Anomalous-viscous Fluid Dynamics Research Articles

Probing the magnetic field strength dependence of the chiral magnetic effect

The article presents a study aimed at probing the dependence of the Chiral Magnetic Effect (CME) on the magnetic field strength using the Anomalous Viscous Fluid Dynamics (AVFD) model in Pb–Pb at LHC energies. The results demonstrate the quadratic dependence of the correlators used for the study of the CME in heavy ion collisions on the number of spectators, a proxy of the magnitude of the magnetic field. The article also presents the extension of this approach to a two dimensional space, formed by both the aforementioned proxy of the magnetic field strength but also a proxy of the final state ellipticity, a key ingredient of the background in these measurements, for each centrality interval. This provides an exciting possibility to experiments to isolate the background contributions from the potential CME signal.

Event shape selection method in search of the chiral magnetic effect in heavy-ion collisions

The search for the chiral magnetic effect (CME) in heavy-ion collisions has been impeded by the significant background arising from the anisotropic particle emission pattern, particularly elliptic flow. To alleviate this background, the event shape selection (ESS) technique categorizes collision events according to their shapes and projects the CME observables to a class of events with minimal flow. In this study, we explore two event shape variables to classify events and two elliptic flow variables to regulate the background. Each type of variable can be calculated from either single particles or particle pairs, resulting in four combinations of event shape and elliptic flow variables. By employing a toy model and the realistic event generator, event-by-event anomalous-viscous fluid dynamics (EBE-AVFD), we discover that the elliptic flow of resonances exhibits correlations with both the background and the potential CME signal, making the resonance flow unsuitable for background control. Through the EBE-AVFD simulations of Au+Au collisions at sNN=200 GeV with various input scenarios, we ascertain that the optimal ESS strategy for background control entails utilizing the single-particle elliptic flow in conjunction with the event shape variable based on particle pairs.

Fourier coefficients of noninterdependent collective motions in heavy-ion collisions

We present a scenario in heavy-ion collisions where different modes of collective motions are noninterdependent, driven by factorized actions in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously. If the probability of particle emission is modulated by each nondependent collective motion with a single-harmonic Fourier expansion, the particle azimuthal distribution should be the product of all these expansions. Consequently, nonleading cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop separately, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving insights into searches for the CME, we also propose feasible experimental tests based on conventional flow harmonics, and demonstrate the emergence of nonleading cross terms with a multiphase transport model.

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.

Utilization of event shape in search of the chiral magnetic effect in heavy-ion collisions

The search for the chiral magnetic effect (CME) has been a subject of great interest in the field of high-energy heavy-ion collision physics, and various observables have been proposed to probe the CME. Experimental observables are often contaminated with background contributions arising from collective motions (specifically elliptic flow) of the collision system. We present a method study of event-shape engineering (ESE) that projects the CME-sensitive $\gamma_{112}$ correlator and its variations ($\gamma_{132}$ and $\gamma_{123}$) to a class of events with minimal flow. We discuss the realization of the zero-flow mode, the sensitivity on the CME signal, and the corresponding statistical significance for Au+Au, Ru+Ru, and Zr+Zr collisions at $\sqrt{s_{\rm NN}} = 200$ GeV with a multiphase transport (AMPT) model, as well as a new event generator, Event-By-Event Anomalous-Viscous Fluid Dynamics (EBE-AVFD).

Systematic study of the chiral magnetic effect with the AVFD model at LHC energies

We present a systematic study of the correlators used experimentally to probe the Chiral Magnetic Effect (CME) using the Anomalous Viscous Fluid Dynamics (AVFD) model in Pb–Pb and Xe–Xe collisions at LHC energies. We find a parametrization that describes the dependence of these correlators on the value of the axial current density (n_5/{mathrm {s}}), which dictates the CME signal, and on the parameter that governs the background in these measurements i.e., the percentage of local charge conservation (LCC) within an event. This allows to deduce the values of n_5/{mathrm {s}} and the LCC percentage that provide a quantitative description of the centrality dependence of the experimental measurements. We find that the results in Xe–Xe collisions at sqrt{s_{mathrm {NN}}} = 5.44 TeV are consistent with a background only scenario. On the other hand, the model needs a significant non-zero value of n_5/{mathrm {s}} to match the measurements in Pb–Pb collisions at sqrt{s_{mathrm {NN}}} = 5.02 TeV.

