Observation of Global Spin Alignment of $\phi$ and $K^{*0}$ Vector Mesons in Nuclear Collisions

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Nature 614 (2023) 244-248, 2023.
Inspire Record 2063245 DOI 10.17182/hepdata.129067

Notwithstanding decades of progress since Yukawa first developed a description of the force between nucleons in terms of meson exchange, a full understanding of the strong interaction remains a major challenge in modern science. One remaining difficulty arises from the non-perturbative nature of the strong force, which leads to the phenomenon of quark confinement at distances on the order of the size of the proton. Here we show that in relativistic heavy-ion collisions, where quarks and gluons are set free over an extended volume, two species of produced vector (spin-1) mesons, namely $\phi$ and $K^{*0}$, emerge with a surprising pattern of global spin alignment. In particular, the global spin alignment for $\phi$ is unexpectedly large, while that for $K^{*0}$ is consistent with zero. The observed spin-alignment pattern and magnitude for the $\phi$ cannot be explained by conventional mechanisms, while a model with a connection to strong force fields, i.e. an effective proxy description within the Standard Model and Quantum Chromodynamics, accommodates the current data. This connection, if fully established, will open a potential new avenue for studying the behaviour of strong force fields.

38 data tables

Global spin alignment of $\phi$ and $K^{*0}$ vector mesons in heavy-ion collisions. The measured matrix element $\rho_{00}$ as a function of beam energy for the $\phi$ and $K^{*0}$ vector mesons within the indicated windows of centrality, transverse momentum ($p_T$) and rapidity ($y$). The open symbols indicate ALICE results for Pb+Pb collisions at 2.76 TeV at $p_{T}$ values of 2.0 and 1.4 GeV/c for the $\phi$ and $K^{*0}$ mesons, respectively, corresponding to the $p_{T}$ bin nearest to the mean $p_{T}$ for the 1.0 – 5.0 GeV/$c$ range assumed for each meson in the present analysis. The red solid curve is a fit to data in the range of $\sqrt{s_{NN}} = 19.6$ to 200 GeV, based on a theoretical calculation with a $\phi$-meson field. Parameter sensitivity of $\rho_{00}$ to the $\phi$-meson field is shown in Ref.5. The red dashed line is an extension of the solid curve with the fitted parameter $G_s^{(y)}$. The black dashed line represents $\rho_{00}=1/3.$

Global spin alignment of $\phi$ and $K^{*0}$ vector mesons in heavy-ion collisions. The measured matrix element $\rho_{00}$ as a function of beam energy for the $\phi$ and $K^{*0}$ vector mesons within the indicated windows of centrality, transverse momentum ($p_T$) and rapidity ($y$). The open symbols indicate ALICE results for Pb+Pb collisions at 2.76 TeV at $p_{T}$ values of 2.0 and 1.4 GeV/c for the $\phi$ and $K^{*0}$ mesons, respectively, corresponding to the $p_{T}$ bin nearest to the mean $p_{T}$ for the 1.0 – 5.0 GeV/$c$ range assumed for each meson in the present analysis. The red solid curve is a fit to data in the range of $\sqrt{s_{NN}} = 19.6$ to 200 GeV, based on a theoretical calculation with a $\phi$-meson field. Parameter sensitivity of $\rho_{00}$ to the $\phi$-meson field is shown in Ref.5. The red dashed line is an extension of the solid curve with the fitted parameter $G_s^{(y)}$. The black dashed line represents $\rho_{00}=1/3.$

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 $\cos \theta^*$.

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Transverse-energy distributions at midrapidity in $p$$+$$p$, $d$$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{NN}}}=62.4$--200~GeV and implications for particle-production models

The PHENIX collaboration Adler, S.S. ; Afanasiev, S. ; Aidala, C. ; et al.
Phys.Rev.C 89 (2014) 044905, 2014.
Inspire Record 1273625 DOI 10.17182/hepdata.63512

