \to (\bar c q)(nP) \ell^+ ν_\ell$ $(q=u,d,s,c;n=1,2,3)$. The obtained branching ratio of $\mathcal{B} (B \rightarrow D_2^{\star}(2460)\ell^{+} ν_{\ell})$ agrees with the experimental data. We predict $\mathcal{B}\left(B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}\right)$$=$$3.76\times 10^{-3}$ and $\mathcal{B}\left(B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}\right)$$=$$1.82\times 10^{-3}$. The branching ratios of decays to $2P$ and $3P$ final states are found to be very small. The ratios $\mathcal{R}(\bar{D}_{2}^{\star 0})=0.045$, $\mathcal{R}({D}_{s2}^{\star})=0.048$ and $\mathcal{R}(χ_{c2})=0.059$ are also obtained. This study focuses on the contribution of relativistic corrections. The wave function of the pseudoscalar includes non-relativistic $S$-wave and relativistic $P$-wave. While for a tensor, it contains non-relativistic $P$-wave and relativistic $P$, $D$ and $F$ waves in its wave function. We find the individual contributions of relativistic partial waves are significant in the decay $B \to D_2^{\star }(2460)\ell^{+} ν_{\ell}$, but the overall contribution of the relativistic effect is $24.4\%$, which is small due to cancellation. Similarly, for the decay $B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}$, the contribution of the relativistic effect is $28.8\%$. While for $B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}$, the individual contributions of relativistic partial waves and the overall relativistic correction are both small, the later of which is $22.1\%$. |
| title | Semirelativistic study on the semileptonic decays of $B_q$ mesons to orbital excited heavy Tensors |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2311.15748 |