Overview of Experimental Searches for CME and CVE

• Huan Zhong Huang (University of California)

STAR measurements in search of the CME and the CMW

• Gang Wang (UCLA)

The study of the chiral magnetic effect in CMS

• Wei Li (Rice University)

Field theoretic perspectives of the chiral magnetic effect with a nonconstant axial chemical potential

• Defu Hou (Central China Normal University)

I will report our works about the field theoretic perspectives of the anomalous transports, especially with a nonconstant axial chemical potential [1,2]. We assess the applicability of the Wigner function formulation in its present form to the chiral magnetic effect and note some issues regarding the conservation and the consistency of the electric current in the presence of an inhomogeneous and time-dependent axial chemical potential. The problems are rooted in the ultraviolet divergence of the underlying field theory associated with the axial anomaly and can be fixed with the Pauli-Villars regularization of the Wigner function. The chiral magnetic current with a nonconstant axial chemical potential is calculated with the regularized Wigner function and the phenomenological implications are discussed. In addition, we study analytically the one-loop contribution to the chiral magnetic effect (CME) using lattice regularization with a Wilson fermion field [3]. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical value of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher-order corrections from QCD dynamics is also assessed. [1] Yan Wu， Defu Hou and Hai-cang Ren, Phys. Rev. D 96 (2017), 096015; [2] Defu Hou, Hui Liu and Hai-cang Ren,  JHEP 1105 (2011) 046; [3] Bo Feng, Defu Hou , Hai-cang Ren, Yan Wu, Phys. Rev. D 95 (2017) , 114023.

A reality check for chiral magnetic transport & holography

• Matthias Kaminski (University of Alabama)

We are going to examine the effects of a strong magnetic field in presence of a chiral anomaly within a charged plasma in a holographic model, and compare to the analogous effects in QCD. Similarities and differences will be highlighted.

Review on holographic methods for the Chiral Magnetic Effect

• Karl Landsteiner (Instituto de Fisica Teorica CSIC/UAM)

Effects of strong magnetic fields in heavy ion collisions

• Shi Pu (Uni. of Tokyo)

A New Correlator to Detect and Characterize the Chiral Magnetic Effect

• Roy Lacey (Stony Brook University)

A charge-sensitive in-event correlator is proposed and tested for its efficacy to detect and characterize charge separation associated with the Chiral Magnetic Effect (CME) in heavy ion collisions. Tests, performed with the aid of two reaction models, indicate discernible responses for background and CME-driven charge separation, relative to the second- (Ψ2) and third-order (Ψ3) event planes, which could serve to identify the CME. The tests also indicate a degree of sensitivity which would enable robust characterization of the CME via Anomalous Viscous Fluid Dynamics (AVFD) model comparisons.

Charge-Balance Correlations from Hydrodynamic Calculations

• Scott Pratt (Michigan State)

Lattice Gauge Theory confidently provides the equation of state, charge susceptibilities, and with less confidence, the diffusion constant and viscosity. These elements, combined with other measurements, strongly constrain the hydrodynamic evolution of high-energy heavy-ion collisions and the evolution of correlation functions indexed by charge. This leads to predictions for the charge balance function. In addition to providing a strong test of whether the QCD matter created in the collision, these effects account for most, if not all, of the observable used to search for parity fluctuations. Results will be provided to illustrate how the degree to which correlations from this effect account for the parity observable measured by STAR, and the range at which it might vary.

Beam energy and collision system dependence of charge separation using the R($\Delta S$) correlator

• Niseem Abdelrahman (State University of New York, Stony Brook)

A charge-sensitive correlator R$(\Delta S)$ is used to detect and characterize charge separation associated with the Chiral Magnetic Effect (CME) in heavy-ion collisions. The correlator gives a concave-shaped response relative to the second-order event plane, $\Psi_2$, and a null response relative to the third-order plane, $\Psi_3$, for CME-driven charge separation~[1]. We will present and discuss R$(\Delta S)$ measurements, relative to $\Psi_2$ and $\Psi_3$, for collisions of Au+Au at $\sqrt{s_{NN}}$= 200, 39, 27 and 19.6 GeV, U+U at $\sqrt{s_{NN}}$= 193 GeV, and Cu+Au, Cu+Cu, d+Au and p+Au at $\sqrt{s_{NN}}$=200 GeV. Measurements for a broad range of transverse momentum, pseudorapidity, and centrality intervals, will be presented and compared to results from the Anomalous Viscous Fluid Dynamics model [2]. [1] N. Magdy, S. Shi, J. Liao, N. Ajitanand, and R. A. Lacey, arXiv:1710.01717 [2] S. Shi, Y. Jiang, E. Lilleskov and J. Liao, arXiv:1711.02496

