Invariant mass distributions of $^3\hbox{He}+\pi^-$ (A), $^3\overline{\hbox{He}}+\pi^+$ (B), $^4\hbox{He}+\pi^-$ (C) and $^4\overline{\hbox{He}}+\pi^+$ (D). The solid bands mark the signal invariant mass regions. The obtained signal count ($N_{\rm Sig}$), background count ($N_{\rm Bg}$), and signal significance are listed in each panel.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

Our measured (anti)hypernuclei lifetimes compared with world data and theoretical predictions (solid triangles). Error bars and boxes represent statistical and systematic uncertainties, respectively. Vertical solid lines with shaded regions show the average lifetime of (anti)hypernuclei and their corresponding uncertainties. The vertical gray line shows the lifetime of the free $\Lambda$.

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

$dN/d(L/\beta\gamma)$ as a function of $L/\beta\gamma$ for $\Lambda$ and $\bar{\Lambda}$, and exponential fits to obtain their lifetimes.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

The $K^{*0}$ mass (upper panel) and width (lower panel) as a function of $p_T$ for minimum bias $p + p$ interactions and for central Au+Au collisions. The solid straight lines are the standard $K^{*0}$ mass (896.1 MeV/$c^2$ ) and width (50.7 MeV/$c^2$), respectively. The dashed and dotted curves are the MC results in minimum bias $p+p$ and for central Au+Au collisions, respectively, after considering detector effects and kinematic cuts. The grey shadows (caps) indicate the systematic uncertainties for the measurement in minimum bias $p + p$ interactions (central Au+Au collisions).

The $K^{*0}$ mass (upper panel) and width (lower panel) as a function of $p_T$ for minimum bias $p + p$ interactions and for central Au+Au collisions. The solid straight lines are the standard $K^{*0}$ mass (896.1 MeV/$c^2$ ) and width (50.7 MeV/$c^2$), respectively. The dashed and dotted curves are the MC results in minimum bias $p+p$ and for central Au+Au collisions, respectively, after considering detector effects and kinematic cuts. The grey shadows (caps) indicate the systematic uncertainties for the measurement in minimum bias $p + p$ interactions (central Au+Au collisions).

The $K^{*0}$ mass (upper panel) and width (lower panel) as a function of $p_T$ for minimum bias $p + p$ interactions and for central Au+Au collisions. The solid straight lines are the standard $K^{*0}$ mass (896.1 MeV/$c^2$ ) and width (50.7 MeV/$c^2$), respectively. The dashed and dotted curves are the MC results in minimum bias $p+p$ and for central Au+Au collisions, respectively, after considering detector effects and kinematic cuts. The grey shadows (caps) indicate the systematic uncertainties for the measurement in minimum bias $p + p$ interactions (central Au+Au collisions).

The $K^{*0}$ mass (upper panel) and width (lower panel) as a function of $p_T$ for minimum bias $p + p$ interactions and for central Au+Au collisions. The solid straight lines are the standard $K^{*0}$ mass (896.1 MeV/$c^2$ ) and width (50.7 MeV/$c^2$), respectively. The dashed and dotted curves are the MC results in minimum bias $p+p$ and for central Au+Au collisions, respectively, after considering detector effects and kinematic cuts. The grey shadows (caps) indicate the systematic uncertainties for the measurement in minimum bias $p + p$ interactions (central Au+Au collisions).

The $K_S^0\pi^\pm$ invariant mass distribution integrated over the $K^{*\pm}$ $p_T$ for minimum bias $p + p$ collisions (upper panel) and for the $50-80\%$ of the inelastic hadronic Au+Au crosssection (lower panel) after the mixed-event background subtraction. The solid curves are fits to Eq. 10 and the dashed lines are the linear function representing the residual background.

The $K^{*0}$ and $K^{*\pm}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in minimum bias $p + p$ and different centralities in Au+Au collisions.

The $K^{*0}$ and $K^{*\pm}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in minimum bias $p + p$ and different centralities in Au+Au collisions.

The $K^{*0}$ and $K^{*\pm}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in minimum bias $p + p$ and different centralities in Au+Au collisions.

The $K^{*0}$ and $K^{*\pm}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in minimum bias $p + p$ and different centralities in Au+Au collisions.

The $(K^* + \bar{K^*})/2$ invariant yields as a function of $m_T − m_0$ for |y| < 0.5 from minimum bias $p + p$ and different centralities in Au+Au collisions. The top $10\% $central data have been multiplied by two for clarity. The lines are fits to Eq. 12. The errors shown are the quadratic sum of statistical and systematic (in the level of $10\% $) uncertainties.

