Addressing the lightest $S$-wave strange $K_0^*(700)/κ$ resonance in four-body semileptonic $\bar{B}_s^0 \to K^0π^+ \ell^-\barν_\ell$ decays

Abstract

As the lightest strange scalar resonance, $K_0^*(700)$ (also called $κ$) has a large width and resides close to the $Kπ$ 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 $K_0^*(700)$ resonance in the four-body final state decays. Firstly, we investigates the $K_0^*(700)$ resonance one twist-2 and two twist-3 light-cone distribution amplitudes (LCDAs), {\it i.e.} $ϕ_{2;K_0^*(700)}(x, μ)$ and $ϕ_{3;K_0^*(700)}^{p;σ}(x, μ)$ by constructing light-cone harmonic oscillator model. For the longitudinal distribution characteristics of the twist-2 LCDA, two typical parametrization schemes, {\it i.e.} $φ_{2;K_0^*(700)}^{\rm (S1)}(x)$ and $φ_{2;K_0^*(700)}^{\rm (S2)}(x)$, are adopted in this paper. Meanwhile, it has enriched theoretical predictions for the first ten-order LCDAs $ξ$-moments. Subsequently, we apply the QCD light-cone sum rules approach to compute the $\bar B_s^0 \to K_0^*(700)$ transition form factors (TFFs) $f_\pm^{\bar B_s^0 K_0^*(700)}(q^2)$ and $f_{\rm T}^{\bar B_s^0 K_0^*(700)}(q^2)$ by taking into account the perturbative $\mathcal{O}(α_s)$ 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 $\bar{B}_s^0 \to K^0π^+ \ell^-\barν_\ell$ with $\ell= (e, μ, τ)$ via the $S$-wave $K_0^*(700)$ resonance, respectively. We expect that the obtained prediction results will provide valuable insights for future experiments and theoretical research.