Polarization in Heavy Ion Physics

Heavy quarkonium production and polarization

We present a perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum $p_T$ at collider energies, which includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the $m_Q^2/p_T^2$ expansion for heavy quark mass $m_Q$. We estimate fragmentation functions in the non-relativistic QCD formalism, and reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization.

Structure of virtual photon polarization in ultrarelativistic heavy-ion collisions

Anisotropy in heavy-ion collisions leads to polarization of both direct and virtual photons, the latter detected via internal conversion to dileptons pairs. Thus measurement of photon polarization probes the anisotropy at all stages of collisions. In order to characterize the polarization of virtual photons, we derive here the general structure of the photon polarization operator, rho^(mu nu), in an anisotropic medium, in terms of the four spectral functions, two transverse and one longitudinal, as usual, plus a new spectral function that reflects anisotropy in asymmetric collisions; and deriv…

磁场与热介质中重夸克的自旋极化探究

Exploring Spin Polarization of Heavy Quarks in Magnetic Fields and Hot Medium

本研究采用LLG方程，结合RHIC与LHC的介质及磁场真实演化，探究磁场与热介质对重夸克自旋极化的双重影响，明确了极化的限制因素及夸克极化的质量依赖规律。

Local polarization and isothermal local equilibrium in relativistic heavy ion collisions

We show that the inclusion of a recently found additional term of the spin polarization vector at local equilibrium which is linear in the symmetrized gradients of the velocity field, and the assumption of hadron production at constant temperature restore the quantitative agreement between hydrodynamic model predictions and local polarization measurements in relativistic heavy ion collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. The longitudinal component of the spin polarization vector turns out to be very sensitive to the temperature value, with a good fit around 155 MeV. The implications of thi…

初始条件和体黏滞效应对高能重离子碰撞中 $\Lambda$ 极化的影响

Initial conditions and bulk viscosity effects on $Λ$ polarization in high-energy heavy ion collisions

本文研究不同初始条件和体黏滞参数化对重离子碰撞中 $\Lambda$ 局域极化的显著影响，并通过与 STAR、ALICE 数据比较，揭示体黏滞对 LHC 能量下纵向极化符号的关键作用。

Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization

We calculate the ${\cal O}(α_s^3)$ short-distance, QCD collinear-factorized coefficient functions for all partonic channels that include the production of a heavy quark pair at short distances. This provides the first power correction to the collinear-factorized inclusive hadronic production of heavy quarkonia at large transverse momentum, $p_T$, including the full leading-order perturbative contributions to the production of heavy quark pairs in all color and spin states employed in NRQCD treatments of this process. We discuss the role of the first power correction in the production rates and…

Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy

We study the polarization of particles in relativistic heavy-ion collisions at very high energy along the beam direction within a relativistic hydrodynamic framework. We show that this component of the polarization decreases much slower with center-of-mass energy compared to the transverse component, even in the ideal longitudinal boost-invariant scenario with non-fluctuating initial state, and that it can be measured by taking advantage of its quadrupole structure in the transverse momentum plane. In the ideal longitudinal boost-invariant scenario, the polarization is proportional to the grad…

Global polarization in heavy-ion collisions based on axial vortical effect

Global polarization of $Λ$ and $\barΛ$ is calculated based on the axial vortical effect (AVE). Simulations are performed within the model of the three-fluid dynamics. Equations of state with the deconfinement transition result in a good agreement with STAR data for both $Λ$ and $\barΛ$ polarization, in particular, with the $Λ$-$\barΛ$ splitting. Suppression of the gravitational-anomaly contribution required for the data reproduction is in agreement with predictions of the QCD lattice simulations. Predictions for the global polarization in forthcoming experiments at lower collision energies are…

Initial state of Heavy-Ion Collisions: Isotropization and thermalization

I discuss how local thermal equilibrium and hydrodynamical flow are reached in heavy-ion collisions in the weak coupling limit.

