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L. Holub

Publications and source records attributed to L. Holub.

At least 37 records · Page 2Linked to original sources

Beam Energy Dependence of Fifth and Sixth-Order Net-proton Number Fluctuations in Au+Au Collisions at RHIC

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants ($C_{5}$, $C_{6}$) and factorial cumulants ($κ_{5}$, $κ_{6}$) of net-proton and proton distributions, from $\sqrt{s_{NN}} = 3 - 200$ GeV Au+Au collisions at RHIC. The net-proton cumulant ratios generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at $\sqrt{s_{NN}}$ = 3 GeV. $C_{6}/C_{2}$ for 0-40\% centrality collisions is increasingly negative with decreasing $\sqrt{s_{NN}}$, while it is positive for the lowest $\sqrt{s_{NN}}$ studied. These observed negative signs are consistent with QCD calculations (at baryon chemical potential, $μ_{B} \leq$ 110 MeV) that include a crossover quark-hadron transition. In addition, for $\sqrt{s_{NN}} \geq$ 11.5 GeV, the measured proton $κ_{n}$, within uncertainties, does not support the two-component shape of proton distributions that would be expected from a first-order phase transition. Taken in combination, the hyper-order proton number fluctuations suggest that the structure of QCD matter at high baryon density, $μ_{B}\sim 750$ MeV ($\sqrt{s_{NN}}$ = 3 GeV) is starkly different from those at vanishing $μ_{B}\sim 20$MeV ($\sqrt{s_{NN}}$ = 200 GeV and higher).

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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 RHIC STAR Experiment

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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Azimuthal anisotropy measurement of (multi-)strange hadrons in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 54.4 GeV

Azimuthal anisotropy of produced particles is one of the most important observables used to access the collective properties of the expanding medium created in relativistic heavy-ion collisions. In this paper, we present second ($v_{2}$) and third ($v_{3}$) order azimuthal anisotropies of $K_{S}^{0}$, $ϕ$, $Λ$, $Ξ$ and $Ω$ at mid-rapidity ($|y|<$1) in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 54.4 GeV measured by the STAR detector. The $v_{2}$ and $v_{3}$ are measured as a function of transverse momentum and centrality. Their energy dependence is also studied. $v_{3}$ is found to be more sensitive to the change in the center-of-mass energy than $v_{2}$. Scaling by constituent quark number is found to hold for $v_{2}$ within 10%. This observation could be evidence for the development of partonic collectivity in 54.4 GeV Au+Au collisions. Differences in $v_{2}$ and $v_{3}$ between baryons and anti-baryons are presented, and ratios of $v_{3}$/$v_{2}^{3/2}$ are studied and motivated by hydrodynamical calculations. The ratio of $v_{2}$ of $ϕ$ mesons to that of anti-protons ($v_{2}(ϕ)/v_{2}(\bar{p})$) shows centrality dependence at low transverse momentum, presumably resulting from the larger effects from hadronic interactions on anti-proton $v_{2}$.

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Measurement of $\rm ^4_ΛH$ and $\rm ^4_ΛHe$ binding energy in Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 3 GeV

Measurements of mass and $Λ$ binding energy of $\rm ^4_ΛH$ and $\rm ^4_ΛHe$ in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=3$ GeV are presented, with an aim to address the charge symmetry breaking (CSB) problem in hypernuclei systems with atomic number A = 4. The $Λ$ binding energies are measured to be $\rm 2.22\pm0.06(stat.) \pm0.14(syst.)$ MeV and $\rm 2.38\pm0.13(stat.) \pm0.12(syst.)$ MeV for $\rm ^4_ΛH$ and $\rm ^4_ΛHe$, respectively. The measured $Λ$ binding-energy difference is $\rm 0.16\pm0.14(stat.)\pm0.10(syst.)$ MeV for ground states. Combined with the $γ$-ray transition energies, the binding-energy difference for excited states is $\rm -0.16\pm0.14(stat.)\pm0.10(syst.)$ MeV, which is negative and comparable to the value of the ground states within uncertainties. These new measurements on the $Λ$ binding-energy difference in A = 4 hypernuclei systems are consistent with the theoretical calculations that result in $\rm ΔB_Λ^4(1_{exc}^{+})\approx -ΔB_Λ^4(0_{g.s.}^{+})<0$ and present a new method for the study of CSB effect using relativistic heavy-ion collisions.