The $(K^* + \bar{K^*})/2$ invariant yields as a function of $m_T − m_0$ for |y| < 0.5 from minimum bias $p + p$ and different centralities in Au+Au collisions. The top $10\% $central data have been multiplied by two for clarity. The lines are fits to Eq. 12. The errors shown are the quadratic sum of statistical and systematic (in the level of $10\% $) uncertainties.

The $(K^* + \bar{K^*})/2$ invariant yields as a function of $m_T − m_0$ for |y| < 0.5 from minimum bias $p + p$ and different centralities in Au+Au collisions. The top $10\% $central data have been multiplied by two for clarity. The lines are fits to Eq. 12. The errors shown are the quadratic sum of statistical and systematic (in the level of $10\% $) uncertainties.

(Color online) The invariant yields for both $(K^{*0} + \bar{K^{*0}})/2$ and $(K^{*+} + K^{*-})/2$ as a function of $p_T$ for |y| < 0.5 in minimum bias $p + p$ interactions. The dotted curve is the fit to the power-law function from Equation 13 for $p_T$ > 0.5 GeV/$c$ and extended to lower values of $p_T$ . The dashed curve is the $K^{*0}$ spectrum fit to the exponential function from Equation 12 and extended to higher values of $p_T$ . The dashed-dotted curve is the fit to the Levy function from Equation 14 for $p_T$ < 4 GeV/$c$. Errors are statistical only.

(Color online) The invariant yields for both $(K^{*0} + \bar{K^{*0}})/2$ and $(K^{*+} + K^{*-})/2$ as a function of $p_T$ for |y| < 0.5 in minimum bias $p + p$ interactions. The dotted curve is the fit to the power-law function from Equation 13 for $p_T$ > 0.5 GeV/$c$ and extended to lower values of $p_T$ . The dashed curve is the $K^{*0}$ spectrum fit to the exponential function from Equation 12 and extended to higher values of $p_T$ . The dashed-dotted curve is the fit to the Levy function from Equation 14 for $p_T$ < 4 GeV/$c$. Errors are statistical only.

(Color online) The $K^*$ $<p_T>$ as a function of $dN_{ch}/d\eta$ compared to that of $\pi^−$, $K^−$, and $p$ for minimum bias $p+p$ (solid symbols) and Au+Au (open symbols) collisions. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

The $K^*/K$ (upper panel) and $\phi/K^*$ (lower panel) yield ratios as a function of the c.m. system energies. The yield ratios for central Au+Au collisions at $\sqrt{s_{NN}}$=130 [35] and 200 GeV and minimum bias $p+p$ interactions at $\sqrt{s_{NN}}$=200 GeV are compared to measurements from e+e- at sqrt(s) of 10.45 GeV [48], 29 GeV [49] and 91 GeV [50,51], pbar-p at sqrt(s) of 5.6 GeV [52] and pp at sqrt(s) of 27.5 GeV [53], 52.5 GeV [54] and 63 GeV [55]. The errors at $\sqrt{s_{NN}}$=130 and 200 GeV correspond to the quadratic sum of the statistical and systematic errors.

The $K^*/K$ (upper panel) and $\phi/K^*$ (lower panel) yield ratios as a function of the c.m. system energies. The yield ratios for central Au+Au collisions at $\sqrt{s_{NN}}$=130 [35] and 200 GeV and minimum bias $p+p$ interactions at $\sqrt{s_{NN}}$=200 GeV are compared to measurements from e+e- at sqrt(s) of 10.45 GeV [48], 29 GeV [49] and 91 GeV [50,51], pbar-p at sqrt(s) of 5.6 GeV [52] and pp at sqrt(s) of 27.5 GeV [53], 52.5 GeV [54] and 63 GeV [55]. The errors at $\sqrt{s_{NN}}$=130 and 200 GeV correspond to the quadratic sum of the statistical and systematic errors.

The $K^{*0}$ v2 (filled stars) as a function of $p_T$ for minimum bias Au+Au collisions compared to the $K^{0}_S$ (open triangles), $\Lambda$ (open circles), and charged hadron (open diamonds) $v_2$. The errors shown are statistical only.

The $K^*$ $R_{AA}$ (filled triangles) and $R_{CP}$ (filled circles) as a function of $p_T$ compared to the $K^{0}_S$ (open circles) and $\Lambda$ (open triangles) $R_{CP}$. The errors shown are statistical only. The dashed line represents the number of binary collisions scaling. The widths of the grey bands represent the systematic uncertainties of $R_{AA}$ (left) and $R_{CP}$ (right) due to the model calculations of $N_{bin}$.