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

Abstract

As the lightest strange scalar resonance,

(also called

$$\kappa $$ κ

) has a large width and resides close to the

$$K\pi $$ K π

threshold, leading to a longstanding debate about its internal structure. Within the framework of the conventional quark-antiquark (

$$q\bar{q}$$ q q ¯

) picture, this paper attempts to research the behaviors of

$$K_0^*(700)$$ K 0 ∗ ( 700 )

resonance in the four-body final state decays. Firstly, we investigate the

$$K_0^*(700)$$ K 0 ∗ ( 700 )

resonance one twist-2 and two twist-3 light-cone distribution amplitudes (LCDAs), i.e.

$$\phi _{2;K_0^*(700)}(x, \mu )$$ ϕ 2 ; K 0 ∗ ( 700 ) ( x , μ )

and

$$\phi _{3;K_0^*(700)}^{p;\sigma }(x, \mu )$$ ϕ 3 ; K 0 ∗ ( 700 ) p ; σ ( x , μ )

, by constructing a light-cone harmonic oscillator model. For the longitudinal distribution characteristics of the twist-2 LCDA, two typical parametrization schemes, i.e.

$$\varphi _{2;K_0^*(700)}^\mathrm{(S1)}(x)$$ φ 2 ; K 0 ∗ ( 700 ) ( S 1 ) ( x )

and

$$\varphi _{2;K_0^*(700)}^\mathrm{(S2)}(x)$$ φ 2 ; K 0 ∗ ( 700 ) ( S 2 ) ( x )

, are adopted in this paper. Meanwhile, it has enriched theoretical predictions for the first ten-order LCDAs

$$\xi $$ ξ

-moments. Subsequently, we apply the QCD light-cone sum rules approach to compute the

$$\bar{B}_s^0 \rightarrow K_0^*(700)$$ B ¯ s 0 → K 0 ∗ ( 700 )

transition form factors (TFFs)

$$f_\pm ^{\bar{B}_s^0 K_0^*(700)}(q^2)$$ f ± B ¯ s 0 K 0 ∗ ( 700 ) ( q 2 )

and

$$f_\textrm{T}^{\bar{B}_s^0 K_0^*(700)}(q^2)$$ f T B ¯ s 0 K 0 ∗ ( 700 ) ( q 2 )

, including the next-to-leading order perturbative

$$\mathcal {O}(\alpha _s)$$ O ( α s )

corrections to the twist-2 LCDA contributions. 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

$$\bar{B}_s^0 \rightarrow K^0\pi ^+ \ell ^-\bar{\nu }_\ell $$ B ¯ s 0 → K 0 π + ℓ - ν ¯ ℓ

with

$$\ell = (e, \mu , \tau )$$ ℓ = ( e , μ , τ )

via the S -wave

$$K_0^*(700)$$ K 0 ∗ ( 700 )

resonance in the

$$K\pi $$ K π

system, respectively. We expect that the obtained prediction results will provide valuable insights for future experiments and theoretical research.