Systematic studies of the centrality and s(NN)**(1/2) dependence of dE(T)/d mu and d N(ch)/d mu in heavy ion collisions at mid-rapidity.

The PHENIX collaboration Adler, S.S. ; Afanasiev, S. ; Aidala, C. ; et al.
Phys.Rev.C 71 (2005) 034908, 2005.
Inspire Record 659749 DOI 10.17182/hepdata.142940

The PHENIX experiment at RHIC has measured transverse energy and charged particle multiplicity at mid-rapidity in Au+Au collisions at sqrt(s_NN) = 19.6, 130 and 200 GeV as a function of centrality. The presented results are compared to measurements from other RHIC experiments, and experiments at lower energies. The sqrt(s_NN) dependence of dE_T/deta and dN_ch/deta per pair of participants is consistent with logarithmic scaling for the most central events. The centrality dependence of dE_T/deta and dN_ch/deta is similar at all measured incident energies. At RHIC energies the ratio of transverse energy per charged particle was found independent of centrality and growing slowly with sqrt(s_NN). A survey of comparisons between the data and available theoretical models is also presented.

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$B$/$A$ ratio from the fit to the data.

$B$/$A$ ratio from the fit to the data.

Parameter $\alpha$ from the fit to the data.

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First Observation of Directed Flow of Hypernuclei $^3_{\Lambda}$H and $^4_{\Lambda}$H in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au Collisions at RHIC

The STAR collaboration Aboona, Bassam ; Adam, Jaroslav ; Adams, Joseph ; et al.
Phys.Rev.Lett. 130 (2023) 212301, 2023.
Inspire Record 2605845 DOI 10.17182/hepdata.136028

We report here the first observation of directed flow ($v_1$) of the hypernuclei $^3_{\Lambda}$H and $^4_{\Lambda}$H in mid-central Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV at RHIC. These data are taken as part of the beam energy scan program carried out by the STAR experiment. From 165 $\times$ 10$^{6}$ events in 5%-40% centrality, about 8400 $^3_{\Lambda}$H and 5200 $^4_{\Lambda}$H candidates are reconstructed through two- and three-body decay channels. We observe that these hypernuclei exhibit significant directed flow. Comparing to that of light nuclei, it is found that the midrapidity $v_1$ slopes of $^3_{\Lambda}$H and $^4_{\Lambda}$H follow baryon number scaling, implying that the coalescence is the dominant mechanism for these hypernuclei production in such collisions.

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$\Lambda$ hyperon and hypernuclei directed flow $v_1$, shown as a function of rapidity, from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. In the case of $^{3}_{\Lambda}$H $v_1$, both two-body (dots) and three-body (triangles) decays are used. The linear terms of the fitting for $#Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H are shown as the yellow-red lines. The rapidity dependence of $v_1$ for $p$, $d$, $t$, $^3$He, and $^4$He are also shown as open markers (circles, diamonds, up-triangles, down-triangles and squares), and the linear terms of the fitting results are shown as dashed lines in the positive rapidity region.

$\Lambda$ hyperon and hypernuclei directed flow $v_1$, shown as a function of rapidity, from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. In the case of $^{3}_{\Lambda}$H $v_1$, both two-body (dots) and three-body (triangles) decays are used. The linear terms of the fitting for $#Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H are shown as the yellow-red lines. The rapidity dependence of $v_1$ for $p$, $d$, $t$, $^3$He, and $^4$He are also shown as open markers (circles, diamonds, up-triangles, down-triangles and squares), and the linear terms of the fitting results are shown as dashed lines in the positive rapidity region.

$\Lambda$ hyperon and hypernuclei directed flow $v_1$, shown as a function of rapidity, from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. In the case of $^{3}_{\Lambda}$H $v_1$, both two-body (dots) and three-body (triangles) decays are used. The linear terms of the fitting for $#Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H are shown as the yellow-red lines. The rapidity dependence of $v_1$ for $p$, $d$, $t$, $^3$He, and $^4$He are also shown as open markers (circles, diamonds, up-triangles, down-triangles and squares), and the linear terms of the fitting results are shown as dashed lines in the positive rapidity region.