Resummed hydrodynamic expansion for an electromagnetic interacting plasma

• Leonardo Tinti (Goethe University)

Anomalous currents produced a renewed interest in the physics of a plasma interacting with an electromagnetic field. In order to carefully study the anomalous currents one must be confident on the formalism for the non-anomalous contributions. We apply a modified version of the method of moments to the Boltzmann-Vlasov equations, in order to extract the behavior of macroscopic quantities and check the convergence properties. We didn't consider a classical gradient expansion, since there is a mounting evidence that the standard Chapman-Enskog expansion has a vanishing radius of convergence. The method of moments, on the other hand, is free from such problems in the absence of external fields. However, if one introduces an electro-magnetic field interacting with the plasma, this systematic expansion breaks down: Successive moments are found to couple not only to energy moments of higher, but also of lower order, which diverge in the ultra-relativistic (massless) limit, or require unrealistic machine precision. We solve the issue using resummed moments which consist of a sum of all the moments of the same tensorial rank, but different energy weights. The resulting equations are always well defined. The evolution of the hydrodynamics moments (four-velocity, energy density, pressure, pressure corrections etc.) is exactly the same as the one provided by the traditional method of moments, which is ill defined only for higher orders. We tested numerically the convergence properties of the resummed expansion for some known solutions of the microscopic theory, and we checked that the convergence remains intact in the simplest case in which the traditional expansion breaks down. Namely the Boltzmann-Vlasov equation for charged mass-less particles coupled to the Maxwell equations in a (0+1)-dimensional expansion.

Lambda polarization from RHIC BES to LHC energies in viscous hydrodynamic approach

• Iurii Karpenko (SUBATECH / CNRS)

We overview the collision energy dependence of different components of polarization of Lambda hyperons in a 3 dimensional hydrodynamic model for heavy ion collisions. We discuss the connection between the polarization observables and the properties of the initial state and hydrodynamic phase of the matter evolution in heavy ion collisions.

Status and outlook of polarization measurements

• Sergei Voloshin (Wayne State University)

Polarization measurements in STAR

• Takafumi Niida (Wayne State University)

Global polarization measurements and their implications regarding the magnetic fields

• Michael Lisa (Ohio State University)

Spectators in non-central heavy-ion collisions create dynamic magnetic fields with magnitudes as large as $10^{14}$ Tesla. The fields may cause a splitting between $\Lambda$ and $\overline{\Lambda}$ polarization through magnetic moment coupling. A signal of such splitting could provide a quantitative estimate of the field strength at freeze-out. The dynamics of the magnetic field are expected to depend on the conductivity of the QGP. The field is of fundamental interest for heavy-ion physics, but is of particular interest to other novel phenomena, e.g. the Chiral Magnetic Effect (CME). The STAR Collaboration observed global hyperon polarization in non-central Au+Au collisions in the energy range of 7.7 to 39 GeV [1]. In this analysis, a magnetic splitting is hinted at, but the improved statistics and resolution achievable with future runs are required to make a definitive measurement of the magnetic field. In 2018, RHIC will run an isobaric system (Zr+Zr and Ru+Ru) as well as 1B 27GeV Au+Au events. The 27GeV dataset will add an important point on the energy trend of the polarization, and may provide the earliest statistical evidence for magnetic splitting. If a measurable splitting existed at top RHIC energy for the isobar system, one would expect a difference in the splitting between the two species, due to a difference in the underlying magnetic field. Observing such a difference would provide robust evidence that the splitting between $\Lambda$ and $\overline{\Lambda}$ polarization is driven by the magnetic field. [1] Nature 548, 62 (2017)

Lambda polarization in peripheral heavy ion collisions

• Laszlo Csernai (University of Bergen)

