The measured differential branching fractions as a function of the invariant hadronic mass squared of the $X_u$ system ($M_X^2$).

The measured differential branching fractions as a function of the light-cone momenta of the hadronic $X_u$ system [$P_+ = (E_X^B - |old{p}_X^B|)$].

The measured differential branching fractions as a function of the light-cone momenta of the hadronic $X_u$ system [$P_- = (E_X^B + |old{p}_X^B|)$].

The background-subtracted yields as a function of $E_\ell^B$.

The background-subtracted yields as a function of $q^2$.

The background-subtracted yields as a function of $M_X$.

The background-subtracted yields as a function of $M_X^2$.

The background-subtracted yields as a function of $P_+$. [$P_+ = (E_X^B - |P_X^B|)$]

The background-subtracted yields as a function of $P_-$. [$P_- = (E_X^B + |P_X^B|)$].

The full experimental correlation matrix for the background-subtracted spectrum of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The full experimental correlation matrix for the background-subtracted spectrum of $q^2$).

The full experimental correlation matrix for the background-subtracted spectrum of $M_X$.

The full experimental correlation matrix for the background-subtracted spectrum of $M_X^2$.

The full experimental correlation matrix for the background-subtracted spectrum of $P_+$.

The full experimental correlation matrix for the background-subtracted spectrum of $P_-$.

Migration matrix of $E_\ell^B$ [in %].

Migration matrix of $q^2$ [in %].

Migration matrix of $M_X$ [in %].

Migration matrix of $M_X^2$ [in %].

Migration matrix of $P_+$ [in %].

Migration matrix of $P_-$ [in %].

The total correction factors and phase space acceptance as a function of the invariant hadronic mass of the $X_u$ system ($M_X$).

The total correction factors and phase space acceptance as a function of the invariant hadronic mass squared of the $X_u$ system ($M_X^2$).

The total correction factors and phase space acceptance as a function of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The total correction factors and phase space acceptance as a function of the four-momentum-transfer squared of the $B$ to the $X_u$ system ($q^2$).

The total correction factors and phase space acceptance as a function of $P_+$.

The total correction factors and phase space acceptance as a function of $P_-$.

The statistical correlations of the differential branching fractions are shown. The matrix elements are ordered for $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The full experimental (statistical and systematical) correlations of the differential branching fractions are shown. The matrix elements are ordered for $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The total partial branching fraction with $E_{\ell}^{B} > 1$ GeV. The order of entries is: the 2D fit result of Phys. Rev. D 104, 012008 (2021), the results calcuated with the differential branching fractions of $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$

The full experimental correlations between the total partial branching fractions from summing the individual bins are shown. The matrix elements are saved in the order of $M_{X}$, $M_{X}^{2}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$.

The first moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The second moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The third moment of the measured differential branching fraction of the lepton energy in the $B$ rest frame ($E_\ell^B$).

The first moment of the measured differential branching fraction of $q^2$.

The second moment of the measured differential branching fraction of $q^2$.

The third moment of the measured differential branching fraction of $q^2$.

The first moment of the measured differential branching fraction of $M_{X}$.

The second moment of the measured differential branching fraction of $M_{X}$.

The third moment of the measured differential branching fraction of $M_{X}$.

The first moment of the measured differential branching fraction of $P_{+}$.

The second moment of the measured differential branching fraction of $P_{+}$.

The third moment of the measured differential branching fraction of $P_{+}$.

The first moment of the measured differential branching fraction of $P_{-}$.

The second moment of the measured differential branching fraction of $P_{-}$.

The third moment of the measured differential branching fraction of $P_{-}$.

The matrix elements are saved in the order of $M_{X}$, $q^{2}$, $E_{\ell}^{B}$, $P_{+}$ and $P_{-}$. For each variable, the entries is ordered for the first, second and third moments.

Transverse mass $m_T$ spectrum at midrapidity of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 158 GeV/c. $m_0$ is the PDG mass of the $\phi$ meson.

Transverse mass $m_T$ spectrum at midrapidity of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 80 GeV/c. $m_0$ is the PDG mass of the $\phi$ meson.

Dependence of the slope parameter $T$ of the transverse momentum spectrum on rapidity $y$, of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 158 GeV/c.

Dependence of the slope parameter $T$ of the transverse momentum spectrum on rapidity $y$, of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 80 GeV/c.

Dependence of the width $\sigma_y$ of the rapidity distributions on $p_T$, of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 158 GeV/c.

Dependence of the width $\sigma_y$ of the rapidity distributions on $p_T$, of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 80 GeV/c.

Rapidity spectrum of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 158 GeV/c.

Rapidity spectrum of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 80 GeV/c.

Rapidity spectrum of $\phi$ mesons produced in minimum bias p+p collisions at beam momentum of 40 GeV/c.

Energy dependence of ratios of total yields of $\phi$ mesons to mean total yields of pions produced in in minimum bias p+p collisions at CERN SPS energies.

Energy dependence of double ratios of total yields of $\phi$ mesons to mean total yields of pions in central Pb+Pb collisions over minimum bias p+p collisions at CERN SPS energies.