Measurements of the midrapidity transverse energy distribution, $d\Et/d\eta$, are presented for $p$$+$$p$, $d$$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV and additionally for Au$+$Au collisions at $\sqrt{s_{_{NN}}}=62.4$ and 130 GeV. The $d\Et/d\eta$ distributions are first compared with the number of nucleon participants $N_{\rm part}$, number of binary collisions $N_{\rm coll}$, and number of constituent-quark participants $N_{qp}$ calculated from a Glauber model based on the nuclear geometry. For Au$+$Au, $\mean{d\Et/d\eta}/N_{\rm part}$ increases with $N_{\rm part}$, while $\mean{d\Et/d\eta}/N_{qp}$ is approximately constant for all three energies. This indicates that the two component ansatz, $dE_{T}/d\eta \propto (1-x) N_{\rm part}/2 + x N_{\rm coll}$, which has been used to represent $E_T$ distributions, is simply a proxy for $N_{qp}$, and that the $N_{\rm coll}$ term does not represent a hard-scattering component in $E_T$ distributions. The $dE_{T}/d\eta$ distributions of Au$+$Au and $d$$+$Au are then calculated from the measured $p$$+$$p$ $E_T$ distribution using two models that both reproduce the Au$+$Au data. However, while the number-of-constituent-quark-participant model agrees well with the $d$$+$Au data, the additive-quark model does not.

43 data tables

Et EMC distributions for sqrt(sNN) = 62.4 GeV Au+Au collisions shown in 5% wide centrality bins.

Et EMC distributions for sqrt(sNN) = 62.4 GeV Au+Au collisions shown in 5% wide centrality bins.

Et EMC distributions for sqrt(sNN) = 62.4 GeV Au+Au collisions shown in 5% wide centrality bins.

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Version 2
Energy and system-size dependence of two- and four-particle $v_2$ measurements in heavy-ion collisions at RHIC and their implications on flow fluctuations and nonflow

The STAR collaboration Agakishiev, G. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.C 86 (2012) 014904, 2012.
Inspire Record 955160 DOI 10.17182/hepdata.101341

We present STAR measurements of azimuthal anisotropy by means of the two- and four-particle cumulants $v_2$ ($v_2\{2\}$ and $v_2\{4\}$) for Au+Au and Cu+Cu collisions at center of mass energies $\sqrt{s_{_{\mathrm{NN}}}} = 62.4$ and 200 GeV. The difference between $v_2\{2\}^2$ and $v_2\{4\}^2$ is related to $v_{2}$ fluctuations ($\sigma_{v_2}$) and nonflow $(\delta_{2})$. We present an upper limit to $\sigma_{v_2}/v_{2}$. Following the assumption that eccentricity fluctuations $\sigma_{\epsilon}$ dominate $v_2$ fluctuations $\frac{\sigma_{v_2}}{v_2} \approx \frac{\sigma_{\epsilon}}{\epsilon}$ we deduce the nonflow implied for several models of eccentricity fluctuations that would be required for consistency with $v_2\{2\}$ and $v_2\{4\}$. We also present results on the ratio of $v_2$ to eccentricity.

28 data tables

The two-particle cumulant $v_2\{2\}^2$ for Au+Au collisions at 200 and 62.4 GeV. Results are shown with like-sign combinations (LS) and charge-independent results (CI) for $0.15 < p_T < 2.0$ GeV/$c$.

The two-particle cumulant $v_2\{2\}^2$ for Au+Au collisions at 200 and 62.4 GeV. Results are shown with like-sign combinations (LS) and charge-independent results (CI) for $0.15 < p_T < 2.0$ GeV/$c$.

The same as the left but for Cu+Cu collisions. The systematic errors are shown as thin lines with wide caps at the ends and statistical errors are shown as thick lines with small caps at the end. Statistical and systematic errors are very small.

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$\rho^{0}$ Photoproduction in AuAu Collisions at $\sqrt{s_{NN}}$=62.4 GeV with STAR

The STAR collaboration Agakishiev, G. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.C 85 (2012) 014910, 2012.
Inspire Record 919778 DOI 10.17182/hepdata.101342

Vector mesons may be photoproduced in relativistic heavy-ion collisions when a virtual photon emitted by one nucleus scatters from the other nucleus, emerging as a vector meson. The STAR Collaboration has previously presented measurements of coherent $\rho^0$ photoproduction at center of mass energies of 130 GeV and 200 GeV in AuAu collisions. Here, we present a measurement of the cross section at 62.4 GeV; we find that the cross section for coherent $\rho^0$ photoproduction with nuclear breakup is $10.5\pm1.5\pm 1.6$ mb at 62.4 GeV. The cross-section ratio between 200 GeV and 62.4 GeV is $2.8\pm0.6$, less than is predicted by most theoretical models. It is, however, proportionally much larger than the previously observed $15\pm 55$% increase between 130 GeV and 200 GeV.

5 data tables

Acceptance corrected invariant mass distributions for the coherently produced $\rho^0$ candidates collected with trigger A (left) and B (right). The fit function (solid) encompasses the Breit-Wigner (dashed), the mass independent contribution from direct $\pi^+\pi^-$ production (dash-dotted), and the interference term (dotted). The hatched area is the contribution from the combinatorial background. The statistical errors are shown.