Relativistic thermodynamics with spin provided the polarization to characterize the spin alignment in rotating systems. Based on a high-resolution, (3+1)D particle-in-cell relativistic (PICR) hydrodynamics simulation, we obtain the polarization vector for Lambda hyperons at NICA and FAIR energies, and find that the y- component of the polarization vector is dominant, while x- and z- components are anti-symmetric in the transverse momentum space. This implies a vanishing contribution to the global polarization inthe EbE c..m. frame. The linear dependence of polarization on impact parameter reveals that the polarization stems from the initial orbital angular momentum; the polarization effect is found to decrease with increasing energy, which is in line with the recent results from RHIC BES program, and is attributed to the more intensive thermal motion of particles at higher energies. The time evolution of the polarization in our calculation agrees with the time evolution of vorticity predicted previously. [1] Y.L. Xie, D.J. Wang, and L. P. Csernai, Phys. Rev. C 95, 031901(R) (2017). [2] Y.L. Xie, M. Bleicher, H. Stöcker, D. J. Wang, and L. P. Csernai, Phys. Rev. C 94, 054907 (2016).

Nonequilibrium axial charge production in expanding color fields

• Naoto Tanji (ECT*)

By a high-energy collision of heavy-ions, strong color fields carrying nonzero topological charges are generated. Quark production in such color fields accompanies the production of axial charges. To find observable consequences of the chiral magnetic effect and related phenomena, first-principles calculations of the axial charge production at the early-stage of heavy-ion collisions are indispensable. I will present first results for real-time lattice computations of the axial charge production from strong color fields in the longitudinally expanding geometry. The quantum dynamics of quarks is described by solving the Dirac equation under classical SU(2) gauge fields with an initial condition motivated by Glasma flux tubes. By employing the Wilson fermion extended to the expanding geometry, the axial anomaly is verified on the real-time lattice.

Out-of-Equilibrium Chiral Magnetic Effect from Chiral Kinetic Theory

• Pengfei Zhuang (Tsinghua University)

World-line Approach to Chiral Kinetic Theory and the Chiral Magnetic Effect

• Niklas Mueller (Brookhaven National Laboratory)

Recent searches for CP- and P- odd phenomena in ultra relativistic heavy-ion collisions have attracted much interest and are a prime motivation for significant theoretical effort. Anomalous and topological effects, such as the Chiral Magnetic Effect (CME), receive important contributions from the pre-equilibrium phase of a collision. While real-time lattice simulations can be used to study the earliest stage, quantitative predictions of experimental signatures are only feasible once the subsequent transport of the messengers of the CME through the fireball are understood. An interesting question is how the chiral imbalance generated at early times persists through a fluctuating background of sphalerons in addition to other "non-anomalous" interactions with the QGP. To address this question, we construct a relativistic chiral kinetic theory using the world-line formulation of quantum field theory. Using this framework we clarify the role of a possible Berry’s phase and that of the chiral anomaly. We discuss how the fate of the Chiral Magnetic Effect could be understood by matching our framework to the results of real-time lattice simulations at early times and to Chiral MagnetoHydrodynamics at late times.

Chiral kinetic theory in noninertial frame

• Xu-Guang Huang (Fudan University)

Chiral kinetic theory is the kinetic theory with chiral anomaly encoded. We discuss the chiral kinetic theory in curved spacetime. More specifically, we derive the chiral kinetic equations in rotating and accelerating frames. We also discuss the consequences from the chiral kinetic equations.

Non-Equilibrium Anomalous Transport of Chiral Fluids from Kinetic Theory

• Di-Lun Yang (RIKEN)

The chiral kinetic theory (CKT) is a useful tool to investigate anomalous transport pertinent to quantum anomalies in and out of equilibrium for weyl-fermion systems, which has been widely applied to study chiral magnetic/vortical effects (CME/CVE) in heavy ion collisions (HIC). However, there exist some fundamental issues such as Lorentz covariance and systematic inclusion of collisions in CKT. Such issues have been recently addressed via phenomenological approaches. Nevertheless, a first-principle derivation based on quantum field theories (QFT) is desired. In this talk, we introduce the QFT derivation of CKT from the Wigner-function approach, which consistently manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. Moreover, we implement such a formalism to investigate second-order responses of chiral fluids near local equilibrium. Such non-equilibrium anomalous transport is dissipative and affected by interactions. For the study of anomalous transport in closed systems preserving energy-momentum conservation such as quark gluon plasmas, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation. We obtain anomalous charge Hall currents engendered by background electric fields and temperature/chemical-potential gradients. Furthermore, CME/CVE currents receive viscous corrections as non-equilibrium modifications stemming from the interplay between side jumps, magnetic-moment coupling, and chiral anomaly. On the other hand, the quantum corrections upon the charge density and energy-density current vanish in the classical RT approximation, which agree with the matching conditions led by CKT with energy-momentum conservation. This talk will be based on the works in arXiv:1801.08253, arXiv:1710.00278 (Phys. Rev. D 97 (2018) no.1, 016004), arXiv:1612.04630 (Phys.Rev. D95 (2017) no.9, 091901, Rapid Communication).

