Spin Alignment Of Vector Mesons Research Articles

Linear response theory for spin alignment of vector mesons in thermal media

Linear response theory for spin alignment of vector mesons in thermal media

Mass splitting and spin alignment for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field in NJL model

Based on the Nambu–Jona–Lasinio (NJL) model, we develop a framework for calculating the spin alignment of vector mesons and applied it to study ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field. We calculate mass spectra for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons and observe mass splitting between the longitudinally polarized state and transversely polarized states. The ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} meson in a thermal equilibrium system is preferred to occupy the state with spin λ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =0$$\\end{document} than those with spin λ=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =\\pm 1$$\\end{document}, because the former state has a smaller energy. As a consequence, we conclude that the spin alignment will be larger than 1/3 if one measures along the direction of the magnetic field, which is qualitatively consistent with the recent STAR data. Around the critical temperature TC=150MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{C}=150~\\hbox {MeV}$$\\end{document}, the positive deviation from 1/3 is proportional to the square of the magnetic field strength, which agrees with the result from the non-relativistic coalescence model. Including the anomalous magnetic moments for quarks will modify the dynamical masses of quarks and thus affect the mass spectra and spin alignment of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons. The discussion of spin alignment in the NJL model may help us better understand the formation of hadron’s spin structure during the chiral phase transition.

Spin alignment of vector mesons from quark dynamics in a rotating medium* *Supported in part by the National Natural Science Foundation of China (NSFC) (12235016, 12221005), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030000), the start-up funding from the University of Chinese Academy of Sciences (UCAS), and the Fundamental Research Funds for the Central Universities

Vorticities in heavy-ion collisions (HICs) are supposed to induce spin alignment and polarization phenomena of quarks and mesons. In this work, we analyze the spin alignment of vector mesons ϕ and ρ induced by rotation from quark dynamics in the framework of the Nambu-Jona-Lasinio (NJL) model. The rotating angular velocity induces mass splitting of spin components for vector mesons . This behavior contributes to the spin alignment of vector mesons in an equilibrium medium and naturally explains the negative deviation of for vector mesons. Incidentally, the positive deviation of under the magnetic field can also be easily understood from quark dynamics.

Spin alignment of vector mesons by glasma fields

Spin alignment of vector mesons by glasma fields

Spin Alignment of Vector Mesons in Heavy-Ion Collisions.

Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ρ_{00} for ϕ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to ϕ meson's spin alignment. We propose that the local correlation or fluctuation of ϕ fields is the dominant mechanism for the observed ϕ meson's spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ρ_{00} agrees with STAR's data. We further predict the azimuthal angle dependence of ρ_{00} which can be tested in future experiments.

Global spin alignment of vector mesons and strong force fields in heavy-ion collisions

Global spin alignment of vector mesons and strong force fields in heavy-ion collisions

Erratum: Practical considerations for measuring global spin alignment of vector mesons in relativistic heavy ion collisions [Phys. Rev. C 98 , 044907 (2018)

Received 9 February 2023DOI:https://doi.org/10.1103/PhysRevC.107.039901©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle & resonance productionRelativistic heavy-ion collisionsPropertiesPolarizationNuclear PhysicsParticles & Fields

Impact of globally spin-aligned vector mesons on the search for the chiral magnetic effect in heavy-ion collisions

In high-energy heavy-ion collisions, the chiral magnetic effect (CME) is predicted to arise from the interplay between the chirality imbalance of quarks in the nuclear medium and the intense magnetic field, and will cause a charge separation along the magnetic field direction. While the search for the CME is still ongoing in experiments at Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), the CME-sensitive observables need to be scrutinized to exclude the non-CME contributions. In this work, we examine the influence of globally spin-aligned ρ mesons on the γ112 correlator, the RΨ2(ΔS) correlator, and the signed balance functions, via a toy model and a multiphase transport model (AMPT). The global spin alignment of vector mesons could originate from non-CME mechanisms in heavy-ion collisions, and is characterized by the 00-component of the spin density matrix, ρ00. We find that the CME observables show similar dependence on ρ00, and could receive a positive (negative) contribution from ρ-decay pions, if the ρ00 of ρ mesons is larger (smaller) than 1/3. Since pions are the most abundant particles in such collisions, the ρ00 measurements for ρ mesons become crucial to the interpretation of the CME data.

Global polarization of hyperons and spin alignment of vector mesons in quark matters