Acceptance corrected invariant mass distributions for the coherently produced $\rho^0$ candidates collected with trigger A (left) and B (right). The fit function (solid) encompasses the Breit-Wigner (dashed), the mass independent contribution from direct $\pi^+\pi^-$ production (dash-dotted), and the interference term (dotted). The hatched area is the contribution from the combinatorial background. The statistical errors are shown.

Transverse momentum distribution of the $\rho^0$ candidates (open distribution) overlaid by the combinatorial background estimated with like-sign pairs (not corrected to the acceptance and reconstruction efficiency) and scaled to match in the high transverse momentum region, $p_T$ ≥ 250 MeV/$c$ (hatched distribution). The plot is based on the dataset collected with trigger B.

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Two-pion Bose-Einstein correlations in central PbPb collisions at sqrt(s_NN) = 2.76 TeV

The ALICE collaboration Aamodt, K. ; Abrahantes Quintana, A. ; Adamova, D. ; et al.
Phys.Lett.B 696 (2011) 328-337, 2011.
Inspire Record 881884 DOI 10.17182/hepdata.56743

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.

14 data tables

Projections of the correlation function C.

Projections of the correlation function C.

Projections of the correlation function C.

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Version 2
Strange and Multi-strange Particle Production in Au+Au Collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The STAR collaboration Aggarwal, M.M. ; Ahammed, Z. ; Alakhverdyants, A.V. ; et al.
Phys.Rev.C 83 (2011) 024901, 2011.
Inspire Record 871561 DOI 10.17182/hepdata.96847

We present results on strange and multi-strange particle production in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ GeV as measured with the STAR detector at RHIC. Mid-rapidity transverse momentum spectra and integrated yields of $K^{0}_{S}$, $\Lambda$, $\Xi$, $\Omega$ and their anti-particles are presented for different centrality classes. The particle yields and ratios follow a smooth energy dependence. Chemical freeze-out parameters, temperature, baryon chemical potential and strangeness saturation factor obtained from the particle yields are presented. Intermediate transverse momentum ($p_T$) phenomena are discussed based on the ratio of the measured baryon-to-meson spectra and nuclear modification factor. The centrality dependence of various measurements presented show a similar behavior as seen in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

58 data tables

Correction factors (acceptance × efficiency) for the most central events ( 0−5% for KS0, Λ and Ξ; 0−20% for Ω) at mid-rapidity (|y| < 1) as a function of pT for the different particle species as obtained via embedding. The branching ratio of the measured decay channel is not factored into this plot.

Correction factors (acceptance × efficiency) for the most central events ( 0−5% for KS0, Λ and Ξ; 0−20% for Ω) at mid-rapidity (|y| < 1) as a function of pT for the different particle species as obtained via embedding. The branching ratio of the measured decay channel is not factored into this plot.

Efficiency corrected pT spectra for the different centrality bins and for the various particles. Note that 7 centrality bins have been used for the KS0 and the Λ while only 6 and 3 have been used for the Ξ and Ω, respectively. Errors are statistical only. The Λ spectra are corrected for the feed-down of the Ξ decay.

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Scaling properties at freeze-out in relativistic heavy ion collisions

The STAR collaboration Aggarwal, M.M. ; Ahammed, Z. ; Alakhverdyants, A.V. ; et al.
Phys.Rev.C 83 (2011) 034910, 2011.
Inspire Record 865572 DOI 10.17182/hepdata.104504

Identified charged pion, kaon, and proton spectra are used to explore the system size dependence of bulk freeze-out properties in Cu+Cu collisions at $\sqrt{s_{NN}}$=200 and 62.4 GeV. The data are studied with hydrodynamically-motivated Blast-wave and statistical model frameworks in order to characterize the freeze-out properties of the system. The dependence of freeze-out parameters on beam energy and collision centrality is discussed. Using the existing results from Au+Au and $pp$ collisions, the dependence of freeze-out parameters on the system size is also explored. This multi-dimensional systematic study furthers our understanding of the QCD phase diagram revealing the importance of the initial geometrical overlap of the colliding ions. The analysis of Cu+Cu collisions, which expands the system size dependence studies from Au+Au data with detailed measurements in the smaller system, shows that the bulk freeze-out properties of charged particles studied here scale with the total charged particle multiplicity at mid-rapidity, suggesting the relevance of initial state effects.