Energy dependence of total yields of $\phi$ mesons produced in minimum bias p+p collisions at CERN SPS energies.

Energy dependence of midrapidity yields of $\phi$ mesons produced in minimum bias p+p collisions at CERN SPS energies.

Widths of rapidity distributions of $\phi$ mesons produced in minimum bias p+p collisions at CERN SPS energies, as a function of beam rapidity.

The particle-level di-jet differential cross section. The systematic uncertainty on the data contains contributions from track finding efficiency, track transverse momentum resolution, calorimeter energy resolution, and unfolding uncertainties. For the theory, values are given for the underlying event and hadronization (UEH) correction uncertainty and the quadrature sum of the UEH and theoretical uncertainties. Both the UEH and theoretical uncertainties include contributions from factorization and renormalization scale uncertainties and PDF uncertainties. An 8.8% uncertainty common to all points due to the integrated luminosity determination is also present, but not included in the systematic values quoted below.

Values of gluon X1 and X2 obtained from the PYTHIA detector-level simulation for the same-sign di-jet topology compared to the gluon X distribution for inclusive jets. The inclusive distribution has been scaled down by a factor of 20 compared to the di-jet distributions.

Values of gluon X1 and X2 obtained from the PYTHIA detector-level simulation for the opposite-sign di-jet topology compared to the gluon X distribution for inclusive jets. The inclusive distribution has been scaled down by a factor of 20 compared to the di-jet distributions.

Di-jet A_LL asymmetry vs parton-level invariant mass for the same-sign di-jet topology. The systematic uncertainty on the mass includes contributions from jet energy scale, the correction to parton-level, and the difference between NLO and PYTHIA cross sections. The systematic uncertainty on the asymmetry includes contributions from trigger and reconstruction bias and residual transverse beam polarization components. A 6.5% uncertainty common to all points due to uncertainty on the measured beam polarizations is also present, but not included in the uncertainties quoted below.

Theoretical predictions for the di-jet A_LL asymmetry for the same-sign topology using the DSSV14 and NNPDFpol1.1 polarized PDF sets. The DSSV14 prediction is presented without uncertainty while the systematic uncertainty on the NNPDFpol1.1 prediction contains contributions from factorization and renormalization scale uncertainties and PDF uncertainties.

Di-jet A_LL asymmetry vs parton-level invariant mass for the opposite-sign di-jet topology. The systematic uncertainty on the mass includes contributions from jet energy scale, the correction to parton-level, and the difference between NLO and PYTHIA cross sections. The systematic uncertainty on the asymmetry includes contributions from trigger and reconstruction bias and residual transverse beam polarization components. A 6.5% uncertainty common to all points due to uncertainty on the measured beam polarizations is also present, but not included in the uncertainties quoted below.

Theoretical predictions for the di-jet A_LL asymmetry for the opposite-sign topology using the DSSV14 and NNPDFpol1.1 polarized PDF sets. The DSSV14 prediction is presented without uncertainty while the systematic uncertainty on the NNPDFpol1.1 prediction contains contributions from factorization and renormalization scale uncertainties and PDF uncertainties.

The amplitude of the transverse single-spin asymmetry for $W^{+-}$ boson production as a function of $P_T^W$, in the |$y^W$| < 1 region, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$. The average boson's rapidity value for each $P_T^W$ bin is $y^W=0.0$.

The amplitude of the transverse single-spin asymmetry for $W^{+-}$ boson production as a function of $y^W$, in the 0.5 GeV/c < $P_T^W$ < 10 GeV/c region, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$. The average boson's transverse-momentum value for each $y^W$-bin is $P_T^W=5.3$ GeV/c.

The amplitude of the transverse single-spin asymmetry for $Z^0$ boson production, measured by STAR in proton+proton collisions at $\sqrt{s}=500$ GeV with a recorded luminosity of 25 $pb^{-1}$.

Axis error includes +- 0.0/0.0 contribution (?////).

The slope parameter r as a function of centrality for collision energy of 200 GeV.

The slope parameter r as a function of centrality for collision energy of 62.4 GeV.

The slope parameter r as a function of centrality for collision energy of 39 GeV.

The slope parameter r as a function of centrality for collision energy of 27 GeV.

The slope parameter r as a function of centrality for collision energy of 19.6 GeV.

The slope parameter r as a function of centrality for collision energy of 11.5 GeV.

The slope parameter r as a function of centrality for collision energy of 7.7 GeV.

$e^+$ $e^-$ invariant mass pair distributions of signal pairs compared to the inclusive unlike sign and reconstructed background pairs in 200 GeV Au+Au minimum-bias collisions.

Signal-to-background ratios in minimum bias p+p and Au+Au collisions.

Signal-to-background ratios in central p+p and Au+Au collisions.

Invariant mass spectrum in the STAR acceptance ($p_T^e$ > 0.2 GeV/c, |$\eta^e$| < 1, and |$y_{ee}$|) from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions.

Invariant mass spectrum in the STAR acceptance ($p_T^e$ > 0.2 GeV/c, |$\eta^e$| < 1, and |$y_{ee}$|) from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions.