The ideal hydrodynamic limit of a fluid with polarization using Lagrangian techniques

• Giorgio Torrieri (Unicamp)

After giving a brief introduction of the expected role of polarization within hydrodynamics, I will describe the difficoulties inherent in defining a hydrodynamic limit when polarization is present. I will argue that the only consistent way of surpassing these difficulties is to use lagrangian techniques, and describe progress in this direction. I conclude by illustrating the connection between polarization and dissipation.

Polarisation in heavy-ion collsions: how to discriminate between different mechanisms?

• Oleg Teryaev (JINR)

The relation of hadrons polarisation in rotating matter to axial anomaly is considered in some detail. The various mechanisms of coupling of hydrodynamical vorticity and helicity to spin are compared. The interplay between mesonic and baryonic degrees of freedom as well as duality between quantum field theory and hydrodynamics are discussed. The senistivity of polarisation observables to dynamics are analyzed.

Relativistic hydrodynamics with spin

• Wojciech FLORKOWSKI (UJK Kielce / IFJ PAN Krakow)

A new framework for relativistic hydrodynamics with spin is proposed. It is based on the conservation laws for charge, energy, momentum, and angular momentum. The conservation laws lead to hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor. The resulting set of differential equations extend the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way.

Disentangle covariant Wigner functions for chiral fermions

• Qun Wang (University of Science and Technology of China)

Phi alignment measurement in STAR

• Aihong Tang (Brookhaven National Lab)

On the Universality of the Chern-Simons Diffusion Rate

• Aldo Lorenzo Cotrone (FI)

To be announced.

Chiral soliton lattice in magnetic fields and rotation

• Naoki Yamamoto (Keio University)

The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. In this talk, we show that CSL appears as a ground state of QCD at nonzero chemical potential in a strong magnetic field or under rapid rotation. We also show that the effective theory for electromagnetic fields in the CSL is given by the axion electrodynamics and that one of the helicity states of photons has the nonrelativistic gapless dispersion relation. A possible realization of the CSL in noncentral heavy ion collisions will be discussed.

Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles

• Enrico Speranza (Frankfurt University)

We study properties of the spin density matrices used in recent formulations of relativistic hydrodynamics of particles with spin 1/2. We show that it is possible to reduce the spin density matrices to the forms linear in the Dirac spin operator. This allows for a natural determination of the spin polarization vectors of particles and antiparticles by the trace of products of the spin density matrices and the Pauli matrices. We demonstrate that the total spin polarization vector obtained in this way agrees with the Pauli-Lubanski four-vector, constructed from an appropriately chosen spin tensor and boosted to the particle rest frame. We further show that several forms of the spin tensor used in the literature give the same Pauli-Lubanski four-vector.

Status of lattice QCD with magnetic field

• Massimo D'Elia (PI)

Competition between the rotational effect and the finite-size effect on relativistic fermions

• Kazuya Mameda (Fundan University)

The rotational effect on QCD is one of the central subjects in heavy-ion collision physics. In this talk, we discuss the importance of the finite-size effect in the low-energy structure of rotating fermions, which is usually absent from discussions. Taking into account this finite-size effect, we show that while the rotational effect cannot solely become physically visible, other external sources (temperature, density, background fields etc.) enable rotation to affect thermodynamic systems. As an example, we also demonstrate that the interplay between magnetic field and rotation changes the breaking structure of chiral symmetry; due to the rotational effect, chiral symmetry is restored as magnetic field increases, which we call the rotational magnetic inhibition.

