Addressing the lightest $S$-wave strange $K_0^{\ast }(700)/\kappa$ resonance in four-body semileptonic ${\bar{B}}_s^0\to K^0{\pi }^{+}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays

Abstract

As the lightest strange scalar resonance, $K_0^{\ast }(700)$ (also called $\kappa$) has a large width and resides close to the $K\pi$ threshold, leading to a longstanding debate about its internal structure. Within the framework of the conventional quark-antiquark ($q\bar{q}$) picture, this paper attempts to research the behaviors of $K_0^{\ast }(700)$ resonance in the four-body final state decays. Firstly, we investigates the $K_0^{\ast }(700)$ resonance one twist-2 and two twist-3 light-cone distribution amplitudes (LCDAs), {\it i.e.} ${\varphi }_{2;K_0^{\ast }(700)}(x,\mu )$ and ${\varphi }_{3;K_0^{\ast }(700)}^{p;\sigma }(x,\mu )$ by constructing light-cone harmonic oscillator model. For the longitudinal distribution characteristics of the twist-2 LCDA, two typical parametrization schemes, {\it i.e.} ${\phi }_{2;K_0^{\ast }(700)}^{(S1)}(x)$ and ${\phi }_{2;K_0^{\ast }(700)}^{(S2)}(x)$, are adopted in this paper. Meanwhile, it has enriched theoretical predictions for the first ten-order LCDAs $\xi$-moments. Subsequently, we apply the QCD light-cone sum rules approach to compute the ${\bar{B}}_s^0\to K_0^{\ast }(700)$ transition form factors (TFFs) $f_{\pm }^{{\bar{B}}_s^0{K}_0^{\ast }(700)}(q^2)$ and $f_{\mathrm{T}}^{{\bar{B}}_s^0{K}_0^{\ast }(700)}(q^2)$ by taking into account the perturbative $\mathcal{O}({\alpha }_s)$ corrections to the twist-2 LCDAs terms. By using the simplified series expansion parameterization, these TFFs are extrapolated over the full physical region. Then, we calculate the differential decay widths and branching fractions for four-body semileptonic decay ${\bar{B}}_s^0\to K^0{\pi }^{+}{\ell }^{-}{\bar{\nu }}_{\ell }$ with $\ell =(e,\mu ,\tau )$ via the $S$-wave $K_0^{\ast }(700)$ resonance, respectively. We expect that the obtained prediction results will provide valuable insights for future experiments and theoretical research.

Comments: 28 pages, 4 figures