26 data tables

Negatively charged pion spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

Negatively charged pion spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Negatively charged kaon spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

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Midrapidity antiproton-to-proton ratio in pp collisions at $\sqrt{s} = 0.9$ and $7$~TeV measured by the ALICE experiment

The ALICE collaboration Aamodt, K. ; Abel, N. ; Abeysekara, U. ; et al.
Phys.Rev.Lett. 105 (2010) 072002, 2010.
Inspire Record 859610 DOI 10.17182/hepdata.55557

The ratio of the yields of antiprotons to protons in pp collisions has been measured by the ALICE experiment at $\sqrt{s} = 0.9$ and $7$ TeV during the initial running periods of the Large Hadron Collider(LHC). The measurement covers the transverse momentum interval $0.45 < p_{\rm{t}} < 1.05$ GeV/$c$ and rapidity $|y| < 0.5$. The ratio is measured to be $R_{|y| < 0.5} = 0.957 \pm 0.006 (stat.) \pm 0.014 (syst.)$ at $0.9$ TeV and $R_{|y| < 0.5} = 0.991 \pm 0.005 (stat.) \pm 0.014 (syst.)$ at $7$ TeV and it is independent of both rapidity and transverse momentum. The results are consistent with the conventional model of baryon-number transport and set stringent limits on any additional contributions to baryon-number transfer over very large rapidity intervals in pp collisions.

2 data tables

The PT dependence of the pbar/p ratio for the central rapidity region ABS(YRAP)<0.5.

The central rapidity pbar/p ratio as a function of the rapidity interval Ybeam-Ybaryon and centre-of-mass energy. As well as the present ALICE measurements this table also lists the values from other experiments (see the text of the paper for details).


K*0 production in Cu+Cu and Au+Au collisions at \sqrt{s_NN} = 62.4 GeV and 200 GeV

The STAR collaboration Aggarwal, M.M. ; Ahammed, Z. ; Alakhverdyants, A.V. ; et al.
Phys.Rev.C 84 (2011) 034909, 2011.
Inspire Record 857694 DOI 10.17182/hepdata.102405

We report on K*0 production at mid-rapidity in Au+Au and Cu+Cu collisions at \sqrt{s_{NN}} = 62.4 and 200 GeV collected by the Solenoid Tracker at RHIC (STAR) detector. The K*0 is reconstructed via the hadronic decays K*0 \to K+ pi- and \bar{K*0} \to K-pi+. Transverse momentum, pT, spectra are measured over a range of pT extending from 0.2 GeV/c to 5 GeV/c. The center of mass energy and system size dependence of the rapidity density, dN/dy, and the average transverse momentum, <pT>, are presented. The measured N(K*0)/N(K) and N(\phi)/N(K*0) ratios favor the dominance of re-scattering of decay daughters of K*0 over the hadronic regeneration for the K*0 production. In the intermediate pT region (2.0 < pT < 4.0 GeV/c), the elliptic flow parameter, v2, and the nuclear modification factor, RCP, agree with the expectations from the quark coalescence model of particle production.

64 data tables

The K$\pi$ pair invariant mass distribution integrated over the $K^{*0}$ $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ =200 GeV after mixed-event background subtraction.

The K$\pi$ pair invariant mass distribution integrated over the $K^{*0}$ $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ =62.4 GeV after mixed-event background subtraction.

The K$\pi$ pair invariant mass distribution integrated over the $K^{*0}$ $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ =200 GeV after mixed-event background subtraction.

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Higher Moments of Net-proton Multiplicity Distributions at RHIC

The STAR collaboration Aggarwal, M.M. ; Ahammed, Z. ; Alakhverdyants, A.V. ; et al.
Phys.Rev.Lett. 105 (2010) 022302, 2010.
Inspire Record 853304 DOI 10.17182/hepdata.73344

We report the first measurements of the kurtosis (\kappa), skewness (S) and variance (\sigma^2) of net-proton multiplicity (N_p - N_pbar) distributions at midrapidity for Au+Au collisions at \sqrt(s_NN) = 19.6, 62.4, and 200 GeV corresponding to baryon chemical potentials (\mu_B) between 200 - 20 MeV. Our measurements of the products \kappa \sigma^2 and S \sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the \sqrt(s_NN) dependence of \kappa \sigma^2. From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for \mu_B below 200 MeV.

40 data tables

$\Delta N_p$ multiplicity distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for 0-5 percent central collisions at midrapidity (| y |< 0.5).

$\Delta N_p$ multiplicity distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for 30-40 percent central collisions at midrapidity (| y |< 0.5).

$\Delta N_p$ multiplicity distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for 70-80 percent central collisions at midrapidity (| y |< 0.5).

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