Chirality evolution in plasma with magnetic monopoles

• Kirill Tuchin (Iowa State University)

We study the electrodynamics of the chiral medium with electric and magnetic charges using the effective Maxwell–Chern–Simons theory extended to include the magnetic current. The exchange of helicity between the chiral medium and the magnetic field, known as the inverse cascade, is controlled by the chiral anomaly equation. In the presence of the magnetic current, the magnetic helicity is dissipated, so that the inverse cascade stops when the magnetic helicity vanishes while the chiral conductivity reaches a non-vanishing stationary value satisfying $\sigma_\chi^2<4\sigma_e\sigma_m$, where $\sigma_e$ , $\sigma_m$ and $\sigma_\chi$ are the electric, magnetic and chiral conductivities respectively. We argue that this state is superconducting and exhibits the Meissner effect for both electric and magnetic fields. Moreover, this state is stable with respect to small magnetic helicity fluctuations; the magnetic helicity becomes unstable only when the inequality mentioned above is violated.

Phase diagram of rotating QCD matter

• xinyang wang (IHEP, Beijing)

Understanding of QCD matter under extreme rapidly rotation is a puzzle and a hot topic in physics because of the applications in many physical environments. The typical off-central heavy ion collisions experiment create a nonzero angular momentum QCD matter. In this talk, I will discuss the QCD phase diagram and respective chiral critical end point of rotating QCD matter by using 2 flavor NJL model with considering vector interaction. The angular velocity \omega is using as a third dimension on the QCD phase diagram, and the new phase transition on temperature angular-velocity plane at certain chemical potential will be systemically discussed. An overall picture of chiral phase transition in a 3-D frame will be represented in the final.

Anomalous Chiral Effects in Viscous Fluid Dynamics: Predictions for Isobaric Collisions

• JINFENG LIAO (INDIANA UNIVERSITY)

Relativistic MHD for astrophysical plasmas: theory and numerical simulations

• Luca Del Zanna (Florence University)

...

The chiral magnetic effect in planar condensed matter systems

• Ana Julia Mizher (KU Leuven)

The chiral magnetic effect (CME) is a macroscopic manifestation of the chiral anomaly. Despite of the effort to observe it in the quark gluon plasma produced in heavy ion collisions, no unumbigous observable could be defined so far. By the other side, certain condensed matter systems that contain Dirac-like charge carriers have shown to be a suitable environment to reproduce the CME. We propose that, besides the zirconium pentatelluride in which the CME has been observed, it must be possible to construct an arrangement based on planar Dirac materials that works as an analogue of the CME.

The influence of the magnetic fields on the elliptic flow in HIC at RHIC and LHC energies

• Gabriele Inghirami (FIAS - Goethe University - Frankfurt (Germany))

The hydrodynamic model of heavy ion collisions has been very successful in providing a description of the dynamical evolution of the QGP in good agreement with the experimental data, in particular after the introduction of the viscous effects. In the last years it has been realized that the huge magnetic fields produced by the electric charges contained in the fast moving nuclei might also have measurable effects on some observables, for example the anisotropic flows. Nevertheless, so far, only very few hydro codes for HIC are able to consistently evolve the magnetic fields coupled with the fluid. ECHO-QGP is one of them, although, at the moment, only in the ideal MHD limit. In this talk, after giving an overview of the code, I will present the results of numerical simulations at RHIC and LHC energies, executed with ECHO-QGP, which suggest that the magnetic fields might slightly enhance the elliptic flow in peripheral collisions. However, given the uncertainties in the estimates of the magnitude of the magnetic field at the beginning of the numerical simulations and the absence, in our model, of important elements like the resistivity of the medium or the final hadronic rescattering, further and more refined investigations are indeed necessary to better assess the present results.

Impact of the vortical pre-equilibrium stage of relativistic heavy ion collisions on quark-gluon plasma dynamics and photon production

• Lucia Oliva (LNS)

The initial non-equilibrium phase in relativistic heavy ion collisions at finite impact parameter experiences a large vorticity induced by the huge orbital angular momentum which is produced by the two colliding nuclei. Embedding this vortical structure in a relativistic transport approach allow us to simulate the evolution of the fireball created in heavy ion collisions at RHIC and LHC energies and investigate the effects of vorticity on quark-gluon plasma. We find that the initial vortical flow in the reaction plane could result in an enhancement of the differential elliptic flow at intermediate and high transverse momenta and modifies particularly the rapidity dependence of the flow harmonics of quark-gluon plasma. We investigate how these effects are transferred to photons, which are studied including the pertinent scattering processes in the collision integral of the Boltzmann equation. Moreover, the impact of the early stage on parton dynamics and photon production is disentangled by comparing hydro-like simulations starting from a standard equilibrium initial condition to a model in which an initial state of color-electric fields with negative pressure decays into partons through the Schwinger mechanism.