We study chiral magnetic effect in collisions of AuAu, RuRu and ZrZr at s = 200GeV. The axial charge evolution is modeled with stochastic hydrodynamics and geometrical quantities are calculated with Monte Carlo Glauber model. By adjusting the relaxation time of magnetic field, we find our results in good agreement with background subtracted data for AuAu collisions at the same energy. We also make prediction for RuRu and ZrZr collisions. We find a weak centrality dependence of initial chiral imbalance, which implies the centrality dependence of chiral magnetic effect signal comes mainly from those of magnetic field and volume factor. Our results also show an unexpected dependence on system size: while the system of AuAu has larger chiral imbalance and magnetic field, it turns out to have smaller signal for chiral magnetic effect due to the larger volume suppression factor.
We give a numerical simulation of the generation of the magnetic field and the charge-separation signal due to the chiral magnetic effect (CME) --- the induction of an electric current by the magnetic field in a parity-odd matter --- in the collisions of isobaric nuclei, $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr, at $\sqrt{s_{\rm NN}}=200$ GeV. We show that such collisions provide an ideal tool to disentangle the CME signal from the possible elliptic-flow driven background effects. We also discuss some other effects that can be tested by using the isobaric collisions.
Isobaric $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{NN}}}=200$ GeV have been conducted at the Relativistic Heavy Ion Collider to circumvent the large flow-induced background in searching for the chiral magnetic effect (CME), predicted by the topological feature of quantum chromodynamics (QCD). Considering that the background in isobar collisions is approximately twice that in Au+Au collisions (due to the smaller multiplicity) and the CME signal is approximately half (due to the weaker magnetic field), we caution that the CME may not be detectable …
Quantum anomaly is a fundamental feature of chiral fermions. In chiral materials the microscopic anomaly leads to nontrivial macroscopic transport processes such as the Chiral Magnetic Effect (CME), which has been in the spotlight lately across disciplines of physics. The quark-gluon plasma (QGP) created in relativistic nuclear collisions provides the unique example of a chiral material consisting of intrinsically relativistic chiral fermions. Potential discovery of CME in QGP is of utmost significance, with extensive experimental searches carried out over the past decade. A decisive new colli…
In this proceeding we will show that the expectations of the isobaric $^{96}_{44}\mathrm{Ru}+^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+^{96}_{40}\mathrm{Zr}$ collisions on chiral magnetic effect (CME) search may not hold as originally anticipated due to large uncertainties in the isobaric nuclear structures. We demonstrate this using Woods-Saxon densities and the proton and neutron densities calculated by the density functional theory. Furthermore, a novel method is proposed to gauge background and possible CME contributions in the same system, intrinsically better than the isobaric co…
Under the approximate chiral symmetry restoration, quark interactions with topological gluon fields in quantum chromodynamics can induce chirality imbalance and parity violation in local domains. An electric charge separation ({\sc cs}) could be generated along the direction of a strong magnetic field ({\bf B}), a phenomenon called the chiral magnetic effect ({\sc cme}). {\sc cs} measurements by azimuthal correlators are contaminated by a major background from elliptic flow anisotropy ($v_2$). Isobaric $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions have been propose…
The isobaric collision experiment at RHIC provides the unique opportunity to detect the possible signal of Chiral Magnetic Effect (CME) in heavy ion collisions. The idea is to contrast the correlation observables of the two colliding systems that supposedly have identical flow-driven background contributions while quite different CME signal contributions due to the 10% variation in their nuclear charge and thus magnetic field strength. With the recently developed quantitative simulation tool for computing CME signal, the Anomalous-Viscous Fluid Dynamics (AVFD), we demonstrate that a joint (mul…
Isobar collisions which were thought to have the same background and different magnetic fields provide an opportunity to verify the chiral magnetic effect (CME) in relativistic heavy-ion collisions. However, the first result from the RHIC-STAR isobar experiment did not observe the CME signal, but discovered that the backgrounds are different between $_{44}^{96}\textrm{Ru}+_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+_{40}^{96}\textrm{Zr}$ collisions. We test eighteen cases of Woods-Saxon parameter settings resulting from different nuclear deformation or nuclear structure effects using a m…
Based on the chiral kinetic approach using quarks and antiquarks from a multiphase transport model as initial conditions, we study the chiral magnetic effect, i.e., the magnetic field induced separation of charged particles in the transverse plane, in non-central isobaric collisions of Zr$+$Zr and Ru$+$Ru, which have the same atomic number but different proton numbers. For the observable $γ^{OS}-γ^{SS}$ related to the difference between the correlations of particles of opposite charges and of same charges, we find a difference between the two collision systems if the magnetic field has a long …
In these proceedings we discuss the recent precision measurements of charge separation difference between Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\rm NN}}=200$ GeV by STAR collaboration. The measurements indicate that the magnitude of the difference in the charge separation attributable to the magnetic fields between the two systems is smaller than previously expected. We also present charge separation measurements on the Chiral Magnetic Effect search from the RHIC BES-II experiment using the Event Plane Detectors (EPD) from Au+Au collisions at $\sqrt{s_{\rm NN}} =$ 27 GeV.