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Higher-Order Cumulants and Correlation Functions of Proton Multiplicity Distributions in $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV Au+Au Collisions at the STAR Experiment

The STAR collaboration Abdallah, Mohamed ; Aboona, Bassam ; Adam, Jaroslav ; et al.
Phys.Rev.C 107 (2023) 024908, 2023.
Inspire Record 2631860 DOI 10.17182/hepdata.134023

We report a measurement of cumulants and correlation functions of event-by-event proton multiplicity distributions from fixed-target Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV measured by the STAR experiment. Protons are identified within the rapidity ($y$) and transverse momentum ($p_{\rm T}$) region $-0.9 < y<0$ and $0.4 < p_{\rm T} <2.0 $ GeV/$c$ in the center-of-mass frame. A systematic analysis of the proton cumulants and correlation functions up to sixth-order as well as the corresponding ratios as a function of the collision centrality, $p_{\rm T}$, and $y$ are presented. The effect of pileup and initial volume fluctuations on these observables and the respective corrections are discussed in detail. The results are compared to calculations from the hadronic transport UrQMD model as well as a hydrodynamic model. In the most central 5% collisions, the value of proton cumulant ratio $C_4/C_2$ is negative, drastically different from the values observed in Au+Au collisions at higher energies. Compared to model calculations including Lattice QCD, a hadronic transport model, and a hydrodynamic model, the strong suppression in the ratio of $C_4/C_2$ at 3 GeV Au+Au collisions indicates an energy regime dominated by hadronic interactions.

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The uncorrected number of charged particles except protons ($N_{\rm ch}$) within the pseudorapidity $−2<\eta<0$ used for the centrality selection for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The centrality classes are expressed in % of the total cross section. The lower boundary of the particle multiplicity ($N_{\rm ch}$) is included for each centrality class. Values are provided for the average number of participants ($\langle N_{\rm part}\rangle$) and pileup fraction. The fraction of pileup for each centrality bin is also shown in the last column. The averaged pileup fraction from the minimum biased collisions is determined to be 0.46%. Values in the parentheses are systematic uncertainty.

The centrality definition determined by $N_{\rm part}$ in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV from the UrQMD model. The centrality definition is only used in the UrQMD calculation.

Main contributors to systematic uncertainty to the proton cumulant ratios: $C_2/C_1$, $C_3/C_2$,and $C_4/C_2$ from 0–5% central 3 GeV Au+Au collisions. The first row shows the values and statistical uncertainties of those ratios. The corresponding values of these ratios along with the statistical uncertainties are listed in the table. The final total value is the quadratic sum of uncertainties from centrality, pileup, and the dominant contribution from TPC hits, DCA, TOF $m^2$, and detector efficiency. Clearly, this analysis is systematically dominant.

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Flow and interferometry results from Au+Au collisions at $\sqrt{\textit{s}_{NN}}$ = 4.5 GeV

The STAR collaboration Adam, J. ; Adamczyk, L. ; Adams, J.R. ; et al.
Phys.Rev.C 103 (2021) 034908, 2021.
Inspire Record 1809043 DOI 10.17182/hepdata.95903

The Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) was extended to energies below $\sqrt{\textit{s}_{NN}}$ = 7.7 GeV in 2015 by successful implementation of the fixed-target mode of operation in the STAR (Solenoidal Track At RHIC) experiment. In the fixed-target mode, ions circulate in one ring of the collider and interact with a stationary target at the entrance of the STAR Time Projection Chamber. The first results for Au+Au collisions at $\sqrt{\textit{s}_{NN}}$ = 4.5 GeV are presented, including directed and elliptic flow of identified hadrons, and radii from pion femtoscopy. The proton flow and pion femtoscopy results agree quantitatively with earlier measurements by Alternating Gradient Synchrotron experiments at similar energies. This validates running the STAR experiment in the fixed-target configuration. Pion directed and elliptic flow are presented for the first time at this beam energy. Pion and proton elliptic flow show behavior which hints at constituent quark scaling, but large error bars preclude reliable conclusions. The ongoing second phase of BES (BES-II) will provide fixed-target data sets with 100 times more events at each of several energies down to $\sqrt{\textit{s}_{NN}}$ = 3.0 GeV.

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Centrality selection for STAR FXT sqrt(sNN) = 4.5 GeV Au+Au collisions

Rapidity dependence of directed flow, v1(y), for protons with transverse momentum 0.4 < pT < 2.0 GeV/c from events with 10-25% centrality.