Production of multiply heavy flavoured baryons from Quark Gluon Plasma in relativistic heavy ion collisions

It is argued that in heavy ion collisions at LHC there could be a sizeable production of baryons containing two or three heavy quarks from statistical coalescence. This production mechanism is peculiar of Quark Gluon Plasma and the predicted rates, in heavy ion collisions at LHC energy, exceed those from a purely hadronic scenario, particularly for Xi_bc and Omega_ccc. Thus, besides the interest in the discovery of these new states, enhanced ratios of these baryons over singly heavy flavoured hadrons, like B or D, in heavy ion collisions with respect to pp at the same energy, would be a clear …

Some aspects of global Lambda polarization in heavy-ion collisions

Large orbital angular momentum can be generated in non-central heavy-ion collisions, and part of it is expected to be converted into final particle's polarization due to the spin-orbit coupling. Within the framework of A Multi-Phase Transport (AMPT) model, we studied the vorticity-induced polarization of $Λ$ hyperons at the midrapidity region $|η|<1$ in Au-Au collisions at energies $\sqrt{s_{NN}}=7.7\sim200$ GeV. Our results show that the global polarization decreases with the collisional energies and is consistent with the recent STAR measurements. This behavior can be understood by less asym…

Shear-induced spin polarization in heavy-ion collisions

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction $\hat{z}$ and the out-plane directio…

Core-corona approach to describe hyperon global polarization in semi-central relativistic heavy-ion collisions

We report on the core-corona model developed to describe the main features of hyperon global polarization in semicentral relativistic heavy-ion collisions as a function of the collision energy. We first neglect the contribution to polarization from hyperons produced in the corona. In this scenario, the global polarization turns out to be described by a delicate balance between the vorticity-to-spin transferring reactions in the core and the predominance of corona over core matter at low energies. We show how this last feature provides a key ingredient missing in our original model that helps t…

Photon-photon production of lepton, quark and meson pairs in peripheral heavy ion collisions

We review our recent results on exclusive production of $μ^+ μ^-$, heavy quark-antiquark, and meson-antimeson pairs in ultraperipheral, ultrarelativistic heavy ion collisions.

Sequential hadronization in heavy ion collisions

Heavy flavor supplies a chance to constrain and improve the hadronization mechanism. We have established a sequential coalescence model with charm conservation and applied it to the charmed hadron production in heavy ion collisions. The charm conservation enhances the earlier hadron production and suppresses the later production. This relative enhancement (suppression) changes significantly the ratios between charmed hadrons in heavy ion collisions.

Classical fields and heavy ion collisions

This is a review of numerical applications of classical gluodynamics to heavy ion collisions. We recall some results from calculations of gluon production, discuss their implications for heavy ion phenomenology, and outline a strategy to calculate the number of quark pairs produced by these classical fields.

Monitoring parton equilibration in heavy ion collisions via dilepton polarization

In this note we discuss how angular distribution of the dileptons produced in heavy ion collisions at RHIC/LHC energies can provide an information about a degree of local equilibration of the quark-gluon plasma produced at different invariant mass regions.

The initial stages of heavy-ion collisions in the Color Glass Condensate framework

In this short review, we present the description of the early stages of a heavy ion collision at high energy in the Color Glass Condensate framework.

重离子碰撞中的重夸克势与热粲夸克产生

Heavy quark potential and thermal charm production in heavy-ion collisions

本研究通过LHC重离子碰撞热粲夸克产生测试三种重夸克势，发现自由能势高估粲夸克产生，HotQCD合作组提出的非屏蔽势结果最接近ALICE实验数据。

Quark spin - thermal vorticity alignment and the Lambda, anti-Lambda polarization in heavy-ion collisions

It has been proposed that the $Λ$ and $\overlineΛ$ polarizations observed in heavy-ion collisions are due to the interaction between quark spin and thermal vorticity. In this work we report on a computation of the relaxation time required for this alignment to occur at finite temperature and baryon chemical potential, considering quarks with a finite mass. The calculation is performed after modelling the interaction by means of an effective vertex which couples the thermal gluons and quarks within the vortical medium. We show that the effect of the quark mass is to reduce the relaxation time a…

重离子碰撞中恒定能量密度下的冻结与自旋极化

Freezeout at constant energy density and spin polarization in heavy-ion collisions

本文发展了几何感知的线性响应理论，在等能量密度超曲面上研究Λ超子自旋极化，发现对等温冻结的修正虽小（≤10%），但对局域极化观测量可能重要。

Vorticity and Particle Polarization in Relativistic Heavy-Ion Collisions

We review studies of vortical motion and the resulting global polarization of $Λ$ and $\barΛ$ hyperons in heavy-ion collisions, in particular, within 3FD model. 3FD predictions for the global midrapidity polarization in the FAIR-NICA energy range are presented. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pu…

