Azimuthal charged-particle correlations and possible local strong parity violation

Magnetic field evolution in [Formula: see text] collisions at [Formula: see text]

In high energy heavy-ion collisions, the high speed valence charges will produce intense electromagnetic fields within the resulting quark-gluon plasma. Utilizing the AMPT model, this paper presents a comprehensive analysis of the magnetic field distribution generated from non-central collisions between [Formula: see text] nuclei at [Formula: see text]. The initial geometric parameters of the collision and the electric conductivity of the quark-gluon plasma have a dominant influence on the evolution of the magnetic field, while the plasma diffusion and the CME effect have a lesser impact and only slightly involve the original magnetic field by inducing new magnetic fields. This finding suggests that the dynamics of the quark-gluon plasma can be roughly decoupled from the effect of the electromagnetic field.

Scaling properties of background- and chiral-magnetically-driven charge separation: Implications for the chiral magnetic effect in heavy ion collisions

The scaling properties of the RΨ2(∆S) correlator and the Δγ correlator are used to investigate a possible chiral-magnetically-driven (CME) charge separation in p+Au, d+Au, Ru+Ru, Zr+Zr, and Au+Au collisions at √SNN = 200 GeV, and in p+Pb (√SNN = 5.02 TeV) and Pb+Pb collisions at √SNN = 5.02 and 2:76 TeV. The results for p+Au, d+Au, p+Pb, and Pb+Pb collisions, show the 1/Nch scaling for background-driven charge separation. However, the results for Au+Au, Ru+Ru, and Zr+Zr collisions show scaling violations which indicate a CME contribution in the presence of a large background. In mid-central collisions, the CME accounts for approximately 27% of the signal + background in Au+Au and roughly a factor of two smaller for Ru+Ru and Zr+Zr, which show similar magnitudes.

Experimental Status of the Chiral Magnetic Effect

Experimental searches for definitive evidence of the Chiral Magnetic Effect in heavy-ion collisions have become increasingly ingenious over the past decade, but a clear separation of any CME signal from flow-related backgrounds remains elusive. Although the isobar analysis by STAR does not appear to show a signal given the current preliminary background estimate, there is a tantalizing statistically significant signal in Au-Au at top RHIC energy using a spectator plane versus participant plane analysis. I discuss the status of these works in some detail, and discuss the possible advantage of an analysis that takes advantage of the expected correlation between the parity-odd event-by-event CME signal and other parity-odd measures such as the net hyperon helicity.

Search for the Chiral Magnetic Effect via Charge-Dependent Azimuthal Correlations Relative to Spectator and Participant Planes in Au+Au Collisions at sqrt[s_{NN}]=200 GeV

The chiral magnetic effect (CME) refers to charge separation along a strong magnetic field due to imbalanced chirality of quarks in local parity and charge-parity violating domains in quantum chromodynamics. The experimental measurement of the charge separation is made difficult by the presence of a major background from elliptic azimuthal anisotropy. This background and the CME signal have different sensitivities to the spectator and participant planes, and could thus be determined by measurements with respect to these planes. We report such measurements in Au+Au collisions at a nucleon-nucleon center-of-mass energy of 200 GeV at the Relativistic Heavy-Ion Collider. It is found that the charge separation, with the flow background removed, is consistent with zero in peripheral (large impact parameter) collisions. Some indication of finite CME signals is seen in midcentral (intermediate impact parameter) collisions. Significant residual background effects may, however, still be present.

Studying the Chiral Magnetic Effect in Pb-Pb and Xe-Xe collisions using the AVFD model

Quantum Chromodynamics permits the formation of charge conjugation parity violating domains inside the medium produced in heavy-ion collisions, resulting in an imbalanced quark chirality. With the presence of a strong magnetic field (as strong as 1015 T) produced by the spectator protons in offcentral heavy-ion collisions, this would lead to an electric-charge separation along the direction of the magnetic field, known as the Chiral Magnetic Effect (CME). Experimental searches commonly utilise strategies involving charge-dependent correlators to measure the charge separation. These correlators are, however, dominated by a large background proportional to the elliptic flow v2. This article presents a systematic study of the correlators used experimentally to probe the CME by using the Anomalous Viscous Fluid Dynamics (AVFD) model in Pb-Pb and Xe-Xe collisions at √sNN = 5.02 TeV and √sNN = 5.44 TeV, respectively. The results from AVFD suggest that Xe-Xe collisions are consistent with a background-only scenario and a significant non-zero value of axial current density (imbalanced quark chirality) is required to describe the measurements in Pb-Pb collisions.

