Probing $|V_{cs}|$ and lepton flavor universality through $D\to K_0^{\ast }(1430)\ell {\nu }_{\ell }$ decay

Abstract

In this paper, we calculate the semileptonic decays $D\to K_0^{\ast }(1430)\ell {\nu }_{\ell }$ with $\ell =(e,\mu )$ induced by $c\to s\ell {\nu }_{\ell }$ transition. For the key component, $D\to K_0^{\ast }(1430)$ transition form factors (TFFs) $f_{\pm }(q^2)$ are calculated within the framework of QCD light cone sum rule. Then, we consider two scenarios for $K_0^{\ast }(1430)$-meson twist-2 distribution amplitude. For the scenario 1 (S1), we take the truncated form based on Gegenbauer polynomial series. Meanwhile, we also consider the scenario 2 (S2) constructed by light cone harmonic oscillator model, where the model parameters are fixed by the $K_0^{\ast }(1430)$-meson twist-2 distribution amplitude tenth-order $\xi$ moments calculated by using the background field theory. For the TFFs at a large recoil point, we have $f_{+}^{(S1)}(0)=0.597_{-0.121}^{+0.122}$ and $f_{-}^{(S1)}(0)=-0.136_{-0.035}^{+0.023}$, $f_{+}^{(S2)}(0)=0.663_{-0.134}^{+0.135}$, and $f_{-}^{(S2)}(0)=-0.202_{-0.046}^{+0.026}$. After extrapolating TFFs to the whole physical $q^2$ region, we calculate the branching fractions of $D^0\to K_0^{\ast +}(1430){\ell }^{-}{\bar{\nu }}_{\ell }$ and $D^{+}\to K_0^{\ast 0}(1430){\ell }^{+}{\nu }_{\ell }$, which at $10^{-4}$-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix $|V_{cs}{|}^{(S1)}=0.973_{-0.183}^{+0.259},|V_{cs}{|}^{(S2)}=0.880_{-0.165}^{+0.234}$, and lepton flavor universality ${\mathcal{R}}_{K_0^{\ast }}^{(S1)}=0.768_{-0.368}^{+0.560},{\mathcal{R}}_{K_0^{\ast }}^{(S2)}=0.764_{-0.365}^{+0.555}$. Finally, we discuss the angular observables of forward-backward asymmetries, lepton polarization asymmetries, and $q^2$-differential flat terms for this decay.

10 pages, 5 figures, published version

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