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Azimuthal transverse single-spin asymmetries of inclusive jets and identified hadrons within jets from polarized $pp$ collisions at $\sqrt{s}$ = 200 GeV

The STAR Collaboration reports measurements of the transverse single-spin asymmetries, $A_N$, for inclusive jets and identified `hadrons within jets' production at midrapidity from transversely polarized $pp$ collisions at $\sqrt{s}$ = 200 GeV, based on data recorded in 2012 and 2015. The inclusive jet asymmetry measurements include $A_N$ for inclusive jets and $A_N$ for jets containing a charged pion carrying a momentum fraction $z>0.3$ of the jet momentum. The identified hadron within jet asymmetry measurements include the Collins effect for charged pions, kaons and protons, and the Collins-like effect for charged pions. The measured asymmetries are determined for several distinct kinematic regions, characterized by the jet transverse momentum $p_{T}$ and pseudorapidity $η$, as well as the hadron momentum fraction $z$ and momentum transverse to the jet axis $j_{T}$. These results probe higher momentum scales ($Q^{2}$ up to $\sim$\,900 GeV$^{2}$) than current, semi-inclusive deep inelastic scattering measurements, and they provide new constraints on quark transversity in the proton and enable tests of evolution, universality and factorization breaking in the transverse-momentum-dependent formalism.

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Pair invariant mass to isolate background in the search for the chiral magnetic effect in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$= 200 GeV

Quark interactions with topological gluon configurations can induce local chirality imbalance and parity violation in quantum chromodynamics, which can lead to the chiral magnetic effect (CME) -- an electric charge separation along the strong magnetic field in relativistic heavy-ion collisions. The CME-sensitive azimuthal correlator observable ($Δγ$) is contaminated by background arising, in part, from resonance decays coupled with elliptic anisotropy ($v_{2}$). We report here differential measurements of the correlator as a function of the pair invariant mass ($m_{\rm inv}$) in 20-50\% centrality Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$= 200 GeV by the STAR experiment at RHIC. Strong resonance background contributions to $Δγ$ are observed. At large $m_{\rm inv}$ where this background is significantly reduced, the $Δγ$ value is found to be significantly smaller. An event-shape-engineering technique is deployed to determine the $v_{2}$ background shape as a function of $m_{\rm inv}$. We extract a $v_2$-independent and $m_{\rm inv}$-averaged signal $Δγ_{\rm sig}$ = (0.03 $\pm$ 0.06 $\pm$ 0.08) $\times10^{-4}$, or $(2\pm4\pm5)\%$ of the inclusive $Δγ(m_{\rm inv}>0.4$ GeV/$c^2$)$ =(1.58 \pm 0.02 \pm 0.02) \times10^{-4}$, within pion $p_{T}$ = 0.2 - 0.8~\gevc and averaged over pseudorapidity ranges of $-1 < η< -0.05$ and $0.05 < η< 1$. This represents an upper limit of $0.23\times10^{-4}$, or $15\%$ of the inclusive result, at $95\%$ confidence level for the $m_{\rm inv}$-integrated CME contribution.

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Collision energy dependence of second-order off-diagonal and diagonal cumulants of net-charge, net-proton and net-kaon multiplicity distributions in Au+Au collisions

We report the first measurements of a complete second-order cumulant matrix of net-charge, net-proton, and net-kaon multiplicity distributions for the first phase of the beam energy scan program at RHIC. This includes the centrality and, for the first time, the pseudorapidity window dependence of both diagonal and off-diagonal cumulants in Au+Au collisions at \sNN~= 7.7-200 GeV. Within the available acceptance of $|η|<0.5$, the cumulants grow linearly with the pseudorapidity window. Relative to the corresponding measurements in peripheral collisions, the ratio of off-diagonal over diagonal cumulants in central collisions indicates an excess correlation between net-charge and net-kaon, as well as between net-charge and net-proton. The strength of such excess correlation increases with the collision energy. The correlation between net-proton and net-kaon multiplicity distributions is observed to be negative at \sNN~= 200 GeV and change to positive at the lowest collision energy. Model calculations based on non-thermal (UrQMD) and thermal (HRG) production of hadrons cannot explain the data. These measurements will help map the QCD phase diagram, constrain hadron resonance gas model calculations, and provide new insights on the energy dependence of baryon-strangeness correlations. An erratum has been added to address the issue of self-correlation in the previously considered efficiency correction for off-diagonal cumulant measurement. Previously considered unidentified (net-)charge correlation results ($σ^{11}_{Q,p}$ and $σ^{11}_{Q,k})$ are now replaced with identified (net-)charge correlation ($σ^{11}_{Q^{PID},p}$ and $σ^{11}_{Q^{PID},k}$)

