Scrutinizing -meson flavor changing neutral current decay into scalar meson with transition

Yin-Long Yang; Ya-Xiong Wang; Hai-Bing Fu; Tao Zhong; Ya-Lin Song

doi:10.1140/epjc/s10052-025-13764-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 64
https://doi.org/10.1140/epjc/s10052-025-13764-3

Regular Article - Theoretical Physics

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

Yin-Long Yang¹, Ya-Xiong Wang¹, Hai-Bing Fu¹^,2^a, Tao Zhong¹ and Ya-Lin Song¹

¹ Department of Physics, Guizhou Minzu University, 550025, Guiyang, People’s Republic of China
² Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, People’s Republic of China

^a fuhb@gzmu.edu.cn

Received: 19 October 2024
Accepted: 30 December 2024
Published online: 24 January 2025

Abstract

In this paper, we investigate the rare decay $B^{0} \to K_{0}^{*} (1430) ℓ^{+} ℓ^{-}$ $B^0\rightarrow K_0^*(1430)\ell ^+\ell ^-$ with $ℓ = (e, μ, τ)$ $\ell =(e,\mu ,\tau )$ and $B^{0} \to K_{0}^{*} (1430) ν \bar{ν}$ $B^0\rightarrow K_0^*(1430)\nu \bar{\nu }$ induced by the flavor changing neutral current transition of $b \to s ℓ^{+} ℓ^{-} (ν \bar{ν})$ $b\rightarrow s\ell ^+\ell ^-(\nu \bar{\nu })$ . Firstly, the $B^{0} \to K_{0}^{*} (1430)$ $B^0\rightarrow K_0^*(1430)$ 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 $K_{0}^{*} (1430)$ $$K_0^*(1430)$$ -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 obtain the three TFFs at large recoil point, i.e., $f_{+}^{B^{0} \to K_{0}^{*}} (0) = 0 . 470_{- 0.101}^{+ 0.086}$ $f_+^{B^0\rightarrow K_0^*}(0)= 0.470_{-0.101}^{+0.086}$ , $f_{-}^{B^{0} \to K_{0}^{*}} (0) = - 0 . 340_{- 0.068}^{+ 0.068}$ $f_-^{B^0\rightarrow K_0^*}(0)= -0.340_{-0.068}^{+0.068}$ , and $f_{T}^{B^{0} \to K_{0}^{*}} (0) = 0 . 537_{- 0.115}^{+ 0.112}$ $f_\textrm{T}^{B^0\rightarrow K_0^*}(0)= 0.537^{+0.112}_{-0.115}$ . Meanwhile, we extrapolate TFFs to the whole physical $q^{2}$ $$q^2$$ -region by using the simplified $z (q^{2})$ $$z(q^2)$$ -series expansion. Furthermore, we calculate the $B^{0} \to K_{0}^{*} (1430) ℓ^{+} ℓ^{-} (ν \bar{ν})$ $B^0\rightarrow K_0^*(1430)\ell ^+\ell ^-(\nu \bar{\nu })$ decay widths, branching fractions, and longitudinal lepton polarization asymmetries of $B^{0} \to K_{0}^{*} (1430) ℓ^{+} ℓ^{-}$ $B^0\rightarrow K_0^*(1430)\ell ^+\ell ^-$ , which lead to $B (B^{0} \to K_{0}^{*} (1430) e^{+} e^{-}) = (6 . 65_{- 2.42}^{+ 2.52}) \times 10^{- 7}$ $\mathcal{B}(B^0\rightarrow K_0^*(1430)e^+e^-) = (6.65^{+2.52}_{-2.42})\times 10^{-7}$ , $B (B^{0} \to K_{0}^{*} (1430) μ^{+} μ^{-}) = (6 . 62_{- 2.41}^{+ 2.51}) \times 10^{- 7}$ $\mathcal{B}(B^0\rightarrow K_0^*(1430)\mu ^+\mu ^-)=(6.62^{+2.51}_{-2.41})\times 10^{-7}$ , $B (B^{0} \to K_{0}^{*} (1430) τ^{+} τ^{-}) = (1 . 88_{- 0.97}^{+ 1.10}) \times 10^{- 8}$ $\mathcal{B}(B^0\rightarrow K_0^*(1430)\tau ^+\tau ^-)=(1.88^{+1.10}_{-0.97})\times 10^{-8}$ , $B (B^{0} \to K_{0}^{*} (1430) ν \bar{ν}) = 3 . 85_{- 1.48}^{+ 1.55} \times 10^{- 6}$ $\mathcal{B}(B^0\rightarrow K_0^*(1430)\nu \bar{\nu })= 3.85^{+1.55}_{-1.48}\times 10^{-6}$ and the integrated longitudinal lepton polarization asymmetries $⟨ A_{P_{L}} ⟩ = (- 0.99, - 0.96, - 0.03)$ $\langle A_{P_L} \rangle = (-0.99, -0.96, -0.03)$ for the cases $ℓ = (e, μ, τ)$ $\ell =(e, \mu , \tau )$ respectively.

Yin-Long Yang and Ya-Xiong Wang contributed equally to this work.

© The Author(s) 2025

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