Invariant mass spectra from SQRT($s_{NN}$ = 200 GeV Au+Au minimum-bias collisions in pT range 0 - 5 GeV/c. The ratio of dielectron yield over cocktail for different pT bins, and the comparison with model calculations.

Invariant mass spectra from SQRT($s_{NN}$ = 200 GeV Au+Au minimum-bias collisions in pT range 5 - 10 GeV/c. The ratio of dielectron yield over cocktail for different pT bins, and the comparison with model calculations.

Invariant mass spectra from SQRT($s_{NN}$ = 200 GeV Au+Au minimum-bias collisions in pT range 1 - 1.5 GeV/c. The ratio of dielectron yield over cocktail for different pT bins, and the comparison with model calculations.

Invariant mass spectra from SQRT($s_{NN}$ = 200 GeV Au+Au minimum-bias collisions in pT range 1.5 - 2 GeV/c. The ratio of dielectron yield over cocktail for different pT bins, and the comparison with model calculations.

Invariant mass spectra from SQRT($s_{NN}$ = 200 GeV Au+Au minimum-bias collisions integrated. The ratio of dielectron yield over cocktail for different pT bins, and the comparison with model calculations.

The integrated dielectron yield as a function of pair pT in invariant mass range 0 - 0.15 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 0.15 - 0.3 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 0.3 - 0.76 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 0.76 - 1.05 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 1.05 - 1.8 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 1.8 - 2.8 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

The integrated dielectron yield as a function of pair pT in invariant mass range 2.8 to 3.5 GeV/c^2 compared with cocktail. The ratio of dielectron yield over cocktail for different mass ranges as a function of pair pT.

Invariant mass spectra from SQRT($s_{NN}$) = 200 GeV Au+Au collisions in different centralities. The ratio of dielectron yield over cocktail for a centrality of 0-10%.

Invariant mass spectra from SQRT($s_{NN}$) = 200 GeV Au+Au collisions in different centralities. The ratio of dielectron yield over cocktail for a centrality of 10-40%.

Invariant mass spectra from SQRT($s_{NN}$) = 200 GeV Au+Au collisions in different centralities. The ratio of dielectron yield over cocktail for a centrality of 40-80%.

Invariant mass spectra from SQRT($s_{NN}$) = 200 GeV Au+Au collisions in different centralities. The ratio of dielectron yield over cocktail for minimum bias.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 0 - 0.15 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 0.15 - 0.3 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 0.3 - 0.76 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 0.76 - 1.05 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 1.05 - 1.8 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 1.8 - 2.8 GeV/c^2, and the comparison with model calculations.

The integrated dielectron yield and ratio of dielectron yield over cocktail in different centralities for mass window 2.8 - 3.5 GeV/c^2, and the comparison with model calculations.

Dielectron invariant mass spectra from minimum-bias.

Dielectron invariant mass spectra from the most central (0-10%) collisions that we are able to achieve most statistics at present.

The ratio of the Npart-scaled dielectron yield between minimum-bias and the most central collisions.

Mass spectrum of the excess (data - cocktail) in the low-mass region in Au+Au minimum-bias collisions compared to model calculations.

The yields scaled by Npart for the $\rho$-like region with the cocktail subtracted.

The Omega-like region without cocktail subtraction as a function of Npart.

The Phi-like region without cocktail subtraction as a function of Npart.

Correlated charm contributions to the dielectron mass spectra for different assumptions of the correlation strength.

Slope parameters Teff versus invariant mass for dielectrons from charm hadron decays.

Omega meson invariant mass distribution from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions after subtraction of the combinatorial background using the mixed-event method.

Phi meson invariant mass distribution from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions after subtraction of the combinatorial background using the mixed-event method.

The widths and mass positions of the omega signal from data compared to the values from the PDG and the full Geant simulation.

The widths and mass positions of the phi signal from data compared to the values from the PDG and the full Geant simulation.

The efficiency and acceptance correction factor as function of pT for mid-rapidity omega and phi mesons.

The pT distributions of the omega meson invariant yields from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions.

The pT distributions of the phi meson invariant yields from SQRT($s_{NN}$) = 200 GeV Au+Au minimum-bias collisions.

Unlike-sign/like-sign pair acceptance difference correction factor with the PHENIX phi acceptance compared with the full acceptance.

Efficiency corrected invariant mass spectra calculated using the STAR data filtered with the PHENIX azimuthal angle acceptance. The data points are compared to cocktail simulations.

The same data points compared to theoretical model calculations of medium vector meson and QGP contributions.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{mixed}$ is plotted.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The correlation between positive and negative charged particles measured by the FTPC and photons measured by the PMD using $v_{dyn}$ for real events.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for third order of m.

$r_{m,1}$ vs multiplicity for third order of m.

The moments $r_{m,1}$(m=1-3) for real and mixed events as a function of order m in a fixed multiplicity bin of 47$\langle \sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }\langle 54$.

The $\Lambda\Lambda$ interaction parameters from this experiment.