Chiral magnetic effect (CME) is a macroscopic transport phenomenon induced by quantum anomaly in the presence of chiral imbalance and an external magnetic field. Relativistic heavy ion collisions provide the unique opportunity to look for CME in a non-Abelian plasma, where the chiral imbalance is created by topological transitions similar to those occurring in the Early Universe. The isobar run at Relativistic Heavy Ion Collider was proposed as a way to separate the possible CME signal driven by magnetic field from the background. The first blind analysis results from this important experiment…
Using two-nucleon and three-nucleon interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit $Δ$ isobar contributions, we calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach. In particular, we present for the first time nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with $Δ$ isobar intermediate states (N3LO$Δ$) recently developed by Piar…
The quark-gluon matter produced in relativistic heavy-ion collisions may contain local domains in which P and CP symmetries are not preserved. When coupled with an external magnetic field, such P- and CP-odd domains will generate electric currents along the magnetic field --- a phenomenon called the chiral magnetic effect (CME). Recently, the STAR Collaboration at RHIC and the ALICE Collaboration at the LHC released data of charge-dependent azimuthal-angle correlators with features consistent with the CME expectation. However, the experimental observable is contaminated with significant backgr…
We investigate the properties of electromagnetic fields in isobaric $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions at $\sqrt{s}$ = 200 GeV by using a multiphase transport model, with special emphasis on the correlation between magnetic field direction and participant plane angle $Ψ_{2}$ (or spectator plane angle $Ψ_{2}^{\rm SP}$), i.e. $\langle{\rm cos}\ 2(Ψ_B - Ψ_{2})\rangle$ [or $\langle{\rm cos}\ 2(Ψ_B - Ψ_{2}^{\rm SP})\rangle$]. We confirm that the magnetic fields of $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ collisions a…
Difference between signal and background of the chiral magnetic effect relative to spectator and participant planes in isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV
We extend a recent three-loop calculation of nuclear matter in chiral perturbation theory by including the effects from two-pion exchange with single and double virtual $Δ(1232)$-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, $\bar E_0 = -16 $MeV, $ρ_0 = 0.16 $fm$^{-3}$, can be well reproduced by adjusting the strength of a two-body term linear in density (and weakening an emerging three-body term quadratic in density). The nuclear matte…
Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densi…
Intense transient electric ({\bf E}) and magnetic ({\bf B}) fields are produced in the high energy heavy-ion collisions. The electromagnetic fields produced in such high-energy heavy-ion collisions are proposed to give rise to a multitude of exciting phenomenon including the Chiral Magnetic Effect. We use a Monte Carlo (MC) Glauber model to calculate the electric and magnetic fields, more specifically their scalar product $\bf{E}\cdot\bf{B}$, as a function of space-time on an event-by-event basis for the Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV for different centrality classes. We also calc…
In this report, we briefly examine the current status of the study of the chiral magnetic effect including theory and experimental progress. We recommend future strategies for resolving uncertainties in interpretation including recommendations for theoretical work, recommendations for measurements based on data collected in the past five years, and recommendations for beam use in the coming years of RHIC. We have specifically investigated the case for colliding nuclear isobars (nuclei with the same mass but different charge) and find the case compelling. We recommend that a program of nuclear …
In a recent preprint arXiv:2203.10029, the authors argue for a multiplicity scaling of the squared inverse width of the $R_{Ψ_{2}}$ distribution to claim a positive signal for the chiral magnetic effect from STAR's isobar data, in stark contradiction to the conclusion reached by the STAR Collaboration. This Comment points out the fallacy of their arguments and reinforces the STAR conclusion.
