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Eur. Phys. J. C (2019) 79:168

https://doi.org/10.1140/epjc/s10052-019-6671-1

Regular Article - Theoretical Physics

Isolating the chiral magnetic effect from backgrounds by pair

invariant mass

Jie Zhao

1,a

, Hanlin Li

1,2

, Fuqiang Wang

1,3,b

Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA

College of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, China

School of Science, Huzhou University, Huzhou 313000, Zhejiang, China

Received: 1 October 2018 / Accepted: 8 February 2019 / Published online: 25 February 2019

Abstract Topological gluon conﬁgurations in quantum

chromodynamics induce quark chirality imbalance in local

domains, which can result in the chiral magnetic effect

(CME) – an electric charge separation along a strong mag-

netic ﬁeld. Experimental searches for the CME in relativis-

tic heavy ion collisions via the charge-dependent azimuthal

correlator (γ ) suffer from large backgrounds arising from

particle correlations (e.g. due to resonance decays) coupled

with the elliptic anisotropy. We propose differential mea-

surements of the γ as a function of the pair invariant mass

inv

), by restricting to high m

inv

thus relatively background

free, and by studying the m

inv

dependence to separate the

possible CME signal from backgrounds. We demonstrate by

model studies the feasibility and effectiveness of such mea-

surements for the CME search.

1 Introduction

Vacuum ﬂuctuations in quantum chromodynamics (QCD)

can result in metastable local domains of gluon ﬁelds with

non-vanishing topological charges [1–3]. Interactions with

those gluon ﬁelds can, under the approximate chiral sym-

metry restoration, change the overall chirality of quarks in

those domains [4,5]. The chirality imbalance yields an elec-

tric charge separation under a strong magnetic ﬁeld, a phe-

nomenon called the chiral magnetic effect (CME) [6–8].

Strong magnetic ﬁelds are generated at early times by the

spectator protons in relativistic heavy ion collisions, raising

the possibility to detect the CME in those collisions [9,10].

An observation of the CME would conﬁrm a fundamental

property of QCD and is therefore of great importance [11].

e-mail: zhao656@purdue.edu

e-mail: fqwang@purdue.edu

CME-like phenomena are not speciﬁc only to QCD and may

have been observed in condense matter physics [12].

A commonly used variable to measure the CME-induced

charge separation in heavy ion collisions is the three-point

correlator [9],

γ ≡cos(α + β −2ψ), (1)

where α and β are the azimuthal angles of two particles and

ψ is that of the reaction plane (span by the beam and impact

parameter directions of the colliding nuclei). Charge sepa-

ration along the magnetic ﬁeld (



B), which is perpendicular

to ψ on average, would yield different values of γ for parti-

cle pairs of same-sign (SS) and opposite-sign (OS) charges:

=−1,γ

=+1. However, there exist background

correlations unrelated to the CME [9,13–20]. For exam-

ple, transverse momentum conservation induces correla-

tions among particles enhancing back-to-back pairs [14–18].

This background is independent of particle charges, affect-

ing SS and OS pairs equally and cancels in the difference,

γ ≡ γ

− γ

. Recent experimental searches have thus

focused on the γ observable [11,21,22]; the CME would

yield γ > 0. There are, however, also mundane physics that

differ between SS and OS pairs. One such physics is reso-

nance/cluster decays [9,13–18], more signiﬁcantly affecting

OS pairs than SS pairs. Backgrounds arise from the cou-

pling of elliptical anisotropy (v

, a common phenomenon

in heavy ion collisions [23]) of resonances/clusters and the

angular correlations between their decay daughters (non-

ﬂow) [9,13,14,17]. Take ρ → π

−

as an example. The

background is (γ )

= r

, where r

= N

/(N

−

)

is the relative abundance of ρ-decay pairs over all OS pairs,

and γ

≡f

2,ρ

=cos(α + β − 2φ

) cos 2(φ

− ψ)

quantiﬁes the ρ decay angular correlations coupled with its

[9,21,22,24].

123

168 Page 2 of 8 Eur. Phys. J. C (2019) 79 :168

Experimentally, signiﬁcant positive γ values have been

observed at the Relativistic Heavy Ion Collider (RHIC)