<sec>Relativistic heavy ion collider (RHIC) as a dedicated nuclear facility has made a few major discoveries in physics. This year marks the 30th year STAR Collaboration formation and the 23th year of STAR detector operation and data collection at RHIC. In the last two decades, STAR has collected many datasets, exhibiting scientific versatility and flexibility of the RHIC facility. The total dataset in the first year is less than 1 million good events, and currently there are about 1 billion events per dataset.</sec><sec>The Global Hyperon Polarization was proposed in 2004. This immediately prompted the STAR Collaboration to search for this phenomenon from the early datasets. The null results were presented at Quark Matter Conference in Shanghai in 2006 and subsequently published. Although there were peripheral and continuous efforts in the following decade, no positive result has been observed experimentally. This situation changed in the following decade with the upgrade of high data rate and time-of-flight (TOF) detector and the progress of the Beam Energy Scan Phase I (BES-I). The experimental discoveries of the global polarization of hyperons in 2017 and the spin alignment of vector mesons in 2023 at RHIC-STAR confirm the theory which was established nearly twenty years ago. The theory and these measurements open the way to studying the properties of the hot and dense nuclear matter created in high-energy heavy ion collisions from a new degree of freedom, spin.</sec><sec>We briefly review these discoveries from the proposals of theory to the experimental measurements, and summarize the related measurements at the existing facilities and the theoretical explanations to the original proposal. The basic understanding and the original proposal are still valid and fundamental, that is, the angular momentum of system can transform into a spin effect observable in experiment. However, it appears that in each case a new model is needed to explain the new experimental observation. We need a more basic theory to help us unify all these spin related phenomena.</sec><sec>Over the past five years, STAR has successfully installed 3 new detectors and we have begun to see the physical analysis results from datasets with those new functions. What makes the STAR detector viable after 20 years of operation is its continuous evolution through successful upgrades, with new scientific programs added year by year. The next big thing is to forward upgrade a tracking system (3 layers of silicon strips and 4 layers of sTGC chambers) and a calorimetry system (electromagnetic and hadronic calorimeters). In addition to studying the spin structure of protons by using the polarized proton beams at RHIC, the upgrades also provide a unique ability to investigate the origin of Λ Global Polarization as a function of rapidity and rapidity (de-)correlations in Au+Au collisions.</sec>

Global spin alignment of vector mesons in heavy ion collisions

In non-central relativistic heavy-ion collisions, the large initial orbital angular momentum results in strong vorticity fields in the quark-gluon plasma, which polarize partons through the spin-orbit coupling. The global polarization of quark matter will be converted to the global polarization of baryons and the global spin alignment of vector mesons. The spin alignment refers to the <inline-formula><tex-math id="M3">\begin{document}$\rho_{00}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20230071_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20230071_M3.png"/></alternatives></inline-formula> element of the spin density matrix for vector mesons. When a vector meson decays to two pseudoscalar mesons, the polar angle distribution for the decay product depends on <inline-formula><tex-math id="M4">\begin{document}$\rho_{00}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20230071_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20230071_M4.png"/></alternatives></inline-formula>, through which the spin alignment can be measured. Theoretical studies show that the global spin polarization of baryons reflects the space-time average of the quark polarization, while the spin alignment of vector mesons reflects the local phase space correlation between the polarization of quark and antiquark. In this article, we review recent theoretical works about the spin alignment of vector mesons. We consider a non-relativistic quark coalescence model in spin and phase space. Within this model, the spin alignment of the vector meson can be described through the phase space correlation of quark's and antiquark's polarization. The contributions to the spin alignment of <i>ϕ</i> mesons from vorticity fields, electromagnetic fields, and effective <i>ϕ</i> meson fields are discussed. The spin alignment of vector mesons opens a new window for the properties of strong interaction fields in heavy-ion collisions.

Global spin alignment of ɸ and K*0 vector mesons in Au+Au collisions from RHIC BES-II program

Global spin alignment is a preferential alignment of a particle’s spin along the orbital angular momentum produced in heavy-ion collisions. The global spin alignment of vector mesons (JP = 1−) ϕ and K*0 may be sensitive to the vorticity in the medium and hadronization mechanisms. The second phase of RHIC Beam Energy Scan (BES-II) program provides higher statistics data sets for Au+Au collisions at √SNN = 7.7 - 19.6 GeV. From this data, we can make high precision measurements of ϕ and K*0 global spin alignment, allowing for more differential studies not possible with the BES-I data. We can also compare global spin alignment between ϕ and K*0, where the lifetime of ϕ is roughly ten times larger than that of K*0 and the latter is more sensitive to hadronic rescattering. We report high precision measurements for the global spin alignment of ϕ at √SNN = 19.6 GeV from BES-II.

Measurement of Global Spin Alignment of Vector Mesons at RHIC

Measurement of Global Spin Alignment of Vector Mesons at RHIC

Rescattering effect on the measurement of K*0 spin alignment in heavy-ion collisions

Spin alignment of vector mesons in noncentral relativistic heavy-ion collisions provides a novel probe of the global quark polarization and hadronization mechanism. In this paper, we discuss the spin alignment of a short-lived vector meson, namely ${K}^{*0}$, arising from the hadronic rescattering process using the UrQMD model. This spin alignment is not related to global quark polarization but cannot be distinguished from those arising from global quark polarization in experiment. The spin alignment parameter ${\ensuremath{\rho}}_{00}$ is found to deviate from 1/3 by up to $\ensuremath{-}0.008$ (0.03) with respect to the reaction (production) plane. These deviations are much larger than the expected signal from all the theoretical models implementing the conventional global quark polarization mechanism as well as the current experimental precision, and should be considered seriously when comparing measurements with theoretical calculations.