The production of $\rm{^3_ΛH}$ and $\rm{{^3_{\overline Λ}\overline H}}$, as well as $\rm{^3H}$, $\rm{^3\overline H}$, $\rm{^3He}$, and $\rm{^3\overline {He}}$ are studied in central collisions of isobars $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr at $\sqrt{s_{\rm{NN}}}=200$ GeV, using the dynamically constrained phase-space coalescence model and the {\footnotesize PACIAE} model with chiral magnetic effect. The yield, yield ratio, coalescence parameters, and strangeness population factor of (anti-)hypertriton and (anti-)nuclei produced in isobaric $^{96}_{44}$Ru+$^{96}_{44}…
The STAR collaboration is currently pursuing the blind analysis of the data for isobar collisions that was performed at RHIC in the year 2018 to make a decisive test of the Chiral Magnetic Effect (CME). Why is it so difficult to detect signals of CME in the experiment? Do we really understand different sources of background? Why observing similar charge separation between p/d+A and A+A does not stop us from pursuing the search for CME? In this contribution, I attempt to address some of these questions and briefly outline a few recent STAR analyses based on new methods and observables to isolat…
We study the properties of neutron star using the chiral quark-meson coupling model, in which the quark-quark hyperfine interaction due to the exchanges of gluon and pion based on chiral symmetry is considered. We also examine the effects of hyperons and $Δ$-isobars in a neutron star. Extending the SU(6) spin-flavor symmetry to more general SU(3) flavor symmetry in the vector-meson couplings to baryons, the maximum mass of neutron star can reach the recently observed, massive pulsar mass, $1.97 \pm 0.04 M_{\odot}$. In this calculation, $Λ$ and $Ξ$ are generated in a neutron star, while $Σ$ and…
The unambiguous observation of a Chiral Magnetic Effect (CME)-driven charge separation is the core aim of the isobar program at RHIC consisting of ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr and ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru collisions at $\sqrt {s_{\rm NN}}\!=\!200$ GeV. We quantify the role of the spatial distributions of the nucleons in the isobars on both eccentricity and magnetic field strength within a relativistic hadronic transport approach (SMASH, Simulating Many Accelerated Strongly-interacting Hadrons). In particular, we introduce isospin-dependent nucleon-nucleon spatial correlations in …
The (3+1)D relativistic hydrodynamics with chiral anomaly is used to obtain a quantitative description of the chiral magnetic effect (CME) in heavy-ion collisions. We find that the charge-dependent hadron azimuthal correlations are sensitive to the CME, and that the experimental observations are consistent with the presence of the effect.
In this note we prove to all orders in the small scale expansion that all off-shell parameters which appear in the chiral effective Lagrangian with explicit Delta(1232) isobar degrees of freedom can be absorbed into redefinitions of certain low-energy constants and are therefore redundant.
Hyperon polarization in isobaric Zr+Zr collisions at $\sqrt{s_{NN}}=200$ GeV: TRENRo3D + CLVisc with an initial longitudinal flow gradient
Hubei Engineering University（湖北工程学院）；Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University（华中师范大学粒子物理与夸克轻子物理教育部重点实验室）；Faculty of Physics, Bielefeld University（比勒费尔德大学物理系）
We employ a 3+1D anomalous hydrodynamics with initial condition generated by HIJING to simulate the chiral vortical effect and the chiral magnetic effect in heavy-ion collisions. This allows us to calculate the charge-dependent two-particle correlations with respect to the reaction plane at different collision energies and centralities. We then compare the computed results with the experimental data and give discussions on the possible background effects.