and the Large Hadron Collider (LHC) [25–29]. The rela-

tive background and CME contributions are under extensive

debate [30]. The recent observations of comparable γ in

small system collisions [31–36], where any CME signals

would average to zero [31,37], challenge the CME inter-

pretation of the measured γ in heavy ion collisions. The

major difﬁculty in distinguishing CME from backgrounds

with the γ observable is their similar behaviors with respect

to the event multiplicity [34–36]. This is because the mag-

netic ﬁeld strength, to which the CME is sensitive, has a

similar dependence as the v

(backgrounds) on the event mul-

tiplicity [10,38–41]. There have been various proposals and

attempts to reduce or eliminate the backgrounds [24,32,42–

46]. The central idea is to “hold” the magnetic ﬁeld ﬁxed (in a

narrow centrality) and vary the event-by-event v

from statis-

tical and dynamical ﬂuctuations [41,44,47]. The ﬁrst attempt

was carried out by STAR [44] where a charge asymmetry

observable was analyzed as a function of the observed event-

by-event v

. A linear dependence was observed, expected

from background, and the intercept was extracted represent-

ing a background-suppressed signal. ALICE [46] divided

their data in each collision centrality according to v

in one

phase space, and found the γ to be approximately pro-

portional to the v

in the phase space of the γ measure-

ment, consistent with background contributions. However,

as recently pointed out by two of us [24], those methods

suppressing background may not completely eliminate it.

Another way to help search for the CME is to compare iso-

baric collisions [47], where the magnetic ﬁelds differ and

the backgrounds are expected to be the same [48]. However,

these simple expectations may not be correct because of the

non-identical isobaric nuclear structures [49].

A new method to search for the CME, as we demonstrate

in this article, is to eliminate the resonance background con-

tributions using particle pair invariant mass (m

inv

)by(i)

applying a lower cut on the m

inv

, (ii) ﬁtting the low m

inv

region by a two-component (TC) model, and (iii) ﬁtting the

low m

inv

region by a two-component model aided by event-

shape engineering (TC+ESE). We illustrate our method using

the AMPT (A Multi-Phase Transport) model [50] and a toy

Monte Carlo (MC) simulation. In both, the resonance masses

are sampled from Breit-Wigner distributions [51,52]. We

use pions within pseudorapidity |η| < 1 and 0.2 < p

2GeV/c, except otherwise speciﬁed.

It is worthwhile to note here, since the CME is generally

alow p

phenomenon, that large m

inv

region may not be the

best place to search for it. If no CME is found at large m

inv

it does not necessarily mean that CME does not exist at low

inv

. However, if a ﬁnite signal is observed at large m

inv

where background sources diminish, it could be a strong evi-

dence for the possible existence of the CME that would call

for further investigations. It is also worthwhile to note that

our low m

inv

ﬁtting procedure is not without assumptions.

Although the background shape may be assessed by the ESE

method, there is still the question of the CME shape as func-

tion of m

inv

. In principle, if the CME and the background

have the same m

inv

shape, then our invariant mass method

would not be able to distinguish the two contributions. Theo-

retical inputs are much needed in this respect. Nevertheless,

our method provides a potentially powerful way to extract

the CME with reasonable assumptions of the m

inv

depen-

dence of the CME, which can be gauged to some extent by

the ﬁtting quality.

The rest of the paper is organized as follows. Section 2

presents the AMPT and toy-model studies by applying a

lower m

inv

cut to extract the γ in the high m

inv

region. Sec-

tion 3 describes a two-component model ﬁt to the γ (m

inv

Section 4 extends the ﬁtting method further by using ESE to

determine the background γ (m

inv

) shape to help extract the

CME signal. Section 5 puts our methods into experimental

context and summarizes the paper.

2 High-m

inv

region

2.1 A transport model study with null CME

AMPT is a parton transport model [50]. It consists of a ﬂuctu-

ating initial condition, parton elastic scatterings, quark coa-

lescence for hadronization, and hadronic interactions. The

initial condition is taken from HIJING [53]. The string melt-

ing version [54] is used in this study. Two-body elastic par-

ton scatterings are treated with Zhang’s Parton Cascade [55],

where the parton scattering cross section is set to 3 mb. After

partons stop interacting, a simple quark coalescence model

is applied to describe the hadronization process that converts

partons into hadrons [56]. Subsequent interactions of these

formed hadrons are modeled by a hadron cascade [56]. How-

ever, it is known that this version of the hadron cascade does

not conserve charge, which is critical to the charge correlation

study here. The hadronic scatterings, while responsible for

the majority of the v

mass splitting, are unimportant for the

main development of v

[57,58], and thus may not be critical

for the CME backgrounds. We thus turn off hadronic cascade

in AMPT for our study here, as was done in Ref. [59]. AMPT

has been quite successful in describing variety of heavy ion

data [52]. It reproduces approximately the measured particle

yields and distributions, and therefore should approximately

describe those of resonances as well, which is relevant to

the CME background study here. We simulate Au+Au colli-

sions at

√

= 200 GeV of various impact parameter (b)

ranges. For simplicity we use the known reaction plane in

our analysis, ﬁxed at ψ = 0.

123

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