Recently, the STAR Collaboration published the most precise measurement of the transverse single-spin asymmetries for charged hadrons inside jets in Phys. Rev. D 106, 072010.

Transverse spin experiments at STAR provide new ways to map out the three-dimensional nature of quark fragmentation and illustrate the interplay between the structure of a hadron and the color environment. The Collins effect describes the azimuthal distribution of hadron fragments from a transversely polarized quark, and thus provides access to both the quark transversity in the proton and the transverse momentum dependent Collins fragmentation function. Transversity is one of the three leading twist parton distribution functions of the nucleon. It describes the transverse spin structure of quarks in a transversely polarized proton. The Collins fragmentation function is one of the most important fragmentation functions in the transverse-momentum-dependent (TMD) formalism. This effect has only been studied in semi-inclusive deep-inelastic scattering (SIDIS) and electron-positron annihilation before the STAR experiment.

The figure presented above shows the first measurement of Collins asymmetry with j_T (momentum transverse to the jet axis) dependence in pp collisions at √s = 200 GeV. The results here are divided into six different jet-p_T bins that probe different hard scales in the experiment. The DMP+2013 and KPRY model expectations are also presented in the plot. Both are based on fits to experimental data from SIDIS and electron-positron processes. Our results slightly favor the KPRY model that treats TMD evolution up to the next-to-leading logarithmic effects; however, significant discrepancies exist between the data and both model calculations. These new results will provide valuable new constraints on the kinematic dependence of the Collins fragmentation function when included in future global analyses.

Posted Oct 28, 2022

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Extracting the data from previous experiments, gluon density grows rapidly towards small momentum fraction (x) with respect to the nucleon. Under the color glass condensate (CGC) framework, the growth is explained by gluon splitting. The nonlinear QCD effects at small x should tame this growth by gluon recombination. The so called “gluon saturation” is reached at the point when the splitting and recombination are balanced. Understanding the nonlinear behavior of the gluon is one of the most important physics goals for RHIC Cold QCD program and the future electron ion collider (EIC) project.

Back-to-back dihadron azimuthal angle correlation has been proposed to be a sensitive probe to directly access the underlying gluon dynamics involved in hard scatterings. With a high gluon density at the initial state, the product of back-to-back dihadron modulation will be suppressed. It is predicted that the density of gluons per unit transverse area is larger in nuclei than in nucleons and is amplified by a factor of A^1/3 for a nucleus with mass number A; thus, nuclei provide a natural environment to study nonlinear gluon evolution.

The STAR Collaboration performed the measurements of back-to-back azimuthal correlations of di-π⁰s produced at forward pseudorapidities (2.6 < η < 4.0) in p+p, p+Al, and p+Au collisions at a center-of-mass energy of 200 GeV. The results have been recently published in Phys. Rev. Lett. 129, 092501. We observe a clear suppression of the correlated yields of back-to-back π⁰ pairs in p+Al and p+Au collisions compared to the p+p data. The observed suppression is larger at smaller transverse momentum, which indicates lower x and Q² . The larger suppression found in p+Au relative to p+Al collisions exhibits a dependence of the saturation scale Q²_s on the mass number A. A linear scaling of the suppression with A^1/3 is observed with a slope of −0.09±01.

Figure: Relative area of back-to-back di-π⁰ correlations at forward pseudorapidities (2.6 < η < 4.0) in p+Au and p+Al with respect to p+p collisions for $p_T^{\mathrm{trig}}$=1.5–2 GeV/c and $p_T^{\mathrm{asso}}$=1–1.5 GeV/c. The area is the integral of the back-to-back correlation after pedestal subtraction. The data points are fitted by a linear function, whose slope (P) is found to be −0.09±01.

Posted August 22, 2022

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The STAR Collaboration recently published the “Pattern of Global Spin Alignment of φ and K^*0 mesons in Heavy- Ion Collisions” in Nature.

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 φ and K^*0, emerge with a surprising pattern of global spin alignment. In particular, the global spin alignment for φ is unexpectedly large, while that for K^*0 is consistent with zero. The ρ₀₀ for φ mesons, averaged over beam energies between 11.5 and 62 GeV is 0.3512 ± 0.0017 (stat.) ± 0.0017 (syst.). Taking the total uncertainty as the sum in quadrature of statistical and systematic uncertainties, our results indicate that the φ-meson ρ₀₀ is above 1/3 with a significance of 7.4σ. Th ρ₀₀ for K^*0, averaged over beam energies of 54.4 GeV and below is 0.3356 ± 0.0034 (stat.) ± 0.0043 (syst.).