Starting from low energy effective chiral Lagrangian with gauged Wess-Zumino Witten term, we have derived a hydrodynamic theory for chiral superfluid. It is a non-abelian hydrodynamics at zero temperature with only superfluid components. With an external electromagnetic field and baryonic and axial baryonic chemical potentials turned on, we are able to identify analogs of various anomaly induced term in normal hydrodynamics, including chiral vortical effect, chiral magnetic effect and chiral electric effect. As an example, we solved the hydrodynamic equations for the ground state and observed …
The amount of axial charge produced in heavy ion collisions is one of the key quantities in understanding chiral magnetic effect. Current phenomenological studies assume large axial charge chemical potential $μ_5$ produced in Glasma phase and assume the conservation of axial charge throughout the evolution, which is valid in the long relaxation time limit. Based on the solution of stochastic hydrodynamics with phenomenological parameters, our study suggests that the situation of heavy ion collisions may be close to the opposite limit, in which axial charge fluctuation approaches thermodynamic …
The temperature dependence of the chiral condensate in isospin-symmetric nuclear matter at varying baryon densities is investigated starting from a realistic free energy density of the correlated nuclear many-body system. The framework is thermal in-medium chiral effective field theory which permits a systematic calculation of the quark mass dependence of the free energy density. One- and two-pion exchange processes, virtual $Δ(1232)$-isobar excitations and Pauli blocking corrections are treated up to and including three-loop order. It is found that nuclear matter remains in the Nambu-Goldston…
We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $Δ$-isobars. The scattering amplitude is evaluated to one-loop $Q^3$ order, where $Q$ is a generic small momentum, using a new approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A sigma term greater than 45 MeV is favored, but the value is not well determined.
The equation of state of the linear sigma model in the mean field approximation is used as input in a relativistic hydrodynamical numerical routine. Longitudinal and transverse energy distributions are calculated and compared with those obtained from the QHD-I equation of state.
A quark interaction with topologically nontrivial gluonic fields, instantons and sphalerons, violates ¶~ and \CP~ symmetry. In the strong magnetic field of a noncentral nuclear collision such interactions lead to the charge separation along the magnetic field, the so-called chiral magnetic effect (CME). Recent results from the STAR collaboration on charge dependent correlations are consistent with theoretical expectations for CME but may have contributions from other effects, which prevents definitive interpretation of the data. Here I propose to use central body-body $U+U$ collisions to disen…
We prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill-posed both in the linearized case around a local equilibrium solution and also in the full nonlinear regime. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be fixed by using different definitions (frames) for the hydrodynamic fields. This leads to a causal theory of ideal chiral hydrodynamics where the vorticity strength is constrained by the coefficient that enco…
We investigate the role of the delta isobar in the reaction $πd\to πd$ at threshold in chiral effective field theory. We discuss the corresponding power counting and argue that this calculation completes the evaluation of diagrams up to the order (m_pi/M_N)^(3/2), with m_pi (M_N) for the pion (nucleon) mass. The net effect of all delta contributions at this order to the pion-deuteron scattering length is (2.4 +/- 0.4)x 10^(-3) m_pi^{-1}.
The STAR isobar data of $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr collisions at $\sqrt{s_{\mathrm{NN}}}= 200$ GeV show that ratios of observables ($R_{\mathcal{O}}$) such as the multiplicity distribution, $p(N_{\mathrm{ch}})$, and the harmonic flow, $v_n$, deviate from unity, when presented as a function of centrality, $c$. These deviations have been attributed to the differences in the shape and radial profiles between $^{96}$Ru and $^{96}$Zr nuclei. In addition, the ratios $R_{\mathcal{O}}(x)$ depend on the choice of the event activity variable $x$, which could be either $N_{\mathrm{ch}}$ …
Matter with chiral fermions is microscopically described by theory with quantum anomaly and macroscopically described (at low energy) by anomalous hydrodynamics. For such systems in the presence of external magnetic field and chirality imbalance, a charge current is generated along the magnetic field direction --- a phenomenon known as the Chiral Magnetic Effect (CME). The quark-gluon plasma created in relativistic heavy ion collisions provides an (approximate) example, for which the CME predicts a charge separation perpendicular to the collisional reaction plane. Charge correlation measuremen…
We determine the kinetic coefficients of ultrasoft pions using chiral perturbation theory at finite temperature close to the chiral limit. This is used to compute the axial charge diffusion and damping coefficients in the hydrodynamic effective theory for these pion waves. We show that to provide a leading order answer for these coefficients one needs to explore the dynamics of hard, soft, and ultrasoft pion modes, which are represented microscopically by the appropriate kinetic and hydrodynamic descriptions..
