Observed best fit differential cross section for the $|y_{H}|$ observable

Observed best fit differential cross section for the $m_{jj}$ (GeV) observable

Observed best fit differential cross section for the $\Delta\eta_{jj}$ observable.

Observed best fit differential cross section for the $\tau_{C}^{j}$ (GeV) observable

Bin-to-bin correlation matrix for the $p_{T}^{H}$ spectrum

Bin-to-bin correlation matrix for the $N_{jets}$ spectrum

Bin-to-bin correlation matrix for the $p_{T}^{j0}$ spectrum

Bin-to-bin correlation matrix for the $|y_{H}|$ spectrum

Bin-to-bin correlation matrix for the $m_{jj}$ spectrum

Bin-to-bin correlation matrix for the $\Delta\eta_{jj}$ spectrum

Bin-to-bin correlation matrix for the $\tau_{C}^{j}$ spectrum

Rotation matrix for the PCA of the SMEFT Wilson coefficients

Correlation matrix of the linear combinations of Wilson coefficients obtained from the PCA, obtained by fitting the observed data to the $p_{T}^{H}$ spectra of all decay channels.

Summary of observed and expected confidence intervals for the first eigenvectors obtained from the PCA of the SMEFT Wilson coefficients.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH3 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 and ISR starting scale SpaceShower:pT0Ref = 1 GeV at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH3 and ISR starting scale SudakovCommon:pTmin=0.7 GeV at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-proton center-of-mass energy 38.8 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-proton center-of-mass energy 8000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-nucleon center-of-mass energy 8160 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-nucleon center-of-mass energy 13000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 38.8 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 8000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-nucleon center-of-mass energy 8160 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 13000 GeV versus the dilepton mass range of the process.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Data from Figure 2, panel b, U+U, 0-0.5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel a, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel b, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel c, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel d, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel e, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel f, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel a, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel a, U+U, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel b, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel b, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel c, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel c, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel d, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel d, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, standard method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, standard, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, standard, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Data of the decay $\bar{B}^+ \to D^* \mu \nu_\mu$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B0 -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 48 - 95: B0 -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 96 - 143: B+ -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 144 - 191: B+ -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ...

Data of the B+/B0 average $B \to D^* e \nu_e$.

Data of the B+/B0 average $B \to D^* \mu \nu_\mu$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 48 - 95: B -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], .....

Data of the B+/B0 and e/mu average $B \to D^* \ell \nu_\ell$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B -> D* l nu_l: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ...

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.

'Identified transverse momentum spectra of $\pi^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $K^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\pi^{−}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{−}$/$K^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/p ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{+}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{-}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'p/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

The centrality dependencies of the $\Delta\gamma\{\psi_\mathrm{ZDC}\}$ for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the a for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A/a using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A/a using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $f_\mathrm{CME}$ using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $f_\mathrm{CME}$ using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $\Delta\gamma_\mathrm{CME}$ using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $\Delta\gamma_\mathrm{CME}$ using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $f_\mathrm{CME}$ from different methods for 20-50% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $f_\mathrm{CME}$ from different methods for 50-80% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $\Delta\gamma_\mathrm{CME}$ from different methods for 20-50% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $\Delta\gamma_\mathrm{CME}$ from different methods for 50-80% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

Parameters of the polynomial fit of net-proton C3/C2 and C4/C2 vs energy in 0-5$\%$ central Au+Au collisions. Polynomial of order 5 and 4 are used to fit C3/C2 and C4/C2 ratio vs energies, respectively.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in STAR Au+Au collisions for nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV for 0-5$\%$ and 70-80$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in Au+Au collisions from UrQMD for 0-5$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions from HRG GCE, HRG GEC excluded volume, HRG CE model.

Cumulants and their ratios up to fourth order in Au+Au collisions at $\sqrt{s_{NN}} = 200 GeV using conventional analytical efficiency corrections and unfolding approaches with various cases of distribution of detector response.

Rapidity dependence of cumulant ratio C4/C2 of net-proton distributions for 0-5$\%$ central Au+Au collisions at nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV.

Significance of deviations in net-proton C4/C2 (or kappa*sigma^2) for central 0-5$\%$ Au+Au collisions and those from UrQMD, HRG and peripheral 70-80$\%$ data.