Revisit the chiral magnetic effect expectation in isobaric collisions at the relativistic heavy ion collider

Isobaric 4496Ru+4496Ru and 4096Zr+4096Zr collisions at ▪ 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 with the collected isobar data statistics, within ∼2σ significance, if the axial charge per entropy density (n5/s) and the QCD vacuum transition probability are system independent. This expectation is generally verified by the Anomalous-Viscous Fluid Dynamics (avfd) model. While our estimate provides an approximate “experimental” baseline, theoretical uncertainties on the cme remain large.

Probe chiral magnetic effect with signed balance function * * A.H. Tang is supported by the US Department of Energy (DE-AC02-98CH10886, DE-FG02-89ER40531)

In this paper a pair of observables are proposed as alternative ways, by examining the fluctuation of net momentum-ordering of charged pairs, to study the charge separation induced by the Chiral Magnetic Effect (CME) in relativistic heavy ion collisions. They are, the out-of-plane to in-plane ratio of fluctuation of the difference between signed balance functions measured in pair’s rest frame, and the ratio of it to similar measurement made in the laboratory frame. Both observables have been studied with simulations including flow-related backgrounds, and for the first time, backgrounds that are related to resonance's global spin alignment. The two observables have similar positive responses to signal, and opposite, limited responses to identifiable backgrounds arising from resonance flow and spin alignment. Both observables have also been tested with two realistic models, namely, a multi-phase transport (AMPT) model and the anomalous-viscous fluid dynamics (AVFD) model. These two observables, when cross examined, will provide useful insights in the study of CME-induced charge separation.

Chiral Magnetic Effect in Isobaric Collisions from Anomalous-Viscous Fluid Dynamics (AVFD)

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 (multiplicity + elliptic-flow) event selection is crucial for this purpose. We further propose to use the absolute difference between RuRu and ZrZr events (after using identical event selection) for detecting CME signal and make predictions for the correlation observables.

Examination of the observability of a chiral magnetically driven charge-separation difference in collisions of the Ru4496+Ru4496 and Zr4096+Zr4096 isobars at energies available at the BNL Relativistic Heavy Ion Collider

Anomalous Viscous Fluid Dynamics (AVFD) model calculations for $\mathrm{^{96}_{44}Ru +\, ^{96}_{44}Ru}$ and $\mathrm{^{96}_{40}Zr +\, ^{96}_{40}Zr}$ collisions ($\sqrt{s_{\rm NN}} = 200$ GeV) are used in concert with a charge-sensitive correlator, to test its ability to detect and characterize the charge separation difference expected from the Chiral Magnetic Effect (CME) in these isobaric collisions. The tests indicate a larger charge separation for $\mathrm{^{96}_{44}Ru +\, ^{96}_{44}Ru}$ than for $\mathrm{^{96}_{40}Zr +\, ^{96}_{40}Zr}$ collisions, and a discernible CME-driven difference of $\sim 10$\% in the presence of realistic non-CME backgrounds. They also indicate a strategy for evaluating the relative influence of the background correlations, present for each isobar. These results suggest that charge separation measurements for these isobaric species could serve to further constrain unambiguous identification and characterization of the CME in upcoming measurements at RHIC.

Responses of the chiral-magnetic-effect–sensitive sine observable to resonance backgrounds in heavy-ion collisions

A new sine observable, $R_{\Psi_2}(\Delta S)$, has been proposed to measure the chiral magnetic effect (CME) in heavy-ion collisions; $\Delta S = \left \langle \sin \varphi_+ \right \rangle - \left \langle \sin \varphi_- \right \rangle$, where $\varphi_\pm$ are azimuthal angles of positively and negatively charged particles relative to the reaction plane and averages are event-wise, and $R_{\Psi_2}(\Delta S)$ is a normalized event probability distribution. Preliminary STAR data reveal concave $R_{\Psi_2}(\Delta S)$ distributions in 200 GeV Au+Au collisions. Studies with a multiphase transport (AMPT) and anomalous-viscous Fluid Dynamics (AVFD) models show concave $R_{\Psi_2}(\Delta S)$ distributions for CME signals and convex ones for typical resonance backgrounds. A recent hydrodynamic study, however, indicates concave shapes for backgrounds as well. To better understand these results, we report a systematic study of the elliptic flow ($v_{2}$) and transverse momentum ($p_{T}$) dependences of resonance backgrounds with toy-model simulations and central limit theorem (CLT) calculations. It is found that the concavity or convexity of $R_{\Psi_2}(\Delta S)$ depends sensitively on the resonance $v_2$ (which yields different numbers of decay $\pi^+\pi^-$ pairs in the in-plane and out-of-plane directions) and $p_T$ (which affects the opening angle of the decay $\pi^+\pi^-$ pair). Qualitatively, low $p_{T}$ resonances decay into large opening-angle pairs and result in more `back-to-back' pairs out-of-plane, mimicking a CME signal, or a concave $R_{\Psi_2}(\Delta S)$. Supplemental studies of $R_{\Psi_3}(\Delta S)$ in terms of the triangular flow ($v_3$), where only backgrounds exist but any CME would average to zero, are also presented.

