Search for the chiral magnetic wave using anisotropic ow of identied particles at RHIC The STAR Collaboration

2025-05-03 0 0 697.83KB 10 页 10玖币

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Search for the chiral magnetic wave

using anisotropic ﬂow of identiﬁed particles at RHIC

(The STAR Collaboration)

(Dated: October 26, 2022)

The chiral magnetic wave (CMW) has been theorized to propagate in the deconﬁned nuclear

medium formed in high-energy heavy-ion collisions, and to cause a diﬀerence in elliptic ﬂow (v2)

between negatively and positively charged hadrons. Experimental data consistent with the CMW

have been reported by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC),

based on the charge asymmetry dependence of the pion v2from Au+Au collisions at √sNN = 27

to 200 GeV. In this comprehensive study, we present the STAR measurements of elliptic ﬂow and

triangular ﬂow of charged pions, along with the v2of charged kaons and protons, as a function of

charge asymmetry in Au+Au collisions at √sNN = 27, 39, 62.4 and 200 GeV. The slope parameters

extracted from the linear dependence of the v2diﬀerence on charge asymmetry for diﬀerent particle

species are reported and compared in diﬀerent centrality intervals. In addition, the slopes of v2for

charged pions in small systems, i.e.,p+Au and d+Au at √sNN = 200 GeV, are also presented and

compared with those in large systems, i.e., Au+Au at √sNN = 200 GeV and U+U at 193 GeV.

Our results provide new insights for the possible existence of the CMW, and further constrain the

background contributions in heavy-ion collisions at RHIC energies.

I. INTRODUCTION

The violation of parity symmetry (P) or combined

charge conjugation and parity symmetry (CP) in the

strong interaction is allowed by quantum chromodynam-

ics, but has never been observed in experiments (see

Ref. [1] for the latest experimental limits). Metastable

P- and CP-odd domains may exist in the hot and dense

nuclear medium created in high-energy heavy-ion col-

lisions, owing to vacuum transitions induced by topo-

logically nontrivial gluon ﬁelds, e.g., sphalerons [2]. In

such domains, a nonzero chirality chemical potential (µ5)

can arise from the chiral anomaly switching the chiral-

ity of quarks, e.g., left-handed quarks may become right-

handed in the presence of the negative topological charge.

The chemical potential µ5, if coupled with an intense

magnetic ﬁeld (−→

B), will induce an electric current along

−→

Bvia the so-called chiral magnetic eﬀect (CME) [3–5]:

−→

Je∝µ5−→

B. The required magnetic ﬁeld, as strong as

B∼1015 T in Au+Au collisions at the top RHIC en-

ergy, can be produced by the energetic spectator protons

in noncentral collisions.

A complementary phenomenon to the CME is the chi-

ral separation eﬀect (CSE) [6, 7], whereby a chirality

current is induced along −→

Bin the presence of a ﬁnite

electric chemical potential (µe): −→

J5∝µe−→

B. The CME

and the CSE intertwine to form a collective excitation,

the chiral magnetic wave (CMW), a long-wavelength hy-

drodynamic mode of chiral charge densities [8–12]. The

CMW is assumed to be a signature of chiral symmetry

restoration [13], and manifests itself in a ﬁnite electric

quadrupole moment of the collision system, where the

“poles” and the “equator” of the produced ﬁreball ac-

quire additional positive and negative charges, respec-

tively [8]. This eﬀect, if present, will be reﬂected in the

measurements of a charge-dependent elliptic ﬂow.

The anisotropic ﬂow quantiﬁes the collective motion

of the expanding medium, and is deﬁned in terms of the

Fourier coeﬃcients of the azimuthal distribution of pro-

duced particles with respect to the nth-order event plane,

Ψn[14]:

dϕ ∝1 +

∞

n=1

2vncos n(ϕ−Ψn),(1)

where ϕ−Ψnis the particle’s azimuthal angle with re-

spect to the event plane angle. The quantity v1is known

as “directed ﬂow”, v2as “elliptic ﬂow” and v3as “tri-

angular ﬂow”. The electric quadrupole moment induced

by the CMW will lead to the increase (decrease) of v2

for negatively (positively) charged hadrons. The modiﬁ-

cation of v2due to this eﬀect is predicted to be propor-

tional to the event-by-event charge asymmetry (Ach) [8],

a proxy for µe,

v±

2−v±

2,base =∓a

2Ach,(2)

where superscript ±denotes the positively or negatively

charged particles, v2,base represents the “usual” v2unre-

lated to the charge separation, ais the quadrupole mo-

ment normalized by the net charge density, and

Ach = (N+−N−)/(N++N−),(3)

with N+(N−) denoting the number of positive (nega-

tive) particles observed in a given event.

