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]

Normalized $p_{\mathrm{T}}$-spectrum ratio as a function as a function of centrality in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}} \in$ $0.5 \leq |\eta|\leq 0.8$.

Normalized $p_{\mathrm{T}}$-spectrum ratio as a function as a function of centrality in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{tracklets}} \in$ $0.5 \leq |\eta|\leq 0.8$.

Normalized $p_{\mathrm{T}}$-spectrum ratio as a function as a function of centrality in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}} \in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

Event fraction distribution as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}} \in -3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

Event fraction distribution as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}} \in |\eta|\leq 0.8$.

Event fraction distribution as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}} \in |\eta|\leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $0.5 \leq |\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $0.5 \leq |\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{tracklets}}$ $\in$ $|\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{tracklets}}$ $\in$ $0.5 \leq |\eta| \leq 0.8$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{tracklets}}$ $\in$ $0.3 \leq |\eta| \leq 0.6$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{tracklets}}$ $\in$ $0.7 \leq |\eta| \leq 1$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

Extracted $c_{\mathrm{s}}^{2}$ as a function of the minimum pseudorapidity gap between the centrality estimation and transverse-momentum spectra measurement in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$.

$k_{2}/k_{2}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

$k_{2}/k_{2}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

$k_{2}/k_{2}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

$k_{3}/k_{3}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

$k_{3}/k_{3}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

$k_{3}/k_{3}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

$\gamma_{\langle [p_{\mathrm{T}}] \rangle}/\gamma_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

$\gamma_{\langle [p_{\mathrm{T}}] \rangle}/\gamma_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

$\gamma_{\langle [p_{\mathrm{T}}] \rangle}/\gamma_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

$\Gamma_{\langle [p_{\mathrm{T}}] \rangle}/\Gamma_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

$\Gamma_{\langle [p_{\mathrm{T}}] \rangle}/\Gamma_{\langle [p_{\mathrm{T}}] angle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

$\Gamma_{\langle [p_{\mathrm{T}}] \rangle}/\Gamma_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

$\kappa_{\langle [p_{\mathrm{T}}] \rangle}/\kappa_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $|\eta| \leq 0.8$.

$\kappa_{\langle [p_{\mathrm{T}}] \rangle}/\kappa_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $E_{\mathrm{T}}$ $\in$ $|\eta| \leq 0.8$.

$\kappa_{\langle [p_{\mathrm{T}}] \rangle}/\kappa_{\langle [p_{\mathrm{T}}] \rangle}^{0-5\%}$ as a function of $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

Correlation between $\langle p_{\mathrm{T}} \rangle / \langle p_{\mathrm{T}} \rangle ^{\mathrm{0-5\%}}$ and $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle / \langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle ^{\mathrm{0-5\%}}$ in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}}$ $\in$ $0.5 \leq |\eta| \leq 0.8$ with $0.45 \leq p_{\mathrm{T}} \leq 50~\mathrm{GeV}/c.$.

$M_{\tau}$ 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 $\Delta\eta = 0.4$.

The extracted kinetic decoupling temperature is derived from $\pi^{-}$–d correlation functions.

This is the mixed event distribution for $\pi^{+}$–d, required for the fitting

This is the mixed event distribution for $\pi^{-}$–d, required for the fitting

The momentum smearing matrix, required for the fitting, used both for $\pi^{-}$–d and $\pi^{+}$–d

$\Delta R_{\rm axis}$ distribution for ${\rm STD-WTA / STD-D^0}$ for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm STD-D^0$ for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm SD-D^0$ with grooming setting ($z_{\rm cut} = 0.1, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm SD-D^0$ with grooming setting ($z_{\rm cut} = 0.2, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm SD-D^0$ with grooming setting ($z_{\rm cut} = 0.1, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm WTA-SD$ with grooming setting ($z_{\rm cut} = 0.1, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for ${\rm WTA-SD / SD-D^0}$ with grooming setting ($z_{\rm cut} = 0.1, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm WTA-SD$ with grooming setting ($z_{\rm cut} = 0.2, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for ${\rm WTA-SD / SD-D^0}$ with grooming setting ($z_{\rm cut} = 0.2, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm STD-SD$ with grooming setting ($z_{\rm cut} = 0.1, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm STD-SD$ with grooming setting ($z_{\rm cut} = 0.2, \beta = 0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for the ratio of $\rm STD-SD$ ($z_{\rm cut} = 0.2, \beta=0$) over $\rm STD-SD$ ($z_{\rm cut} = 0.1, \beta=0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for the ratio of $\rm SD-D^0$ ($z_{\rm cut} = 0.2, \beta=0$) over $\rm SD-D^0$ ($z_{\rm cut} = 0.1, \beta=0$) for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.