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Non-monotonic energy dependence of net-proton number fluctuations

Non-monotonic variation with collision energy ($\sqrt{s_{\rm NN}}$) of the moments of the net-baryon number distribution in heavy-ion collisions, related to the correlation length and the susceptibilities of the system, is suggested as a signature for the Quantum Chromodynamics (QCD) critical point. We report the first evidence of a non-monotonic variation in kurtosis times variance of the net-proton number (proxy for net-baryon number) distribution as a function of \rootsnn with 3.1$σ$ significance, for head-on (central) gold-on-gold (Au+Au) collisions measured using the STAR detector at RHIC. Data in non-central Au+Au collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of $\sqrt{s_{\rm NN}}$.

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Observation of $D_{s}^{\pm}/D^0$ enhancement in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$ = 200 GeV

We report on the first measurement of charm-strange meson $D_s^{\pm}$ production at midrapidity in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$ = 200 GeV from the STAR experiment. The yield ratio between strange ($D_{s}^{\pm}$) and non-strange ($D^{0}$) open-charm mesons is presented and compared to model calculations. A significant enhancement, relative to a PYTHIA simulation of $p$+$p$ collisions, is observed in the $D_{s}^{\pm}/D^0$ yield ratio in Au+Au collisions over a large range of collision centralities. Model calculations incorporating abundant strange-quark production in the quark-gluon plasma (QGP) and coalescence hadronization qualitatively reproduce the data. The transverse-momentum integrated yield ratio of $D_{s}^{\pm}/D^0$ at midrapidity is consistent with a prediction from a statistical hadronization model with the parameters constrained by the yields of light and strange hadrons measured at the same collision energy. These results suggest that the coalescence of charm quarks with strange quarks in the QGP plays an important role in $D_{s}^{\pm}$ meson production in heavy-ion collisions.

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Measurement of transverse single-spin asymmetries of $π^0$ and electromagnetic jets at forward rapidity in 200 and 500 GeV transversely polarized proton-proton collisions

The STAR Collaboration reports measurements of the transverse single-spin asymmetry (TSSA) of inclusive $π^0$ at center-of-mass energies ($\sqrt s$) of 200 GeV and 500 GeV in transversely polarized proton-proton collisions in the pseudo-rapidity region 2.7 to 4.0. The results at the two different energies show a continuous increase of the TSSA with Feynman-$x$, and, when compared to previous measurements, no dependence on $\sqrt s$ from 19.4 GeV to 500 GeV is found. To investigate the underlying physics leading to this large TSSA, different topologies have been studied. $π^0$ with no nearby particles tend to have a higher TSSA than inclusive $π^0$. The TSSA for inclusive electromagnetic jets, sensitive to the Sivers effect in the initial state, is substantially smaller, but shows the same behavior as the inclusive $π^0$ asymmetry as a function of Feynman-$x$. To investigate final-state effects, the Collins asymmetry of $π^0$ inside electromagnetic jets has been measured. The Collins asymmetry is analyzed for its dependence on the $π^0$ momentum transverse to the jet thrust axis and its dependence on the fraction of jet energy carried by the $π^0$. The asymmetry was found to be small in each case for both center-of-mass energies. All the measurements are compared to QCD-based theoretical calculations for transverse-momentum-dependent parton distribution functions and fragmentation functions. Some discrepancies are found, which indicates new mechanisms might be involved.

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Global polarization of $Ξ$ and $Ω$ hyperons in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV

Global polarization of $Ξ$ and $Ω$ hyperons has been measured for the first time in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV. The measurements of the $Ξ^-$ and $\barΞ^+$ hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay $Ξ\rightarrowΛ+π$, as well as by measuring the polarization of the daughter $Λ$-hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over $Ξ^-$ and $\barΞ^+$, is measured to be $\langle P_Ξ\rangle = 0.47\pm0.10~({\rm stat.})\pm0.23~({\rm syst.})\,\%$ for the collision centrality 20\%-80\%. The $\langle P_Ξ\rangle$ is found to be slightly larger than the inclusive $Λ$ polarization and in reasonable agreement with a multi-phase transport model (AMPT). The $\langle P_Ξ\rangle$ is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of $Ω$, $\langle P_Ω\rangle = 1.11\pm0.87~({\rm stat.})\pm1.97~({\rm syst.})\,\%$ was obtained by measuring the polarization of daughter $Λ$ in the decay $Ω\rightarrow Λ+ K$, assuming the polarization transfer factor $C_{ΩΛ}=1$.