We introduce a model for the real-time evolution of a relativistic fluid of quarks coupled to non-equilibrium dynamics of the long wavelength (classical) modes of the chiral condensate. We solve the equations of motion numerically in 3+1 space-time dimensions. Starting the evolution at high temperature in the symmetric phase, we study dynamical trajectories that either cross the line of first-order phase transitions or evolve through its critical endpoint. For those cases, we predict the behavior of the azimuthal momentum asymmetry for high-energy heavy-ion collisions at nonzero impact paramet…
The conservation of an axial current modified by the gravitational chiral anomaly implies the universal transport phenomenon (Kinematical Vortical Effect) dependent solely on medium vorticity and acceleration but not dependent explicitly on its temperature and density. This general analysis is verified for the case of massless fermions with spin 1/2.
The temperature dependence of the chiral condensate in isospin-symmetric nuclear matter at varying baryon density is investigated using thermal in-medium chiral effective field theory. This framework provides a realistic approach to the thermodynamics of the correlated nuclear many-body system and permits calculating systematically the pion-mass dependence of the free energy per particle. One- and two-pion exchange processes, $Δ(1232)$-isobar excitations, Pauli blocking corrections and three-body correlations are treated up to and including three loops in the expansion of the free energy densi…
Using relativistic conformal hydrodynamics coupled to the linear $σ$ model we study the evolution of matter created in heavy--ion collisions. We focus the study on the influence of the dynamics of the chiral fields on the charged-hadron elliptic flow $v_2$ for a temperature--independent as well as for a temperature--dependent $η/s$ that is calculated from kinetic theory. We find that $v_2$ is not very sensitive to the coupling of chiral fields to the hydrodynamic evolution, but the temperature dependence of $η/s$ plays a much bigger role on this observable.
In this work, we start with chiral kinetic theory and construct the spin hydrodynamic framework for a chiral spinor system. Using the 14-moment expansion formalism, we obtain the equations of motion of second-order dissipative relativistic fluid dynamics with non-trivial spin polarization density. In a chiral spinor system, the spin alignment effect could be treated in the same framework as the Chiral Vortical Effect (CVE). However, the quantum corrections due to fluid vorticity induce not only CVE terms in the vector/axial charge currents but also corrections to the stress tensor. In this fra…
In the framework of chiral kinetic theory (CKT), we consider a system of right- and left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out that the eigenmodes of these equations, namely the hydrodynamic …
We study the chiral behavior of the nucleon and $Δ$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $πN$ and $πΔ$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $πN…
By making use of a covariant formulation of the chiral kinetic theory in the relaxation-time approximation, we derive the first-order dissipative hydrodynamics equations for a charged chiral plasma with background electromagnetic fields. We identify the global equilibrium state for a rotating chiral plasma confined to a cylindrical region with realistic boundary conditions. Then, by using linearized hydrodynamic equations, supplemented by the Maxwell equations, we study hydrodynamic modes of magnetized rotating chiral plasma in the regimes of high temperature and high density. We find that, in…
We analyze the combined effects of hydrodynamic fluctuations and chiral magnetic effect (CME) for a chiral medium in the presence of a background magnetic field. Based on the recently developed non-equilibrium effective field theory, we show fluctuations give rise to a CME-related positive contribution to magnetoresistance, while the early studies without accounting for the fluctuations find a CME-related negative magnetoresistance. At zero axial relaxation rate, the fluctuations contribute to the transverse conductivity in addition to the longitudinal one.
Using second--order dissipative hydrodynamics coupled self-consistently to the linear $σ$ model we study the 2+1 dimensional evolution of the fireball created in Au+Au relativistic collisions. We analyze the influence of the dynamics of the chiral fields on the charged-hadron elliptic flow $v_2$ and on the ratio $v_4/(v_2)^2$ for a temperature-independent as well as for a temperature-dependent viscosity-to-entropy ratio $η/s$ calculated from the linearized Boltzmann equation in the relaxation time approximation. We find that $v_2$ is not very sensitive to the coupling of chiral sources to the …