Rapidity-dependent charge-dependent flow, global polarisation and chiral magnetic effect in heavy ion collisions

An extremely strong magnetic field (as strong as 1015 T) is created in the off-central heavy-ion collisions by the spectator protons which "miss" the collisions, flying past each other rather than colliding. The magnetic field is interesting to be studied as it is expected to leave distinct imprints in the distribution of final state charged particles. In addition, novel QCD phenomena are anticipated to emerge with the presence of a strong magnetic field and the formation of charge-parity violating domains inside the medium produced in heavy-ion collisions. The aim of this article is to review two methods utilised by the experimental searches to probe the early magnetic field: the directed flow of charged hadrons (and heavy-flavour hadrons D0 and ¯D0) and the global polarisation of Λ and ¯Λ hyperons. Furthermore, this article is also dedicated to review the searches for one of the novel QCD phenomena, the chiral magnetic effect, at the LHC and RHIC.

Signatures of Chiral Magnetic Effect in the Collisions of Isobars

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 collider experiment, dedicated to detecting CME in the collisions of isobars, was performed in 2018 with analysis now underway. In this Letter, we develop the state-of-the-art theoretical tool for describing CME phenomena in these collisions and propose an appropriate isobar subtraction strategy for best background removal. Based on that, we make quantitative predictions for signatures of CME in the collisions of isobars. A new and robust observable that is independent of axial charge uncertainty-the ratio between isobar-subtracted γ- and δ- correlators-is found to be -(0.41±0.27) for event-plane measurement and -(0.90±0.45) for reaction-plane measurement.

Probing the Effects of Strong Electromagnetic Fields with Charge-Dependent Directed Flow in Pb-Pb Collisions at the LHC

The first measurement at the LHC of charge-dependent directed flow (v_{1}) relative to the spectator plane is presented for Pb-Pb collisions at sqrt[s_{NN}]=5.02  TeV. Results are reported for charged hadrons and D^{0} mesons for the transverse momentum intervals p_{T}>0.2  GeV/c and 3<p_{T}<6  GeV/c in the 5%-40% and 10%-40% centrality classes, respectively. The difference between the positively and negatively charged hadron v_{1} has a positive slope as a function of pseudorapidity η, dΔv_{1}/dη=[1.68±0.49(stat)±0.41(syst)]×10^{-4}. The same measurement for D^{0} and D[over ¯]^{0} mesons yields a positive value dΔv_{1}/dη=[4.9±1.7(stat)±0.6(syst)]×10^{-1}, which is about 3 orders of magnitude larger than the one of the charged hadrons. These measurements can provide new insights into the effects of the strong electromagnetic field and the initial tilt of matter created in noncentral heavy ion collisions on the dynamics of light (u, d, and s) and heavy (c) quarks. The large difference between the observed Δv_{1} of charged hadrons and D^{0} mesons may reflect different sensitivity of the charm and light quarks to the early time dynamics of a heavy ion collision. These observations challenge some recent theoretical calculations, which predicted a negative and an order of magnitude smaller value of dΔv_{1}/dη for both light flavor and charmed hadrons.

Spin Hydrodynamic Generation in the Charged Subatomic Swirl

Recently there have been significant interests in the spin hydrodynamic generation phenomenon from multiple disciplines of physics. Such phenomenon arises from global polarization effect of microscopic spin by macroscopic fluid rotation and is expected to occur in the hot quark-gluon fluid (the "subatomic swirl") created in relativistic nuclear collisions. This was indeed discovered in experiments which however revealed an intriguing puzzle: a polarization difference between particles and anti-particles. We suggest a novel application of a general connection between rotation and magnetic field: a magnetic field naturally arises along the fluid vorticity in the charged subatomic swirl. We establish this mechanism as a new way for generating long-lived in-medium magnetic field in heavy ion collisions. Due to its novel feature, this new magnetic field provides a nontrivial explanation to the puzzling observation of a difference in spin hydrodynamic generation for particles and anti-particles in heavy ion collisions.