Rapidity dependence of directed flow, v1(y), for negative pions with transverse momentum pT > 0.2 GeV/c and total momentum magnitude |p| < 1.6 GeV/c from events within 10-30% centrality. Here, the BBC-based Event Plane method is used. Plotted error bars are statistical only, and systematic errors are of comparable size.

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Probing Strangeness Canonical Ensemble with $K^{-}$, $\phi(1020)$ and $\Xi^{-}$ Production in Au+Au Collisions at ${\sqrt{s_{NN}} = {3\,GeV}}$

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Lett.B 831 (2022) 137152, 2022.
Inspire Record 1897327 DOI 10.17182/hepdata.110657

We report the first multi-differential measurements of strange hadrons of $K^{-}$, $\phi$ and $\Xi^{-}$ yields as well as the ratios of $\phi/K^-$ and $\phi/\Xi^-$ in Au+Au collisions at ${\sqrt{s_{\rm NN}} = \rm{3\,GeV}}$ with the STAR experiment fixed target configuration at RHIC. The $\phi$ mesons and $\Xi^{-}$ hyperons are measured through hadronic decay channels, $\phi\rightarrow K^+K^-$ and $\Xi^-\rightarrow \Lambda\pi^-$. Collision centrality and rapidity dependence of the transverse momentum spectra for these strange hadrons are presented. The $4\pi$ yields and ratios are compared to thermal model and hadronic transport model predictions. At this collision energy, thermal model with grand canonical ensemble (GCE) under-predicts the $\phi/K^-$ and $\phi/\Xi^-$ ratios while the result of canonical ensemble (CE) calculations reproduce $\phi/K^-$, with the correlation length $r_c \sim 2.7$ fm, and $\phi/\Xi^-$, $r_c \sim 4.2$ fm, for the 0-10% central collisions. Hadronic transport models including high mass resonance decays could also describe the ratios. While thermal calculations with GCE work well for strangeness production in high energy collisions, the change to CE at $\rm{3\,GeV}$ implies a rather different medium property at high baryon density.

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$K^-$ (a), invariant yields as a function of $m_T-m_0$ for various rapidity regions in 0--10\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\phi$ meson (b) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 0--10\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\Xi^-$ (c) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 0--10\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

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Measurements of Proton High Order Cumulants in 3 GeV Au+Au Collisions and Implications for the QCD Critical Point

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Rev.Lett. 128 (2022) 202303, 2022.
Inspire Record 1981670 DOI 10.17182/hepdata.115559

We report cumulants of the proton multiplicity distribution from dedicated fixed-target Au+Au collisions at 3.0 GeV, measured by the STAR experiment in the kinematic acceptance of rapidity ($y$) and transverse momentum ($p_{\rm T}$) within $-0.5 < y<0$ and $0.4 < p_{\rm T} <2.0 $ GeV/$c$. In the most central 0--5% collisions, a proton cumulant ratio is measured to be $C_4/C_2=-0.85 \pm 0.09 ~(\rm stat.) \pm 0.82 ~(\rm syst.)$, which is less than unity, the Poisson baseline. The hadronic transport UrQMD model reproduces our $C_4/C_2$ in the measured acceptance. Compared to higher energy results and the transport model calculations, the suppression in $C_4/C_2$ is consistent with fluctuations driven by baryon number conservation and indicates an energy regime dominated by hadronic interactions. These data imply that the QCD critical region, if created in heavy-ion collisions, could only exist at energies higher than 3 GeV.

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$\sqrt{s_{NN}}$ = 3.0 GeV data (black markers), GM (red histogram), and single and pile-up contributions from unfolding. Vertical lines on markers represent statistical uncertainties. Single, pile-up and single+pile-up collisions are shown in solid blue markers, dashed green and dashed magenta curves, respectively. Analysis is performed on 0–5% central events, indicated by a black arrow.

$\sqrt{s_{NN}}$ = 3.0 GeV data (black markers), GM (red histogram), and single and pile-up contributions from unfolding. Vertical lines on markers represent statistical uncertainties. Single, pile-up and single+pile-up collisions are shown in solid blue markers, dashed green and dashed magenta curves, respectively. Analysis is performed on 0–5% central events, indicated by a black arrow.

Centrality dependence of the proton cumulant ratios for Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV. Protons are from $-0.5 < y < 0$ and $0.4 < p_{T} < 2.0$ GeV/$c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $\langle N_{\rm{part}} \rangle$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as gold dashed line.

