Prospective analysis of CKM element $|V_{cd}|$ and $D^+$-meson decay constant from leptonic decays $D^+ \to \ell^+ ν$
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| Format: | Preprint |
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2024
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| _version_ | 1866917839374385152 |
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| author | Wang, Ya-Xiong Tian, Hai-Jiang Yang, Yin-Long Zhong, Tao Fu, Hai-Bing |
| author_facet | Wang, Ya-Xiong Tian, Hai-Jiang Yang, Yin-Long Zhong, Tao Fu, Hai-Bing |
| contents | The leptonic decay of $D^+$-meson has attracted significant interest due to its unique characteristics. In this paper, we carry out an investigation into the $D^+$-meson leptonic decays $D^+\to \ell^+ν_{\ell}$ with $\ell=(e,μ,τ)$ by employing the QCD sum rules approach. In which the $D^+$-meson decay constant $f_{D^+}$ is an important input parameter in the process. To enhance the accuracy of our calculations for $f_{D^+}$, we consider the quark propagator and vertex up to dimension-six within the framework of background field theory. Consequently, we obtain the QCD sum rule expression for $f_{D^+}$ up to dimension-six condensates, yielding $f_{D^+}=203.0\pm1.5~\mathrm{MeV}$. Our results are in good agreement with BESIII measurements and theoretical predictions. We also present the integrated decay widths for the $D^+$-meson in three channels $Γ(D^+\to e^+ν_e)=(5.263_{-0.075}^{+0.076})\times10^{-21}~\mathrm{GeV}$, $Γ(D^+\to μ^+ν_μ)=(2.236_{-0.032}^{+0.032})\times10^{-16}~\mathrm{GeV}$ and $Γ(D^+\to τ^+ν_τ)=(5.958_{-0.085}^{+0.086})\times10^{-16}~\mathrm{GeV}$. Accordingly, we compute the branching fraction $\mathcal{B}(D^+\to\ell^+ν_{\ell})$ with the electron, muon and tau channels, which are $\mathcal{B}(D^+\to e^+ν_e)=(8.260_{-0.118}^{+0.119})\times10^{-9}$, $\mathcal{B}(D^+\toμ^+ν_μ)=(3.508_{-0.050}^{+0.051})\times10^{-4}$ and $\mathcal{B}(D^+\toτ^+ν_τ)=(0.935_{-0.013}^{+0.013})\times10^{-3}$. Furthermore, we present our prediction for the CKM matrix element $|V_{cd}|$ using the branching fraction $\mathcal{B}(D^+\toμ^+ν_μ)$ obtained from BESIII Collaboration, yielding $|V_{cd}|=0.227_{-0.001}^{+0.002}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prospective analysis of CKM element $|V_{cd}|$ and $D^+$-meson decay constant from leptonic decays $D^+ \to \ell^+ ν$ Wang, Ya-Xiong Tian, Hai-Jiang Yang, Yin-Long Zhong, Tao Fu, Hai-Bing High Energy Physics - Phenomenology The leptonic decay of $D^+$-meson has attracted significant interest due to its unique characteristics. In this paper, we carry out an investigation into the $D^+$-meson leptonic decays $D^+\to \ell^+ν_{\ell}$ with $\ell=(e,μ,τ)$ by employing the QCD sum rules approach. In which the $D^+$-meson decay constant $f_{D^+}$ is an important input parameter in the process. To enhance the accuracy of our calculations for $f_{D^+}$, we consider the quark propagator and vertex up to dimension-six within the framework of background field theory. Consequently, we obtain the QCD sum rule expression for $f_{D^+}$ up to dimension-six condensates, yielding $f_{D^+}=203.0\pm1.5~\mathrm{MeV}$. Our results are in good agreement with BESIII measurements and theoretical predictions. We also present the integrated decay widths for the $D^+$-meson in three channels $Γ(D^+\to e^+ν_e)=(5.263_{-0.075}^{+0.076})\times10^{-21}~\mathrm{GeV}$, $Γ(D^+\to μ^+ν_μ)=(2.236_{-0.032}^{+0.032})\times10^{-16}~\mathrm{GeV}$ and $Γ(D^+\to τ^+ν_τ)=(5.958_{-0.085}^{+0.086})\times10^{-16}~\mathrm{GeV}$. Accordingly, we compute the branching fraction $\mathcal{B}(D^+\to\ell^+ν_{\ell})$ with the electron, muon and tau channels, which are $\mathcal{B}(D^+\to e^+ν_e)=(8.260_{-0.118}^{+0.119})\times10^{-9}$, $\mathcal{B}(D^+\toμ^+ν_μ)=(3.508_{-0.050}^{+0.051})\times10^{-4}$ and $\mathcal{B}(D^+\toτ^+ν_τ)=(0.935_{-0.013}^{+0.013})\times10^{-3}$. Furthermore, we present our prediction for the CKM matrix element $|V_{cd}|$ using the branching fraction $\mathcal{B}(D^+\toμ^+ν_μ)$ obtained from BESIII Collaboration, yielding $|V_{cd}|=0.227_{-0.001}^{+0.002}$. |
| title | Prospective analysis of CKM element $|V_{cd}|$ and $D^+$-meson decay constant from leptonic decays $D^+ \to \ell^+ ν$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2411.10660 |