Hydrodynamic helicity polarization in relativistic heavy ion collisions

We study helicity polarization through the (3+1) dimensional relativistic viscous hydrodynamic models at $\sqrt{s_{NN}}=200$GeV Au+Au collisions. Similar to the local spin polarization, we consider the helicity polarization beyond global equilibrium and investigate the contributions induced by thermal vorticity, shear viscous tensor, and the fluid acceleration. We find that the local helicity polarization induced by thermal vorticity dominates over other contributions. It also implies that in the low-energy collisions, the the fluid vorticity as part of thermal vorticity may play the crucial r…

Helicity polarization in relativistic heavy ion collisions

We discuss the helicity polarization which can be locally induced from both vorticity and helicity charge in non-central heavy ion collisions. Helicity charge redistribution can be generated in viscous fluid and contributes to azimuthal asymmetry of the polarization along global angular momentum or beam momentum. We also discuss on detecting the initial net helicity charge from topological charge fluctuation or initial color longitudinal field by the helicity polarization correlation of two hyperons and the helicity alignment of vector mesons in central heavy ion collisions.

Relativistic heavy ion collisions --- Where are we now? Where do we go?

Various aspects of the current status of ultrarelativistic heavy ion collisions are reviewed. Perspectives of heavy ion physics in the future are given as well.

Some Aspects of the Theory of Heavy Ion Collisions

We review the theoretical aspects relevant in the description of high energy heavy ion collisions, with an emphasis on the learnings about the underlying QCD phenomena that have emerged from these collisions.

重离子碰撞早期由磁场动力学诱导的夸克自旋极化

Dynamical induced quark spin polarization by magnetic field at the early stage of heavy-ion collisions

本文基于手征动理学理论研究重离子碰撞预热阶段磁场诱导的夸克自旋极化，揭示夸克相互作用对自旋衰减的双重影响及早期QGP偏离楞次定律的量子修正机制。

On Ambiguity of Definition of Shear and Spin-Hall Contributions to $Λ$ Polarization in Heavy-Ion Collisions

Recently proposed thermal-shear and spin-Hall contributions to the particle polarization in heavy-ion collisions are discussed. Alternative definitions of the thermal-shear contribution, i.e. those of Becattini-Buzzegoli-Palermo on the one hand and Liu-Yin on the other, are very similar in the midrapidity region while quite different at forward-backward rapidities, which are measured in fixed-target experiments. It is shown that the thermal-shear contribution to the global polarization with momentum averaging extended to all momenta is very different within these alternative definitions. The s…

相对论重离子碰撞中夸克偶素产生的最新理论进展

Recent theoretical developments in quarkonia production in relativistic heavy ion collisions

本文综述了相对论重离子碰撞中夸克偶素产生的最新理论进展，重点涵盖其热性质、重夸克有限温度势及实时演化研究。

Landau hydrodynamic solution for non-central heavy ion collisions

The manuscript presents generalization of the Landau hydrodynamic solution for multiparticle production applied for non-central relativistic heavy ion collisions. Obtained solution enables to calculate anisotropy parameter $v_2$ for different rapidities with respect to the initial conditions for hydrodynamics.

Vorticity and Spin Polarization in Heavy Ion Collisions: Transport Models

Heavy ion collisions generate strong fluid vorticty in the produced hot quark-gluon matter which could in turn induce measurable spin polarization of hadrons. We review recent progress on the vorticity formation and spin polarization in heavy ion collisions with transport models. We present an introduction to the fluid vorticity in non-relativistic and relativistic hydrodynamics and address various properties of the vorticity formed in heavy ion collisions. We discuss the spin polarization in a vortical fluid using the Wigner function formalism in which we derive the freeze-out formula for the…

Spin Dependent Fragmentation Functions for Heavy Flavor Baryons and Single Heavy Hyperon Polarization

Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are calculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicity included. $Λ_b$ , $Λ_c$ and $Ξ_c$ production rate and polarization at LEP energies are calculated and, where possible, compared with experiment. A different approach, also relying on a heavy quark-diquark model, is proposed for the small momentum transfer inclusive production of polarized heavy flavor hyperons. The predicted $Λ_c$ polarization is roughly in agreement with experiment.

Femto-cyclones and hyperon polarization in Heavy-Ion Collisions

We study the structure of vorticity and hydrodynamic helicity fields in peripheral heavy-ion collisions using the kinetic Quark-Gluon String Model. The angular momentum conservation within this model holds with a good accuracy. We observe the formation of specific toroidal structures of vorticity field (vortex sheets). Their existence is mirrored in the polarization of hyperons of the percent order.