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Measurements of ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$ Lifetimes and Yields in Au+Au Collisions in the High Baryon Density Region

The STAR collaboration Abdallah, Mohamed ; Aboona, Bassam ; Adam, Jaroslav ; et al.
Phys.Rev.Lett. 128 (2022) 202301, 2022.
Inspire Record 1946124 DOI 10.17182/hepdata.114372

We report precision measurements of hypernuclei ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$ lifetimes obtained from Au+Au collisions at \snn = 3.0 GeV and 7.2 GeV collected by the STAR experiment at RHIC, and the first measurement of ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$ mid-rapidity yields in Au+Au collisions at \snn = 3.0 GeV. ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$, being the two simplest bound states composed of hyperons and nucleons, are cornerstones in the field of hypernuclear physics. Their lifetimes are measured to be $221\pm15(\rm stat.)\pm19(\rm syst.)$ ps for ${}^3_\Lambda \rm{H}$ and $218\pm6(\rm stat.)\pm13(\rm syst.)$ ps for ${}^4_\Lambda \rm{H}$. The $p_T$-integrated yields of ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$ are presented in different centrality and rapidity intervals. It is observed that the shape of the rapidity distribution of ${}^4_\Lambda \rm{H}$ is different for 0--10% and 10--50% centrality collisions. Thermal model calculations, using the canonical ensemble for strangeness, describes the ${}^3_\Lambda \rm{H}$ yield well, while underestimating the ${}^4_\Lambda \rm{H}$ yield. Transport models, combining baryonic mean-field and coalescence (JAM) or utilizing dynamical cluster formation via baryonic interactions (PHQMD) for light nuclei and hypernuclei production, approximately describe the measured ${}^3_\Lambda \rm{H}$ and ${}^4_\Lambda \rm{H}$ yields. Our measurements provide means to precisely assess our understanding of the fundamental baryonic interactions with strange quarks, which can impact our understanding of more complicated systems involving hyperons, such as the interior of neutron stars or exotic hypernuclei.

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The measured $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H lifetimes from STAR (2021)

B.R. times dN/dy of $^{3}_{\Lambda}$H vs y in 3 GeV 0-10% Au+Au collisions

B.R. times dN/dy of $^{4}_{\Lambda}$H vs y in 3 GeV 0-10% Au+Au collisions

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Disappearance of partonic collectivity in $\sqrt{s_{NN}}$ = 3 GeV Au+Au collisions at RHIC

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Lett.B 827 (2022) 137003, 2022.
Inspire Record 1897294 DOI 10.17182/hepdata.110656

We report on the measurements of directed flow $v_1$ and elliptic flow $v_2$ for hadrons ($\pi^{\pm}$, $K^{\pm}$, $K_{S}^0$, $p$, $\phi$, $\Lambda$ and $\Xi^{-}$) from Au+Au collisions at $\sqrt{s_{NN}}$ = 3 GeV and $v_{2}$ for ($\pi^{\pm}$, $K^{\pm}$, $p$ and $\overline{p}$) at 27 and 54.4 GeV with the STAR experiment. While at the two higher energy midcentral collisions the number-of-constituent-quark (NCQ) scaling holds, at 3 GeV the $v_{2}$ at midrapidity is negative for all hadrons and the NCQ scaling is absent. In addition, the $v_1$ slopes at midrapidity for almost all observed hadrons are found to be positive, implying dominant repulsive baryonic interactions. The features of negative $v_2$ and positive $v_1$ slope at 3 GeV can be reproduced with a baryonic mean-field in transport model calculations. These results imply that the medium in such collisions is likely characterized by baryonic interactions.