Importance of Isobar Density Distributions on the Chiral Magnetic Effect Search

Under the approximate chiral symmetry restoration, quark interactions with topological gluon fields in quantum chromodynamics can induce a chirality imbalance and parity violation in local domains. An electric charge separation (CS) could be generated along the direction of a strong magnetic field (B), a phenomenon called the chiral magnetic effect (CME). CS measurements by azimuthal correlators are contaminated by major backgrounds from elliptic flow anisotropy (v_{2}). Isobaric _{44}^{96}Ru+_{44}^{96}Ru and _{40}^{96}Zr+_{40}^{96}Zr collisions have been proposed to identify the CME (expected to differ between the two systems) out of the backgrounds (to be almost the same). We show, by using the density functional theory calculations of the proton and neutron distributions, that these expectations may not hold as originally anticipated because the two systems may have sizable differences in eccentricity and v_{2}.

Chiral magnetic effect search in p+Au, d+Au and Au+Au collisions at RHIC

Metastable domains of fluctuating topological charges can change the chirality of quarks and induce local parity violation in quantum chromodynamics. This can lead to observable charge separation along the direction of the strong magnetic field produced by spectator protons in relativistic heavy-ion collisions, a phenomenon called the chiral magnetic effect (CME). A major background source for CME measurements using the charge-dependent azimuthal correlator (Δϒ) is the intrinsic particle correlations (such as resonance decays) coupled with the azimuthal elliptical anisotropy (v2). In heavy-ion collisions, the magnetic field direction and event plane angle are correlated, thus the CME and the v2-induced background are entangled. In this report, we present two studies from STAR to shed further lights on the background issue. (1) The Δϒ should be all background in small system p+Au and d+Au collisions, because the event plane angles are dominated by geometry fluctuations uncorrelated to the magnetic field direction. However, significant Δϒ is observed, comparable to the peripheral Au+Au data, suggesting a background dominance in the latter, and likely also in the mid-central Au+Au collisions where the multiplicity and v2 scaled correlator is similar. (2) A new approach is devised to study Δϒ as a function of the particle pair invariant mass (minv) to identify the resonance backgrounds and hence to extract the possible CME signal. Signal is consistent with zero within uncertainties at high minv. Signal at low minv, extracted from a two-component model assuming smooth mass dependence, is consistent with zero within uncertainties.

New experimental constrains on chiral magnetic effect using charge-dependent azimuthal correlation in pPb and PbPb collisions at the LHC

Studies of charge-dependent azimuthal correlations for the same- and oppositesign particle pairs are presented in PbPb collisions at 5 TeV and pPb collisions at 5 and 8.16 TeV, with the CMS experiment at the LHC. The azimuthal correlations are evaluated with respect to the second- and also higher-order event planes, as a function of particle pseudorapidity and transverse momentum, and event multiplicity. By employing an event-shape engineering technique, the dependence of correlations on azimuthal anisotropy flow is investigated. Results presented provide new insights to the origin of observed charge-dependent azimuthal correlations, and have important implications to the search for the chiral magnetic effect in heavy ion collisions.

Phenomenology of anomalous chiral transports in heavy-ion collisions

High-energy Heavy-ion collisions can generate extremely hot quark-gluon matter and also extremely strong magnetic fields and fluid vorticity. Once coupled to chiral anomaly, the magnetic fields and fluid vorticity can induce a variety of novel transport phenomena, including the chiral magnetic effect, chiral vortical effect, etc. Some of them require the environmental violation of parity and thus provide a means to test the possible parity violation in hot strongly interacting matter. We will discuss the underlying mechanism and implications of these anomalous chiral transports in heavy-ion collisions.

Observation of Charge-Dependent Azimuthal Correlations in p-Pb Collisions and Its Implication for the Search for the Chiral Magnetic Effect

Charge-dependent azimuthal particle correlations with respect to the second-order event plane in p-Pb and PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV have been studied with the CMS experiment at the LHC. The measurement is performed with a three-particle correlation technique, using two particles with the same or opposite charge within the pseudorapidity range |η|<2.4, and a third particle measured in the hadron forward calorimeters (4.4<|η|<5). The observed differences between the same and opposite sign correlations, as functions of multiplicity and η gap between the two charged particles, are of similar magnitude in p-Pb and PbPb collisions at the same multiplicities. These results pose a challenge for the interpretation of charge-dependent azimuthal correlations in heavy ion collisions in terms of the chiral magnetic effect.