Figure: Global spin alignment of φ and K^*0 vector mesons in heavy-ion collisions. The measured matrix element ρ₀₀ as a function of beam energy for the φ 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. The red solid curve is a fit to data in the range of $\sqrt{s_{\mathrm{NN}}}$ = 19.6 to 200 GeV, based on a theoretical calculation with a φ-meson field. Th red dashed line is an extension of the solid curve with the fitted parameter G_s^(y). The black dashed line represents ρ₀₀ = 1/3.

Measurements of the global spin alignment of vector mesons is argued to provide new knowledge about the vector meson fields. The vector meson fields are an essential part of the nuclear force that binds nucleons inside atomic nuclei, and are also pivotal in describing properties of nuclear structure and nuclear matter. The ρ₀₀ for the φ meson has a desirable feature in that all contributions depend on squares of field amplitudes; it can be regarded as a field analyzer which makes it possible to extract the imprint of the φ-meson field even if the field fluctuates strongly in space-time. Another important feature worthy of mention is that an essential contribution to the φ-meson ρ₀₀ is from the term $~S\cdot(\mathrm{E}_{\phi}\times \mathrm{p})$, where E_φ is the electric part of the φ-meson field induced by the local, net strangenes current density, and S and p are the spin and momentum of the strange (anti)quarks, respectively. Such a term is nothing but the quark version of the spin-orbit force which, at the nucleon level, plays a key role in the nuclear shell structure. Our measurements of a signal based on global spin alignment for vector mesons reveal a surprising pattern and a value for φ meson that is orders of magnitude larger than can be explained by conventional effects. This work provides a potential new avenue for understanding the strong interaction at work at the sub-nucleon level.

Posted January 19, 2023

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With the discovery of the quark-gluon plasma (QGP) at the Relativistic Heavy Ion Collider (RHIC), physicists are starting to investigate the phase structure of the QCD matter, especially in the high baryon density region. The stark differences between the properties of QGP and lower energy nuclear matter draw interest to the thermodynamic processes, specifically those related to the nature of phase transitions. Experimenters can access the QCD phase diagram, expressed in temperature (T) and baryonic chemical potential (μ_B), and search for phase boundaries by varying the heavy-ion collision energy. At regions of equal baryon and anti-baryon density, μ_B = 0, theoretical approaches work well, with lattice QCD calculations predicting a smooth cross-over transition from hadronic matter to a QGP. In addition, Lattice QCD calculations have predicted a positive cumulant ratio of net-proton (proton minus anti-proton) C₄/C₂ for the formation of QGP matter at μ_B = 200 MeV [1]. However, at finite μ_B, the existence and the nature of the phase transition are not well understood.

Recent reports on net-proton fluctuation measurements from RHIC's Beam Energy Scan program (BES-I) have demonstrated the non-monotonic collision energy dependence in the 4^TH order net-proton cumulant ratio C₄/C₂ from the top 5% central Au+Au collisions of the range of 7.7 – 200 GeV [2].

Figure: Collision energy dependence of the ratios of cumulants, C₄ /C₂ , for proton (squares) and net-proton (red circles) from top 5% Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for proton from the $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV collisions is shown as a filled square. HADES data of 2.4 GeV top 10% collisions is also shown. The vertical black and gray bars are the statistical and systematic uncertainties, respectively. In addition, results from the HRG model, based on both Canonical Ensemble (CE) and Grand-Canonical Ensemble (GCE), and transport model UrQMD are presented.

In this Letter [3], we report cumulants and their ratios of proton multiplicity distribution from $\sqrt{s_{\mathrm{NN}}}$ =3 GeV Au+Au collisions. The new data are measured by the STAR experiment configured in fixed-target mode. At this collision energy, the corresponding baryonic chemical potential μ_B ~ 750 MeV, close to the largest value ever reached in heavy ion collisions. Protons are measured with the acceptance (-0.5 < y < 0 and 0.4 < p_T < 2.0 GeV/c). The rapidity and transverse momentum dependencies of the cumulant ratios C₂/C₁, C₃/C₂ , and C₄/C₂ are discussed. As shown in the figure, a suppression with respect to the Poisson baseline is observed in proton C₄/C₂ = -0.85 0.09 (stat) 0.82 (syst) in the most central collisions at $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV. The hadronic transport model UrQMD reproduces the observed trend in the centrality dependence of the cumulant ratios. This new result is consistent with fluctuations driven by baryon number conservation at the high baryon density region. These data imply that the QCD critical region, if created in heavy-ion collisions, could only exist at energies higher than $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV.

References:
[1] A. Bazavov et al. (HotQCD), Phys. Rev. D96, 074510 (2017) and R. Bellwied et al., Phys.
Rev. D104, 094508 (2021).
[2] (STAR Collaboration), Phys. Rev. Lett. 126 (2021) 92301.
[3] (STAR Collaboration), Phys. Rev. Lett. 128, (2022) 202303.

Posted May 29, 2022

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