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 $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

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 ${\rm {d}(\rm {\overline{d}})}$.

$p_{T}$ dependence of $v_{2}$ for $\pi^{+}$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{+}$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{-}$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{-}$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{-}$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{-}$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{-}$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{+}$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{+}$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{+}$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{+}$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{+}$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{-}$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{-}$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{-}$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{-}$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{-}$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{0}_{S}$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{0}_{S}$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{0}_{S}$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{0}_{S}$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $K^{0}_{S}$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $p$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $p$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $p$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $p$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $p$ in Au+Au collisions at 4.5 GeV

$p_{T}$ dependence of $v_{2}$ for $\Lambda$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $\Lambda$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $\Lambda$ in Au+Au collisions at 3.5 GeV

$p_{T}$ dependence of $v_{2}$ for $\Lambda$ in Au+Au collisions at 3.9 GeV

$p_{T}$ dependence of $v_{2}$ for $\Lambda$ in Au+Au collisions at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{+}$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{+}$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{+}$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{+}$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{+}$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{-}$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{-}$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{-}$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{-}$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\pi^{-}$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{+}$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{+}$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{+}$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{+}$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{+}$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{-}$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{-}$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{-}$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{-}$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{-}$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{0}_{S}$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{0}_{S}$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{0}_{S}$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{0}_{S}$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $K^{0}_{S}$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $p$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $p$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $p$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $p$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $p$ at 4.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\Lambda$ at 3 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\Lambda$ at 3.2 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\Lambda$ at 3.5 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\Lambda$ at 3.9 GeV

The number of constituent quarks $n_q$ scaled $v_2$ as a function of $n_q$ scaled transverse kinetic energy for $\Lambda$ at 4.5 GeV

The energy dependence of $p_T$ integrated $v_2$ for $\pi^{\pm}$, $K^{\pm}$, $K^{0}_{S}$, $p$, and $\Lambda$ in 10-40\% centrality from Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 3.0, 3.2, 3.5, 3.9, and 4.5 GeV.

The energy dependence of $n_{q}$ scaled $v_{2}$ ratios of $v_{2}^{q}(\pi^{+}) / v_{2}^{q}(K^{+})$ and $v_{2}^{q}(p) / v_{2}^{q}(K^{+})$ at ($m_T - m_0$)/$n_q$ = 0.4 GeV/$c^2$

UrQMD model calculations for net-proton cumulant ratios and proton factorial cumulant ratios in Au+Au collisions from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV for 0-5$\%$ centrality. Same choices of centrality definition are used as used for experimental data.

Significance of deviations of central 0-5$\%$ data from various choices of baselines or references.

Cumulant ratios C2/C1 and C4/C2 of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of multiplicity (RefMult3X).

Cumulant ratios C2/C1 and C4/C2 of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of average multiplicity (RefMult3X) for 8 centrality bins from 0-10$\%$ to 70-80$\%$. Data with and without CBWC are given.

Cumulant ratios C2/C1 and C4/C2 of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of average multiplicity (RefMult3X) for 16 centrality bins from 0-5$\%$ to 75-80$\%$. Data with and without CBWC are given.

Reference multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV from BES-II. Three choices of multiplicity distributions (RefMult3 scaled by efficiency factor of $\epsilon$ = 0.83 or 83$\%$ to mimic RefMult3 of BES-I, RefMult3, and RefMult3X) are presented.

Cumulant ratios C2/C1 and C4/C2 of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV from BES-II as a function of centrality obtained with various centrality definitions.

Reference multiplicity distributions (RefMult3, RefMult3X, and RefMult3A) in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV from UrQMD model. The RefMult3 and RefMult3X distributions have been scaled by an efficiency factor of $\epsilon$ = 77.9$\%$ to mimic the distribution in experimenal data.

Cumulant ratios C2/C1 and C4/C2 of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV from UrQMD model as a function of centrality obtained with various centrality definitions (RefMult3, RefMult3X, and RefMult3A). The RefMult3 and RefMult3X distributions have been scaled by an efficiency factor of $\epsilon$ = 77.9$\%$ to mimic the distribution in experimenal data.

Collision energy dependence of net-proton C4/C2 in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 - 27 GeV from BES-II obtained with RefMult3 centrality definition.

Difference between net-proton C4/C2 (0-5$\%$) data from various choices of baselines or references as a function of collision energy from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV.

The distributions of the variables used in the simultaneous fit for the SR. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the predicted uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.

Expected and observed 95% upper limits on the product of the cross section and branching fraction$\sigma(\mathrm{pp} \ ightarrow W\mathrm{a})\mathcal{B}(W ightarrow \ell^{+} v_{\ell})\mathcal{B}(\mathrm{a} \rightarrow Z\gamma)\mathcal{B}(Z \rightarrow \ell^{+} \ell^{-})$ s a function of the ALP mass from 110 to 400 GeV

Expected and observed 95% upper limits on the photophobic ALP model parameter $1/f_{\mathrm{a}}$ as a function of ALP mass reinterpreted from $1/f_{\mathrm{a}}=2~\mathrm{TeV}^{-1}$