New correlator to detect and characterize the chiral magnetic effect

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- ($\Psi_{2}$) and third-order ($\Psi_{3}$) 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.

Anomalous chiral transport in heavy ion collisions from Anomalous-Viscous Fluid Dynamics

Chiral anomaly is a fundamental aspect of quantum theories with chiral fermions. How such microscopic anomaly manifests itself in a macroscopic many-body system with chiral fermions, is a highly nontrivial question that has recently attracted significant interest. As it turns out, unusual transport currents can be induced by chiral anomaly under suitable conditions in such systems, with the notable example of the Chiral Magnetic Effect (CME) where a vector current (e.g. electric current) is generated along an external magnetic field. A lot of efforts have been made to search for CME in heavy ion collisions, by measuring the charge separation effect induced by the CME transport. A crucial challenge in such effort, is the quantitative prediction for the CME signal. In this paper, we develop the Anomalous-Viscous Fluid Dynamics (AVFD) framework, which implements the anomalous fluid dynamics to describe the evolution of fermion currents in QGP, on top of the neutral bulk background described by the VISH2+1 hydrodynamic simulations for heavy ion collisions. With this new tool, we quantitatively and systematically investigate the dependence of the CME signal to a series of theoretical inputs and associated uncertainties. With realistic estimates of initial conditions and magnetic field lifetime, the predicted CME signal is quantitatively consistent with measured change separation data in 200GeV Au–Au collisions. Based on analysis of Au–Au collisions, we further make predictions for the CME observable to be measured in the planned isobaric (Ru–Ru v.s. Zr–Zr) collision experiment, which could provide a most decisive test of the CME in heavy ion collisions.

Quantifying the chiral magnetic effect from anomalous-viscous fluid dynamics**This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration. The work is also supported in part by the National Science Foundation under Grant No. PHY-1352368 (SS and JL), by

The Chiral Magnetic Effect (CME) is a macroscopic manifestation of fundamental chiral anomaly in a many-body system of chiral fermions, and emerges as an anomalous transport current in the fluid dynamics framework. Experimental observation of the CME is of great interest and has been reported in Dirac and Weyl semimetals. Significant efforts have also been made to look for the CME in heavy ion collisions. Critically needed for such a search is the theoretical prediction for the CME signal. In this paper we report a first quantitative modeling framework, Anomalous Viscous Fluid Dynamics (AVFD), which computes the evolution of fermion currents on top of realistic bulk evolution in heavy ion collisions and simultaneously accounts for both anomalous and normal viscous transport effects. AVFD allows a quantitative understanding of the generation and evolution of CME-induced charge separation during the hydrodynamic stage, as well as its dependence on theoretical ingredients. With reasonable estimates of key parameters, the AVFD simulations provide the first phenomenologically successful explanation of the measured signal in 200 AGeV AuAu collisions.

Quantifying the Chiral Magnetic Effect from Anomalous-Viscous Fluid Dynamics

In this contribution we report a recently developed Anomalous-Viscous Fluid Dynamics (AVFD) framework, which simulates the evolution of fermion currents in QGP on top of the bulk expansion from data-validated VISHNU hydrodynamics. With reasonable estimates of initial conditions and magnetic field lifetime, the predicted CME signal is quantitatively consistent with change separation measurements in 200GeV Au-Au collisions at RHIC. We further develop the event-by-event AVFD simulations that allow direct evaluation of two-particle correlations arising from CME signal as well as the non-CME backgrounds. Finally we report predictions from AVFD simulations for the upcoming isobaric (Ru-Ru v.s. Zr-Zr ) collisions that could provide the critical test of the CME in heavy ion collisions.