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

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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Comparison of transverse single-spin asymmetries for forward $π^{0}$ production in polarized $pp$, $p\rm{Al}$ and $p\rm{Au}$ collisions at nucleon pair c.m. energy $\sqrt{s_{\mathrm{NN}}}= 200$ GeV

The STAR Collaboration reports a measurement of the transverse single-spin asymmetries, $A_{N}$, for neutral pions produced in polarized proton collisions with protons ($pp$), with aluminum nuclei ($p\rm{Al}$) and with gold nuclei ($p\rm{Au}$) at a nucleon-nucleon center-of-mass energy of 200 GeV. Neutral pions are observed in the forward direction relative to the transversely polarized proton beam, in the pseudo-rapidity region $2.7<η<3.8$. Results are presented for $π^0$s observed in the STAR FMS electromagnetic calorimeter in narrow Feynman x ($x_F$) and transverse momentum ($p_T$) bins, spanning the range $0.17 2.5$ GeV/$c$. It is further observed that the value of $A_N$ is significantly larger for events with a large-$p_T$ isolated $π^0$ than for events with a non-isolated $π^0$ accompanied by additional jet-like fragments. The nuclear dependence $r(A)$ is similar for isolated and non-isolated $π^0$ events.

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Measurement of inclusive charged-particle jet production in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV

The STAR Collaboration at the Relativistic Heavy Ion Collider reports the first measurement of inclusive jet production in peripheral and central Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV. Jets are reconstructed with the anti-k$_{T}$ algorithm using charged tracks with pseudorapidity $|η|<1.0$ and transverse momentum $0.2<p_{T,jet}^{ch}<30$ GeV/$c$, with jet resolution parameter $R$=0.2, 0.3, and 0.4. The large background yield uncorrelated with the jet signal is observed to be dominated by statistical phase space, consistent with a previous coincidence measurement. This background is suppressed by requiring a high-transverse-momentum (high-$p_T$) leading hadron in accepted jet candidates. The bias imposed by this requirement is assessed, and the $p_T$ region in which the bias is small is identified. Inclusive charged-particle jet distributions are reported in peripheral and central Au+Au collisions for $5<p_{T,jet}^{ch}<25$ GeV/$c$ and $5<p_{T,jet}^{ch}<30$ GeV/$c$, respectively. The charged-particle jet inclusive yield is suppressed for central Au+Au collisions, compared to both the peripheral Au+Au yield from this measurement and to the $pp$ yield calculated using the PYTHIA event generator. The magnitude of the suppression is consistent with that of inclusive hadron production at high $p_T$, and that of semi-inclusive recoil jet yield when expressed in terms of energy loss due to medium-induced energy transport. Comparison of inclusive charged-particle jet yields for different values of $R$ exhibits no significant evidence for medium-induced broadening of the transverse jet profile for $R<0.4$ in central Au+Au collisions. The measured distributions are consistent with theoretical model calculations that incorporate jet quenching.

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Measurement of Groomed Jet Substructure Observables in \pp Collisions at $\sqrt{s} = 200$ GeV with STAR