Charge-Dependent Directed Flow in Cu+Au Collisions at sqrt[s_{NN}]=200 GeV

We present the first measurement of charge-dependent directed flow in Cu+Au collisions at sqrt[s_{NN}]=200  GeV. The results are presented as a function of the particle transverse momentum and pseudorapidity for different centralities. A finite difference between the directed flow of positive and negative charged particles is observed that qualitatively agrees with the expectations from the effects of the initial strong electric field between two colliding ions with different nuclear charges. The measured difference in directed flow is much smaller than that obtained from the parton-hadron-string-dynamics model, which suggests that most of the electric charges, i.e., quarks and antiquarks, have not yet been created during the lifetime of the strong electric field, which is of the order of, or less than, 1  fm/c.

Chiral Magnetic Effect and Anomalous Transport from Real-Time Lattice Simulations

We present a first-principles study of anomaly induced transport phenomena by performing real-time lattice simulations with dynamical fermions coupled simultaneously to non-Abelian SU(N_{c}) and Abelian U(1) gauge fields. Investigating the behavior of vector and axial currents during a sphaleron transition in the presence of an external magnetic field, we demonstrate how the interplay of the chiral magnetic and chiral separation effect leads to the formation of a propagating wave. We further analyze the dependence of the magnitude of the induced vector current and the propagation of the wave on the amount of explicit chiral symmetry breaking due to finite quark masses.

Quantum Phase Transitions with Parity-Symmetry Breaking and Hysteresis

Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models1-3. Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report for the first time the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system is made of an ultra-cold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature4, the investigation of macroscopic quantum tunneling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points5.

Anomaly-Induced Dynamical Refringence in Strong-Field QED

We investigate the impact of the Adler-Bell-Jackiw anomaly on the nonequilibrium evolution of strong-field quantum electrodynamics (QED) using real-time lattice gauge theory techniques. For field strengths exceeding the Schwinger limit for pair production, we encounter a highly absorptive medium with anomaly induced dynamical refractive properties. In contrast to earlier expectations based on equilibrium properties, where net anomalous effects vanish because of the trivial vacuum structure, we find that out-of-equilibrium conditions can have dramatic consequences for the presence of quantum currents with distinctive macroscopic signatures. We observe an intriguing tracking behavior, where the system spends longest times near collinear field configurations with maximum anomalous current. Apart from the potential relevance of our findings for future laser experiments, similar phenomena related to the chiral magnetic effect are expected to play an important role for strong QED fields during initial stages of heavy-ion collision experiments.

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review

The hot and dense matter generated in heavy-ion collisions may contain domains which are not invariant under P and CP transformations. Moreover, heavy-ion collisions can generate extremely strong magnetic fields as well as electric fields. The interplay between the electromagnetic field and triangle anomaly leads to a number of macroscopic quantum phenomena in these P- and CP-odd domains known as anomalous transports. The purpose of this article is to give a pedagogical review of various properties of the electromagnetic fields, the anomalous transport phenomena, and their experimental signatures in heavy-ion collisions.

Simulating Chiral Magnetic and Separation Effects with Spin-Orbit Coupled Atomic Gases

The chiral magnetic and chiral separation effects-quantum-anomaly-induced electric current and chiral current along an external magnetic field in parity-odd quark-gluon plasma-have received intense studies in the community of heavy-ion collision physics. We show that analogous effects occur in rotating trapped Fermi gases with Weyl-Zeeman spin-orbit coupling where the rotation plays the role of an external magnetic field. These effects can induce a mass quadrupole in the atomic cloud along the rotation axis which may be tested in future experiments. Our results suggest that the spin-orbit coupled atomic gases are potential simulators of the chiral magnetic and separation effects.

Azimuthal Anisotropy in U+U and Au+Au Collisions at RHIC

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, v_{2}{2} and v_{2}{4}, for charged hadrons from U+U collisions at sqrt[s_{NN}]=193  GeV and Au+Au collisions at sqrt[s_{NN}]=200  GeV. Nearly fully overlapping collisions are selected based on the energy deposited by spectators in zero degree calorimeters (ZDCs). Within this sample, the observed dependence of v_{2}{2} on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. We also show that v_{2} vs multiplicity can be better described by models, such as gluon saturation or quark participant models, that eliminate the dependence of the multiplicity on the number of binary nucleon-nucleon collisions.

Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC

Local parity-odd domains are theorized to form inside a quark-gluon plasma which has been produced in high-energy heavy-ion collisions. The local parity-odd domains manifest themselves as charge separation along the magnetic field axis via the chiral magnetic effect. The experimental observation of charge separation has previously been reported for heavy-ion collisions at the top RHIC energies. In this Letter, we present the results of the beam-energy dependence of the charge correlations in Au+Au collisions at midrapidity for center-of-mass energies of 7.7, 11.5, 19.6, 27, 39, and 62.4 GeV from the STAR experiment. After background subtraction, the signal gradually reduces with decreased beam energy and tends to vanish by 7.7 GeV. This implies the dominance of hadronic interactions over partonic ones at lower collision energies.

Axial current generation from electric field: chiral electric separation effect

We study a relativistic plasma containing charged chiral fermions in an external electric field. We show that with the presence of both vector and axial charge densities, the electric field can induce an axial current along its direction and thus cause chirality separation. We call it the chiral electric separation effect (CESE). On a very general basis, we argue that the strength of CESE is proportional to μ(V)μ(A) with μ(V) and μ(A) the chemical potentials for vector charge and axial charge. We then explicitly calculate this CESE conductivity coefficient in thermal QED at leading-log order. The CESE can manifest a new gapless wave mode propagating along the electric field. Potential observable effects of CESE in heavy-ion collisions are also discussed.

Charge separation relative to the reaction plane in Pb-Pb collisions at sqrt[s(NN)] = 2.76 TeV

Measurements of charge-dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at sqrt[s(NN)] = 2.76 TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudorapidity range |η| < 0.8 are presented as a function of the collision centrality, particle separation in pseudorapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge-dependent azimuthal correlations observed at RHIC and LHC energies.

Chiral magnetic wave at finite baryon density and the electric quadrupole moment of the quark-gluon plasma

The chiral magnetic wave is a gapless collective excitation of quark-gluon plasma in the presence of an external magnetic field that stems from the interplay of chiral magnetic and chiral separation effects; it is composed of the waves of the electric and chiral charge densities coupled by the axial anomaly. We consider a chiral magnetic wave at finite baryon density and find that it induces the electric quadrupole moment of the quark-gluon plasma produced in heavy ion collisions: the "poles" of the produced fireball (pointing outside of the reaction plane) acquire additional positive electric charge, and the "equator" acquires additional negative charge. We point out that this electric quadrupole deformation lifts the degeneracy between the elliptic flows of positive and negative pions leading to v(2)(π(+))<v(2)(π(-)), and estimate the magnitude of the effect.

Chiral magnetic effect in lattice QCD with a chiral chemical potential

We perform a first lattice QCD simulation including a two-flavor dynamical fermion with a chiral chemical potential. Because the chiral chemical potential gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD matter by Monte Carlo simulation. By applying an external magnetic field to this system, we obtain a finite induced current along the magnetic field, which corresponds to the chiral magnetic effect. The obtained induced current is proportional to the magnetic field and to the chiral chemical potential, which is consistent with an analytical prediction.

Gravitational anomaly and transport phenomena

Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic fluid can also induce a current via the chiral vortical effect. The related transport coefficients can be calculated via Kubo formulas. We evaluate the Kubo formula for the anomalous vortical conductivity at weak coupling and show that it receives contributions proportional to the gravitational anomaly coefficient. The gravitational anomaly gives rise to an anomalous vortical effect even for an uncharged fluid.

Fluid-gravity model for the chiral magnetic effect

We consider the STU model as a gravity dual of a strongly coupled plasma with multiple anomalous U(1) currents. In the bulk we add additional background gauge fields to include the effects of external electric and magnetic fields on the plasma. Reducing the number of chemical potentials in the STU model to two and interpreting them as quark and chiral chemical potential, we obtain a holographic description of the chiral magnetic and chiral vortical effects (CME and CVE) in relativistic heavy-ion collisions. These effects formally appear as first-order transport coefficients in the electromagnetic current. We compute these coefficients from our model using fluid-gravity duality. We also find analogous effects in the axial-vector current. Finally, we briefly discuss a variant of our model, in which the CME/CVE is realized in the late-time dynamics of an expanding plasma.