物质中重夸克的自旋极化：来自有效场论的预测

Spin polarization of heavy quarks in matter: predictions from effective field theories

本研究利用两种有效场论分析LHC重离子碰撞中重夸克自旋极化，发现仅需一个与涡度相关的自由参数即可预测小到中等p_T区间的极化结果，且粲夸克与底夸克的该参数差异不大。

Probing the linear polarization of photons in ultraperipheral heavy ion collisions

We propose to measure the linear polarization of the external electromagnetic fields of a relativistic heavy ion through azimuthal asymmetries in dilepton production in ultraperipheral collisions. The asymmetries estimated with the equivalent photon approximation are shown to be sizable.

Recent developments in chiral and spin polarization effects in heavy-ion collisions

We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions. We present updated experimental results for the chiral magnetic effect and related phenomena. The time evolution of the magnetic fields in different models is discussed. The newly developed quantum kinetic theory for massive fermions is reviewed. We present theoretical and experimental results for the polarization of $Λ$ hyperons and the $ρ_{00}$ value of vector mesons.

Vacuum polarization radiative correction to the parity violating electron scattering on heavy nuclei

The effect of vacuum polarization on the parity violating asymmetry in the elastic electron-nucleus scattering is considered. Calculations are performed in the high-energy approximation with an exact account for the electric field of the nucleus. It is shown that the radiative correction to the parity violating asymmetry is logarithmically enhanced and the value of the correction is about -1%.

A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions

We perform a systematic study of the spin polarization of hyperons in heavy-ion collisions using the MUSIC hydrodynamic model with A Multi-Phase Transport (AMPT) pre-equilibrium dynamics. Our model calculations nicely describe the measured collision-energy, centrality, rapidity, and $p_T$ dependence of $Λ$ polarization. We also study and predict the global spin polarization of $Ξ^-$ and $Ω^-$ as a function of collision energy, which provides a baseline for the studies of the magnetic moment, spin, and mass dependence of the spin polarization. For the local spin polarization, we calculate the r…

$Λ$ spin polarization in event-by-event relativistic heavy-ion collisions

We present a systematic study of $Λ$ hyperon's polarization observables using event-by-event (3+1)D relativistic hydrodynamics. The effects of initial hot spot size and QGP's specific shear viscosity on the polarization observables are quantified. We examine the effects of the two formulations of the thermal shear tensor on the polarization observables using the same hydrodynamic background. With event-by-event simulations, we make predictions for the Fourier coefficients of $Λ$'s longitudinal polarization $P^z$ with respect to the event planes of different orders of anisotropic flow. We propo…

Double fermionic contributions to the heavy-quark vacuum polarization

We compute the virtual O(α_s^3 n_f^2) corrections to the heavy quark vector current correlator in terms of expansions in the external momentum and as an exact numerical solution. As a byproduct, the available high-energy expansion at the three-loop level is extended.

Polarization probes of vorticity in heavy ion collisions

We discuss the information that can be deduced from a measurement of particle (hyperon or vector meson) polarization in ultrarelativistic nuclear collisions. We describe the sensitivity of polarization to initial conditions, hydrodynamic evolution and mean free path, and find that the polarization observable is sensitive to all details and stages of the system's evolution. We suggest that an experimental investigation covering production plane and reaction plane polarizations, as well as the polarization of jet-associated particles in the plane defined by the jet and particle direction, can he…

相对论重离子碰撞中自旋3/2强子的整体张量极化与夸克自旋关联

Global tensor polarization of spin $3/2$ hadrons and quark spin correlations in relativistic heavy ion collisions

本文研究相对论重离子碰撞中自旋3/2强子的整体张量极化，揭示其二阶和三阶张量极化分别对夸克胶子等离子体中局域两夸克和三夸克自旋关联敏感，并建立了可测张量极化与夸克自旋关联之间的定量关系。

How EIC can help us to understand heavy-ion collisions

I give a brief overview of the science cases of the Electron-Ion Collider (EIC) with a particular emphasis on the connections to the physics of ultrarelativistic heavy-ion collisions.

Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD

New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed.