In this letter, measurements of the shared momentum fraction ($z_{\rm{g}}$) and the groomed jet radius ($R_{\rm{g}}$), as defined in the SoftDrop algorihm, are reported in \pp collisions at $\sqrt{s} = 200$ GeV collected by the STAR experiment. These substructure observables are differentially measured for jets of varying resolution parameters from $R = 0.2 - 0.6$ in the transverse momentum range $15 < p_{\rm{T, jet}} < 60$ GeV$/c$. These studies show that, in the $p_{\rm{T, jet}}$ range accessible at $\sqrt{s} = 200$ GeV and with increasing jet resolution parameter and jet transverse momentum, the $z_{\rm{g}}$ distribution asymptotically converges to the DGLAP splitting kernel for a quark radiating a gluon. The groomed jet radius measurements reflect a momentum-dependent narrowing of the jet structure for jets of a given resolution parameter, i.e., the larger the $p_{\rm{T, jet}}$, the narrower the first splitting. For the first time, these fully corrected measurements are compared to Monte Carlo generators with leading order QCD matrix elements and leading log in the parton shower, and to state-of-the-art theoretical calculations at next-to-leading-log accuracy. We observe that PYTHIA 6 with parameters tuned to reproduce RHIC measurements is able to quantitatively describe data, whereas PYTHIA 8 and HERWIG 7, tuned to reproduce LHC data, are unable to provide a simultaneous description of both $z_{\rm{g}}$ and $R_{\rm{g}}$, resulting in opportunities for fine parameter tuning of these models for \pp collisions at RHIC energies. We also find that the theoretical calculations without non-perturbative corrections are able to qualitatively describe the trend in data for jets of large resolution parameters at high $p_{\rm{T, jet}}$, but fail at small jet resolution parameters and low jet transverse momenta.

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Measurements of $W$ and $Z/γ^*$ cross sections and their ratios in $p+p$ collisions at RHIC

We report on the $W$ and $Z/γ^*$ differential and total cross sections as well as the $W^+$/$W^-$ and $(W^+ + W^-)$/$(Z/γ^*)$ cross-section ratios measured by the STAR experiment at RHIC in $p+p$ collisions at $\sqrt{s} = 500$ GeV and $510$ GeV. The cross sections and their ratios are sensitive to quark and antiquark parton distribution functions. In particular, at leading order, the $W$ cross-section ratio is sensitive to the $\bar{d}/\bar{u}$ ratio. These measurements were taken at high $Q^2 \sim M_W^2,M_Z^2$ and can serve as input into global analyses to provide constraints on the sea quark distributions. The results presented here combine three STAR data sets from 2011, 2012, and 2013, accumulating an integrated luminosity of 350 pb$^{-1}$. We also assess the expected impact that our $W^+/W^-$ cross-section ratios will have on various quark distributions, and find sensitivity to the $\bar{u}-\bar{d}$ and $\bar{d}/\bar{u}$ distributions.

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Measurement of inclusive J/$ψ$ polarization in p+p collisions at $\sqrt{s}$ = 200 GeV by the STAR experiment

We report on new measurements of inclusive J/$ψ$ polarization at mid-rapidity in p+p collisions at $\sqrt{s}$ = 200 GeV by the STAR experiment at RHIC. The polarization parameters, $λ_θ$, $λ_ϕ$, and $λ_{θϕ}$, are measured as a function of transverse momentum ($p_T$) in both the Helicity and Collins-Soper (CS) reference frames within $p_T< 10$ GeV/$C$. Except for $λ_θ$ in the CS frame at the highest measured $p_T$, all three polarization parameters are consistent with 0 in both reference frames without any strong $p_T$ dependence. Several model calculations are compared with data, and the one using the Color Glass Condensate effective field theory coupled with non-relativistic QCD gives the best overall description of the experimental results, even though other models cannot be ruled out due to experimental uncertainties.

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Measurement of the mass difference and the binding energy of the hypertriton and antihypertriton

According to the CPT theorem, which states that the combined operation of charge conjugation, parity transformation and time reversal must be conserved, particles and their antiparticles should have the same mass and lifetime but opposite charge and magnetic moment. Here, we test CPT symmetry in a nucleus containing a strange quark, more specifically in the hypertriton. This hypernucleus is the lightest one yet discovered and consists of a proton, a neutron, and a $Λ$ hyperon. With data recorded by the STAR detector{\cite{TPC,HFT,TOF}} at the Relativistic Heavy Ion Collider, we measure the $Λ$ hyperon binding energy $B_Λ$ for the hypertriton, and find that it differs from the widely used value{\cite{B_1973}} and from predictions{\cite{2019_weak, 1995_weak, 2002_weak, 2014_weak}}, where the hypertriton is treated as a weakly bound system. Our results place stringent constraints on the hyperon-nucleon interaction{\cite{Hammer2002, STAR-antiH3L}}, and have implications for understanding neutron star interiors, where strange matter may be present{\cite{Chatterjee2016}}. A precise comparison of the masses of the hypertriton and the antihypertriton allows us to test CPT symmetry in a nucleus with strangeness for the first time, and we observe no deviation from the expected exact symmetry.

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