Practical considerations for the effect of finite coverage on the azimuthal dependence of global spin alignment

The global spin alignment of vector mesons is a powerful probe to study the vorticity field of the system produced in non-central relativistic heavy-ion collisions. Since the experimental observables of global spin alignment are sensitive to many factors, proper corrections are need to be taken care of when measuring the global spin alignment of vector mesons. In this paper, we propose a method to correct the effect of finite pseudo-rapidity coverage when extract the azimuthal dependence of spin alignment parameter $\rho_{00}$. The effects of the finite pseudo-rapidity coverage on the azimuthal dependence of $\phi$ meson spin alignment and the potentially exist intrinsic spin alignment effects are taken into consideration. The method presented in this paper is verified in a Monte-Carlo simulation, it allows the measurements of azimuthal dependence of global spin alignment to be conducted properly and accurately.

Spin alignment of vector mesons as a probe of spin hydrodynamics and freeze-out

We argue that a detailed analysis of the spin alignment of vector mesons can serve as a probe of two little-understood aspects of spin dynamics in a vortical fluid: The degree of relaxation between vorticity and particle spin polarization, and the degree of coherence of the hadron wave function at freeze-out. We illustrate these with a coalescence model.

Anomalous spin polarization from turbulent color fields

We study the important, yet widely overlooked, role of gluons for spin transport with a connection to local parity violation in quark gluon plasmas. We employ the formalism of quantum kinetic theory to quarks in weakly coupled quantum chromodynamics to derive the source terms for quark spin polarization. These source terms involve parity-odd correlators of dynamically generated color fields in near-equilibrium quark gluon plasmas and give rise to locally fluctuating axial charge currents. Our results provide a possible explanation for the spin alignment of vector mesons measured in high-energy nuclear collisions.

Improved quark coalescence model for spin alignments of vector mesons

We propose an improved quark coalescence model for spin alignment of vector mesons by spin density matrix with phase space dependence. Within this model we propose an understanding of spin alignments of vector mesons ϕ and K*0 in the static limit: a large positive deviation of ρ00 for ϕ mesons from 1/3 may come from the electric part of the vector ϕ field, while a negative deviation of ρ00 for K*0 mesons may come from the electric part of vorticity fields. In the low-pT region, ρ00 for K*0 mesons is proportional to pT2, which is qualitatively agree with experimental results.

Global polarization and spin alignment measurements

Recent experimental results on global polarization of hyperons and spin alignment of vector mesons in heavy-ion collisions are reviewed, especially in context of the energy dependence and particle species dependence. New results on local polarization along the beam direction at the LHC are discussed with previous measurements at RHIC. Future outlook of these measurements and possible future directions for better understanding of local vorticity field are briefly discussed.

Spin alignment measurement of vector mesons produced in high energy collisions

This paper covers the recent experimental development on spin alignment measurements of [Formula: see text] and [Formula: see text] vector mesons in heavy-ion and [Formula: see text] collisions at RHIC and LHC energies. Measurements in [Formula: see text] collisions at LEP energies are also discussed. Spin alignment of vector mesons is studied by measuring the second diagonal element [Formula: see text] of spin density matrix. The spin density matrix element [Formula: see text] is obtained by measuring the angular distribution of vector meson decay daughter with respect to the quantization axis in vector meson rest frame. Measured [Formula: see text] values for vector mesons are found to be larger than [Formula: see text] at high momentum in [Formula: see text] collisions at LEP energies, suggesting the preferential production of vector meson with helicity zero state from the fragmentation process. The [Formula: see text] values are found to be smaller than [Formula: see text] ([Formula: see text] implies no spin alignment) for [Formula: see text] and [Formula: see text] vector mesons at low transverse momentum in Pb–Pb collisions at [Formula: see text] TeV. These observations are qualitatively consistent with the expectation from models which attribute the spin alignment effect due to polarization of quarks in the presence of large initial angular momentum in noncentral heavy-ion collisions and its subsequent hadronization by the process of recombination. No significant spin alignment effect is observed for [Formula: see text] [Formula: see text] in mid-central Pb–Pb collisions and for vector mesons in [Formula: see text] collisions. However, the preliminary results of [Formula: see text] for [Formula: see text] mesons are larger than [Formula: see text] at intermediate [Formula: see text] in Au–Au collisions at RHIC energies and can be attributed to the presence of [Formula: see text] meson field. Although there is evidence of spin alignment effect of vector mesons in heavy-ion collisions but the measured effect is surprisingly larger in context of hyperon polarization. Therefore, these results will trigger further theoretical study.

Local spin alignment of vector mesons in relativistic heavy-ion collisions

We investigate the spin alignment of vector mesons arising from locally polarized quarks and anti-quarks (local spin alignment) in heavy-ion collisions. We find that ρ00≠1/3 does not necessarily signal the global polarization of quarks and anti-quarks along the orbital angular momentum of the system, but may also originate from their local spin polarization. Such local spin polarization could be induced by local vorticity arising from the anisotropic expansion of the fireball. We further propose experimental observables that can distinguish between the local and the global spin alignments. Measurements of these observables in heavy-ion collisions can probe the vorticity pattern and shed light on the puzzles of ϕ and K⁎0 spin alignments.