$M_{\tau}$ distribution in signal region, (OS$\mu$, Belle II)

$M_{\tau}$ distribution in signal region, (SS$e$, Belle)

$M_{\tau}$ distribution in signal region, (SS$e$, Belle II)

$M_{\tau}$ distribution in signal region, (SS$\mu$, Belle)

$M_{\tau}$ distribution in signal region, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$e$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$e$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$e$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$e$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$e$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$e$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$\mu$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$\mu$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$e$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$e$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$\mu$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$\mu$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$e$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$e$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$\mu$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$\mu$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$e$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$e$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$\mu$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$\mu$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (OS$e$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (OS$e$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (OS$\mu$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (OS$\mu$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (SS$e$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (SS$e$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (SS$\mu$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (SS$\mu$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$e$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$e$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$e$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$e$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle II)

Signal-selection efficiency as a function of the di-tau invariant mass squared $q^2$ for simulated events in the SR. The error bars indicate the statistical uncertainty.

The systematic covariance matrix for the $e^+e^- \to \pi^+ \pi^- \pi^0$ cross section measurement at the Belle II. The 212 x 212 matrix of the energy ranges from 0.62 to 3.50 GeV. This covariance matrix includes all systematic uncertainty given in Table I. The total covariance matrix for the measured cross section can be obtained by adding statistical and systematic covariance matrices.

This table provides the ``inverse'' of the total (stat.+ sys.) covariance matrix. This matrix can be used for a chi-square fit of the mass spectrum. We provide this inverse matrix since special care is needed to take the inverse of the given covariance matrix.

Full experimental (statistical and systematic) correlations (in \%) of the normalized partial decay rates over the $\overline{B}^0\to D^{*+} e^- \bar\nu_e$ and $\overline{B}^0\to D^{*+} \mu^- \bar\nu_\mu$ decays.

Measured partial decay rates $\Delta\Gamma$ (in units of $10^{-15}$ GeV) using the matrix inversion unfolding method

Average of normalized decay rates that are determined using the matrix inversion unfolding method

Full experimental (statistical and systematic) correlations (in \%) of the partial decay rates determined with the matrix inversion unfolding method for the $\overline{B}^0\to D^{*+} e^- \bar\nu_e$ and $\overline{B}^0\to D^{*+} \mu^- \bar\nu_\mu$ decays.

Full experimental (statistical and systematic) correlations (in \%) of the normalized partial decay rates determined using the matrix inversion unfolding method

Expected and observed candidates for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) as a function of the reduced mediator candidate mass.

Exclusion regions in the plane of the sine of the mixing angle $\theta$ and scalar mass $m_S$

Exclusion regions in the plane of the coupling $g_Y = 2v/fa$ with the vacuum expectation value $v$ and the ALP mass $m_a$

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$100.0cm

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$)

The full experimental statistical correlations for the averaged spectrum are shown. The index of the entry corresponds to the index of the corresponding central value.

The full experimental systematic correlations for the averaged spectrum are shown. The index of the entry corresponds to the index of the corresponding central value.

The individual measured shapes. The 160 entries correspond to the 10 bins in w, cosThetaL, cosThetaV, and chi. Index 0-40: B0 --> D* e nu Index 40-80: B0 --> D* mu nu Index 80-120: B+ --> D* e nu Index 120-160: B+ --> D* mu nu For the binning see the file 'Binning.yaml'.

The full experimental statistical correlations for the individual spectra are shown. The index of the entry corresponds to the index of the corresponding central value.

The full experimental systematic correlations for the individual spectra are shown. The index of the entry corresponds to the index of the corresponding central value.

Best fit of the cross section.

Correlation matrix for the individual sources of systematic uncertainty considered in the analysis, for the combined opposite sign (OS) and same sign (SS) binned-template profile likelihood fit to data. The OS or SS refers to the charge signs of the primary lepton and the soft muon. The gamma parameters are NPs used to describe the effect of the limited statistics of the samples.