Scrutinizing $B^0$-meson flavor changing neutral current decay into scalar $K_0^{\ast }(1430)$ meson with $b\to s{\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$ transition

Abstract

In this paper, we investigate the rare decay $B^0\to K_0^{\ast }(1430){\ell }^{+}{\ell }^{-}$ with $\ell =(e,\mu ,\tau )$ and $B^0\to K_0^{\ast }(1430)\nu \bar{\nu }$ induced by the flavor changing neutral current transition of $b\to s{\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$. Firstly, the $B^0\to K_0^{\ast }(1430)$ transition form factors (TFFs) are calculated by using the QCD light-cone sum rule approach up to next-to-leading order accuracy. In which the $K_0^{\ast }(1430)$-meson twist-2 and twist-3 LCDAs have been calculated both from the SVZ sum rule in the background field theory framework and light-cone harmonic oscillator model. Then, we obtained the three TFFs at large recoil point, {\it i.e.,} $f_{+}^{B^0\to K_0^{\ast }}(0)=0.470_{-0.101}^{+0.086}$, $f_{-}^{B^0\to K_0^{\ast }}(0)=-0.340_{-0.068}^{+0.068}$, and $f_{\mathrm{T}}^{B^0\to K_0^{\ast }}(0)=0.537_{-0.115}^{+0.112}$. Meanwhile, we extrapolated TFFs to the whole physical $q^2$-region by using the simplified $z(q^2)$-series expansion. Furthermore, we calculate the $B^0\to K_0^{\ast }(1430){\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$ decay widths, branching fractions, and longitudinal lepton polarization asymmetries of $B^0\to K_0^{\ast }(1430){\ell }^{+}{\ell }^{-}$, which lead to $\mathcal{B}(B^0\to K_0^{\ast }(1430)e^{+}{e}^{-})=(6.65_{-2.42}^{+2.52})\times 10^{-7}$, $\mathcal{B}(B^0\to K_0^{\ast }(1430){\mu }^{+}{\mu }^{-})=(6.62_{-2.41}^{+2.51})\times 10^{-7}$, $\mathcal{B}(B^0\to K_0^{\ast }(1430){\tau }^{+}{\tau }^{-})=(1.88_{-0.97}^{+1.10})\times 10^{-8}$, $\mathcal{B}(B^0\to K_0^{\ast }(1430)\nu \bar{\nu })=3.85_{-1.48}^{+1.55}\times 10^{-6}$ and the integrated longitudinal lepton polarization asymmetries $⟨A_{P_L}⟩=(-0.99,-0.96,-0.03)$ for the cases $\ell =(e,\mu ,\tau )$ respectively.

Comments: 17 pages, 3 figures, comments welcome