Experimental measurements of such a linear depen-

dence between v±

2and Ach is quantiﬁed by the slope pa-

rameter, r2=d∆v2/dAch, where ∆v2=v−

2−v+

2. Al-

though recent STAR measurements [15] observe no pre-

deﬁned CME signatures in the isobar data (96Ru+96Ru

and 96Zr+96Zr), we cannot exclude the possibility that

the CMW observable has a better signal-to-background

ratio than the CME ones. Past measurements have been

performed with charged pions in Au+Au collisions by

the STAR collaboration at RHIC [16] as well as with

charged hadrons in Pb+Pb collisions by the ALICE col-

laboration at the Large Hadron Collider (LHC) [17, 18].

arXiv:2210.14027v1 [nucl-ex] 25 Oct 2022

In both cases, the r2slopes are of the same order of

magnitude as predicted by theoretical calculations of the

CMW [8–12]. In particular, the STAR results exhibit

the expected centrality dependence. However, non-CMW

mechanisms could also contribute to the splitting of v±

as a function of Ach. A hydrodynamic study [20] claims

that the simple viscous transport of charges, combined

with certain initial conditions, will lead to a sizeable v2

splitting for charged pions. According to the analyti-

cal calculation of the anisotropic Gubser ﬂow [19], the

∆v2for pions is proportional to both the shear viscosity

and the isospin chemical potential (µI) [20, 21]. On the

other hand, charge asymmetry Ach can also be linearly

related to µIwith the help of a statistical model, which

consequently connects ∆v2and Ach. This model further

predicts negative r2slopes for charged kaons and protons

with larger magnitudes than the pion slopes, because µI

as well as the strangeness chemical potential µSwill af-

fect these particles diﬀerently. These predictions warrant

the extension of our measurements to kaons and protons.

Local charge conservation (LCC) [18, 22–24] is also

able to qualitatively explain the ﬁnite r2slope observed

from data, when convoluted with the characteristic de-

pendence of v2on particle pseudorapidity (η) and trans-

verse momentum (pT). This is demonstrated with lo-

cally charge-conserved clusters, e.g., a pair of particles

with opposite charges, originating from a ﬂuid element

or a resonance decay. Such a pair could contribute to a

non-zero Ach in an experiment, when one of the particles

escapes the limited detector acceptance. If this process

preferentially occurs in a phase space with smaller v2,

such as a lower-pTor higher-ηregion, then there would

be a positive r2slope, whether the escaping particle is

positive or negative. For example, the escape of a π+

with smaller v2eﬀectively increases the v2of detected

π+’s, and decreases the observed Ach, causing a negative

slope for detected π+’s. Conversely, the escape of a π−

with smaller v2increases the v2of detected π−’s, and also

increases the observed Ach, causing a positive slope for

detected π−’s. A realistic estimate of such contributions,

however, appears to be smaller than that observed in the

STAR measurements [16]. Ref. [22] also proposes a test

with the r3measurements, deﬁned as r3=d∆v3/dAch

with ∆v3=v−

3−v+

3, which should yield ﬁnite slopes ac-

cording to the LCC picture, while no slope is expected

from the CMW picture. Recently the CMS collaboration

at the LHC [25] has observed that normalized r2and r3

slopes are very similar to each other for charged hadrons

in Pb+Pb collisions at 5.02 TeV, supporting the LCC

picture. Such a test with the STAR data at 200 GeV is

reported in this paper.

The CMS measurements [25] also show, for charged

hadrons, a very similar Ach dependence of ∆v2in p+Pb

and Pb+Pb collisions at 5.02 TeV. In p+Pb collisions, the

magnetic ﬁeld direction is presumably decoupled from

the event plane [26], and the r2slopes are dominated by

non-CMW contributions. The similar r2slopes in p+Pb

and Pb+Pb collisions [25] suggest that the r2slopes mea-

10−5−0 5 10

0.5−

0.5

1.5

)

-2

(GeV c

Au+Au 200 GeV

< 1 GeV/c

|<1, 0.15 < pη|

)pp(

FIG. 1. Particle identiﬁcation by the STAR TPC and TOF

detectors. nσdenotes the deviations from the theoretical

ln(dE/dx) curves measured by the TPC (here for kaons),

while m2denotes the mass information deduced from the

TOF.

sured in Pb+Pb are unlikely to originate from the CMW.

This disappearance of the CMW could arise from the

fact that the magnetic ﬁeld strength drops in the vac-

uum much faster at the LHC energies than at RHIC [27],

and at the time of quark production, the magnetic ﬁeld

could become too weak to initiate the CMW. The poten-

tial diﬀerence in the physics mechanisms between RHIC

and the LHC motivates us to present STAR measure-

ments of r2in small systems, i.e.,p+Au and d+Au at

200 GeV, and to compare them with results for Au+Au

and U+U collisions.

This paper is organized in the following way. The

STAR experiment and data collection are brieﬂy intro-

duced in Sec. II. The analysis methods and systematic

uncertainties are described in Sec. III. The STAR results

of the Ach dependence of identiﬁed particle anisotropic

ﬂow are presented and discussed in Sec. IV, where we

report: (A) the Ach dependence of mean pTand mean

|η|, and the ∆v2slope for charged pions selected using

diﬀerent phase space requirements; (B) the r2slopes for

charged kaons and protons; (C) the r3slope for charged

pions; (D) the r2slopes for charged pions in p+Au, d+Au

and U+U. A summary is given in Sec. V.

II. EXPERIMENTAL SETUP AND DATA

SELECTION

The STAR detector complex consists of a series of sub-

systems located in both midrapidity and forward-rapidity

regions. The main detectors involved in this work are

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SearchforthechiralmagneticwaveusinganisotropicowofidentiedparticlesatRHIC(TheSTARCollaboration)(Dated:October26,2022)Thechiralmagneticwave(CMW)hasbeentheorizedtopropagateinthedeconnednuclearmediumformedinhigh-energyheavy-ioncollisions,andtocauseadierenceinellipticow(v2)betweennegativelyandpositiv...

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Search for the chiral magnetic wave using anisotropic ow of identied particles at RHIC The STAR Collaboration

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