Correlation matrix for the correlated systematic uncertainties of the forward rapidity $\eta$ meson cross section.

Correlation matrix for the correlated systematic uncertainties of the central rapidity $\eta$ meson cross section.

The invariant yields of $\phi$ and $\omega+\rho$ mesons as a function of $\langle N_{\rm part}\rangle$ in Au+Au collisions. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

$R_{AA}$ of $\phi$ meson as a function of $p_T$ for in Au+Au collisions at $\sqrt{s_{_{NN}}}=200$~GeV, compared with Cu+Au collisions at $1.2<|y|<2.2$. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

$R_{AA}$ of $\phi$ meson as a function of $\langle N_{\rm part}\rangle$ for $1.2<|y|<2.2$ in Au+Au collisions at $\sqrt{s_{_{NN}}}=200$~GeV. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

Correlations (stat.+syst.) between the $d\Gamma_i/d w$ bins for the individual $B \rightarrow D \ell \nu$ modes (40x40). Element indices 0-39 are organized as: - Indices 0-9: $B^+ \to D^0 e^+ \nu_e$ in $w$ bins 0-9 - Indices 10-19: $B^+ \to D^0 \mu^+ \nu_\mu$ in $w$ bins 0-9 - Indices 20-29: $B^0 \to D^- e^+ \nu_e$ in $w$ bins 0-9 - Indices 30-39: $B^0 \to D^- \mu^+ \nu_\mu$ in $w$ bins 0-9 where $w$ bins 0-9 correspond to: 0: [1.00, 1.06], 1: [1.06, 1.12], 2: [1.12, 1.18], 3: [1.18, 1.24], 4: [1.24, 1.30], 5: [1.30, 1.36], 6: [1.36, 1.42], 7: [1.42, 1.48], 8: [1.48, 1.54], 9: [1.54, 1.59]

$\xi$ distributions for different jet $p_T$ bins.

$\xi$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

$r$ distributions for different jet $p_T$ bins.

$M_{\tau}$ 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)

$R_{\rm p}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm N}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm N}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm N}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm d}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm d}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm d}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 0 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 1 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 2 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 3 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 4 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 5 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs. '<dN_{ch}/d \eta>^{1/3}' for mT bin 6 for Pb-Pb collisions at 5020 GeV.

$R_{\rm p}$ vs.'<dN_{ch}/d \eta>^{1/3}' for mT bin 7 for Pb-Pb collisions at 5020 GeV.

proton-deuteron (same charge) correlation function for centrality 0-10% from Pb-Pb collisions at 5020 GeV

proton-deuteron (same charge) correlation function for centrality 10-30% from Pb-Pb collisions at 5020 GeV

proton-deuteron (same charge) correlation function for centrality 30-50% from Pb-Pb collisions at 5020 GeV

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 $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})/v_{0}$ for inclusive charged particles is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 10$–$20% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})/v_{0}$ for inclusive charged particles is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 30$–$40% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})/v_{0}$ for inclusive charged particles is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 60$–$70% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for pions is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 10$–$20% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for kaons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 10$–$20% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for protons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 10$–$20% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for pions is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 30$–$40% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for kaons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 30$–$40% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for protons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 30$–$40% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for pions is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 60$–$70% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for kaons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 60$–$70% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

The $p_\mathrm{T}$ dependence of $v_{0}(p_\mathrm{T})$ for protons is measured in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV within the 60$–$70% centrality interval, using a two-particle correlation method with a pseudorapidity gap of $\Delta\eta = 0.4$.

pion-deuteron (opposite charge) correlation function for centrality 0-10% from Pb-Pb collisions at 5020 GeV

pion-deuteron (opposite charge) correlation function for centrality 10-30% from Pb-Pb collisions at 5020 GeV

pion-deuteron (opposite charge) correlation function for centrality 30-50% from Pb-Pb collisions at 5020 GeV

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for ${\rm \overline{p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for ${\rm \overline{p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for ${\rm \overline{p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for ${\rm {p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for ${\rm {p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for ${\rm {p}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for ${\rm K^{ 0}_S}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for ${\rm K^{ 0}_S}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for ${\rm K^{ 0}_S}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for ${\rm K^{\pm}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for ${\rm K^{\pm}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for ${\rm K^{\pm}}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for $\pi^{\pm}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for $\pi^{\pm}$, rescaled value from 2760GeV to 5020GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for $\pi^{\pm}$, rescaled value from 2760 GeV to 5020 GeV.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $0-10\%$ centrality for ${\rm {d}(\rm {\overline{d}})}$.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $10-30\%$ centrality for ${\rm {d}(\rm {\overline{d}})}$.

$R_{\rm inv}$ vs. $m_{\rm T}$ for $30-50\%$ centrality for ${\rm {d}(\rm {\overline{d}})}$.