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Event plane resolution as a function of collision centrality from Au+Au collisions at $\sqrt{s_{NN}}$=3 (a), 27 and 54.4 GeV (b). In case of the 3 GeV collisions, $\Psi_{1}$ is used to determine the event plane resolutions for the first and second harmonic coefficients shown as $R_{11}$ and $R_{12}$ in left panel. In the 27 and 54.4 GeV collisions, $\Psi_{2}$ is used to evaluate the second order event plane resolution, see right panel. In all cases, the statistic uncertainties are smaller than symbol sizes.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

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Light Nuclei Collectivity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au Collisions at RHIC

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Lett.B 827 (2022) 136941, 2022.
Inspire Record 1986611 DOI 10.17182/hepdata.115569

In high-energy heavy-ion collisions, partonic collectivity is evidenced by the constituent quark number scaling of elliptic flow anisotropy for identified hadrons. A breaking of this scaling and dominance of baryonic interactions is found for identified hadron collective flow measurements in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. In this paper, we report measurements of the first- and second-order azimuthal anisotropic parameters, $v_1$ and $v_2$, of light nuclei ($d$, $t$, $^{3}$He, $^{4}$He) produced in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions at the STAR experiment. An atomic mass number scaling is found in the measured $v_1$ slopes of light nuclei at mid-rapidity. For the measured $v_2$ magnitude, a strong rapidity dependence is observed. Unlike $v_2$ at higher collision energies, the $v_2$ values at mid-rapidity for all light nuclei are negative and no scaling is observed with the atomic mass number. Calculations by the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, are in good agreement with our observations, implying baryonic interactions dominate the collective dynamics in 3 GeV Au+Au collisions at RHIC.

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The rapidity and $p_{T}$ dependencies of $v_{1}$ for $p$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{1}$ for $d$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{1}$ within $-0.1<y<0$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

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Global $\Lambda$-hyperon polarization in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Rev.C 104 (2021) L061901, 2021.
Inspire Record 1897216 DOI 10.17182/hepdata.110658

Global hyperon polarization, $\overline{P}_\mathrm{H}$, in Au+Au collisions over a large range of collision energy, $\sqrt{s_\mathrm{NN}}$, was recently measured and successfully reproduced by hydrodynamic and transport models with intense fluid vorticity of the quark-gluon plasma. While naïve extrapolation of data trends suggests a large $\overline{P}_\mathrm{H}$ as the collision energy is reduced, the behavior of $\overline{P}_\mathrm{H}$ at small $\sqrt{s_\mathrm{NN}}<7.7$ GeV is unknown. Operating the STAR experiment in fixed-target mode, we measured the polarization of $\Lambda$ hyperons along the direction of global angular momentum in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV. The observation of substantial polarization of $4.91\pm0.81(\rm stat.)\pm0.15(\rm syst.)$% in these collisions may require a reexamination of the viscosity of any fluid created in the collision, of the thermalization timescale of rotational modes, and of hadronic mechanisms to produce global polarization.

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The measured invariant-mass distributions of two classes of $\Lambda$-hyperon decays. The decay classes are defined using the scalar triple product $\left(\vec{p}_\Lambda\times\vec{p}_p^*\right)\cdot \vec{B}_{\rm STAR}$, which is positive for right decays and negative for left decays. The right decay class has a notably sharper invariant-mass distribution than the left decay class, and this is due to the effects of daughter tracks crossing in the STAR TPC with the STAR magnetic field anti-parallel to the lab frame's z direction. The opposite pattern is obtained by flipping the sign of the STAR magnetic field or by reconstructing $\bar{\Lambda}$ hyperons.

The signal polarizations extracted according to the restricted invariant-mass method as a function of $\phi_\Lambda - \phi_p^*$, for positive-rapidity $\Lambda$ hyperons. The sinusoidal behavior is driven by non-zero net $v_1$. The vertical shift corresponds to the vorticity-driven polarization; in collider mode, where the net $v_1$ is zero, this dependence on $\phi_\Lambda - \phi_p^*$ does not exist.

The integrated Global $\Lambda$-hyperon Polarization in mid-central collisions at $\sqrt{s_{\rm NN}}=3$ GeV. The trend of increasing $\overline{P}_{\rm H}$ with decreasing $\sqrt{s_{\rm NN}}$ is maintained at this low collision energy. Previous experimental results are scaled by the updated $\Lambda$-hyperon decay parameter $\alpha_\Lambda=0.732$ for comparison with this result. Recent model calculations extended to low collision energy show disagreement between our data and AMPT and rough agreement with the 3-Fluid Dynamics (3FD) model. Previous measurements shown alongside our data can be found at: https://www.hepdata.net/record/ins750410?version=2; https://www.hepdata.net/record/ins1510474?version=1; https://www.hepdata.net/record/ins1672785?version=2; https://www.hepdata.net/record/ins1752507?version=2.

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