Production, Decay, and Polarization of Excited Heavy Hadrons

We discuss the production via fragmentation of excited heavy mesons and baryons, and their subsequent decay. In particular, we consider the question of whether a net polarization of the initial heavy quark may be detected, either in a polarization of the final ground state or in anisotropies in the decay products of the excited hadron. The result hinges in part on a nonperturbative parameter which measures the net transverse alignment of the light degrees of freedom in the fragmentation process. We use existing data on charmed mesons to extract this quantity for certain excited mesons. Using t…

通过介质极化、弹性碰撞和辐射过程研究重夸克的能量损失

Study of the heavy quarks energy loss through medium polarization, elastic collision and radiative processes

本文在夸克-胶子等离子体平衡相中比较研究了重夸克通过介质极化、弹性碰撞和辐射三种机制的能量损失，并通过计算核修正因子R_AA揭示了低动量下介质极化的显著贡献。

Estimates of hyperon polarization in heavy-ion collisions at collision energies $\sqrt{s_{NN}}=$ 4--40 GeV

Global polarization of $Λ$ and $\barΛ$ hyperons in Au+Au collisions at collision energies $\sqrt{s_{NN}}=$ 4-40 GeV in the midrapidity region and total polarization, i.e. averaged over all rapidities, are studied within the scope of the thermodynamical approach. The relevant vorticity is simulated within the model of the three-fluid dynamics (3FD). It is found that the performed rough estimate of the global midrapidity polarization quite satisfactorily reproduces the experimental STAR data on the polarization, especially its collision-energy dependence. The total polarization increases with th…

Lambda polarization in heavy ion collisions: from RHIC BES to LHC energies

STAR collaboration at RHIC has recently measured the polarization of $Λ$ hyperons in non-central heavy ion collisions in the RHIC Beam Energy Scan (BES) program. The magnitude of the polarization was found to decrease from few percents at the lowest BES energies to $\approx0.2$% at the top RHIC energy. The polarization signal has been reproduced in different hydrodynamic calculations assuming a thermodynamic spin-vorticity coupling mechanism at the Cooper-Frye hypersurface. In this work an extension of our existing calculations of the $Λ$ polarization in the RHIC BES program to the top RHIC an…

AdS/CFT for the early stages of heavy ion collisions

I give a brief introduction to the AdS/CFT correspondence targeted at heavy-ion physicists. I also review some insights to our understanding of the early stages of heavy-ion collisions coming from selected studies made using methods of the AdS/CFT correspondence.

Basic phenomenology for relativistic heavy-ion collisions

Basic concepts used to interpret the soft-hadronic data collected in relativistic heavy-ion collisions are reviewed at the elementary level.

超子纵向极化与矢量介子自旋对齐在重离子碰撞热模型中的研究

Hyperon longitudinal polarization and vector meson spin alignment in a thermal model for heavy-ion collisions

研究通过热模型探讨重离子碰撞中超子纵向极化与矢量介子自旋对齐的共同机制，发现两者存在相关性，但模型尚无法完全定量解释数据。

Heavy quark polarizations of $e^+e^-\to q \bar q h$ in the general two Higgs doublet model

The polarizations of the heavy quark ($q=t$ or $b$) in the process $e^+e^- \to q \bar q h$ have been calculated in the general two Higgs doublet model. The CP violating normal polarization of the top quark can reach 8%, and $2 \sim 3%$ for the bottom quark, while it is zero in the standard model. The longitudinal and transverse polarizations of the bottom quark can be significantly different from those in SM and consequently could aslo be used as the probe of the new physics.

Lambda^0 polarization as a probe for production of deconfined matter in ultra-relativistic heavy-ion collisions

We study the polarization change of Lambda^0's produced in ultra-relativistic heavy-ion collisions with respect to the polarization observed in proton-proton collisions as a signal for the formation of a Quark-Gluon Plasma (QGP). Assuming that, when the density of participants in the collision is larger than the critical density for QGP formation, the Lambda^0 production mechanism changes from recombination type processes to the coalescence of free valence quarks, we find that the Lambda^0 polarization depends on the relative contribution of each process to the total number of Lambda^0's produ…

Heavy-quark spin polarization induced by the Kondo effect in a magnetic field

We propose a new mechanism of the heavy-quark spin polarization (HQSP) in quark matter induced by the Kondo effect under external magnetic field. The Kondo effect is caused by a condensate between a heavy and a light quark called the Kondo condensate leading to a mixing of the heavy and light quark spins. Thus the HQSP is driven through the Kondo effect from light quarks coupling with the magnetic field in quark matter. For demonstration, we employ the Nambu--Jona-Lasinio type model under a magnetic field, and investigate the HQSP within the linear response theory with vertex corrections requi…