# Polar Codes for SCMA Systems

Monirosharieh Vameghestahbanati, Ian Marsland, Ramy H. Gohary, and Halim
Yanikomeroglu
Department of Systems and Computer Engineering, Carleton University, Ottawa,
ON, Canada
Email: {mvamegh, ianm, gohary<EMAIL_ADDRESS>
###### Abstract

In this paper, we design and compare multilevel polar coding (MLPC) and bit-
interleaved polar coded modulation (BIPCM) for uplink sparse code multiple
access (SCMA) systems that operate over fast and block fading channels. Both
successive cancellation (SC) and successive cancellation list (SCL) decoding
algorithms are considered. Simulation results show that, with either decoder,
BIPCM performs better than its MLPC counterpart. Also, both BIPCM and MLPC
exhibit a performance advantage over LTE turbo-coded and WiMAX LDPC SCMA
systems when the SCL technique is used for decoding.

##  I Introduction

The ever-increasing demand to accommodate various types of users and
applications entails the emergence of novel techniques that are capable of
coping with their requirements. The recently developed non-orthogonal multiple
access (NOMA) waveform configuration of sparse code multiple access (SCMA) [1]
provides an innovative paradigm that can address the aforementioned demand
[2].

In SCMA, sparse multidimensional codewords of multiple users are superimposed
over shared orthogonal resources, whereby the number of users typically
exceeds the number of resources. In essence, SCMA constitutes an instance of
overloaded code division multiple access (CDMA) with two major differences:
Firstly, in SCMA, the input binary data stream is directly encoded to
multidimensional complex codewords chosen from a codebook set that is
different for each user. In contrast, in CDMA the input data stream is mapped
to QAM symbols followed by a CDMA spreader. Secondly, in SCMA the spreading
matrix is restricted to be sparse such that only a few users overlap in each
shared resource in order to minimize the multiuser interference; such a
restriction is not imposed in CDMA.

The performance of SCMA systems can be improved by channel coding, e.g., turbo
and LDPC codes. In [3], the bit error probability (BER) performance of turbo-
coded SCMA systems was studied. A turbo principle with an iterative multiuser
receiver for SCMA systems was proposed in [4] and an uplink LDPC-coded SCMA
system was studied in [5].

Another class of channel codes is that of polar codes, which is based on
channel polarization [6]. Channel polarization involves synthesizing, out of
$N$ independent binary discrete memoryless channel, a set of $N$ _polarized_
channels called the bit channels. Compared with other coding techniques, polar
codes introduce an emerging type of error correcting code with the ability to
achieve the capacity of discrete memoryless channels when the codeword length
approaches infinity. They also provide lower-complexity encoders and decoders
compared with turbo and LDPC codes when decoded by successive cancellation
(SC) [7]. On the other hand, it is critical to construct polar codes to obtain
the best performance when the codeword length is finite [8]. In [9],
successive cancellation list (SCL) decoding of polar codes was proposed to
improve their performance at finite codeword lengths but with higher
complexity compared to the SC decoding.

As both SCMA and polar coding are possible candidates for 5G systems [2], it
is important to investigate the design of polar codes for SCMA systems from
different aspects over different channel models. A polar code design method
for SCMA systems over additive white Gaussian noise (AWGN) was presented in
[10]. In this paper, we design and compare the performance of two polar-coded
schemes for uplink SCMA systems operating over two types of channels, fast and
block fading. The first scheme is the so-called bit-interleaved polar coded
modulation (BIPCM), whereas the other scheme is the so-called multilevel polar
coding (MLPC). The underlying polar codes are designed using a Monte-Carlo
simulation-based method , proposed in [6], that can be applied to different
channels. However, instead of calculating the Bhattacharyya parameters of the
bit channels as in [6], the BER is used [8].

BIPCM is the combination of bit-interleaved coded modulation (BICM) with polar
coding [11, 12]. In BIPCM, the message word for each user is encoded using a
_single_ polar encoder to produce the output codeword. The codeword is then
interleaved and passed to a signal mapper. A signal mapper maps the coded bits
into points in the signal constellation with a certain labelling scheme. One
such a labelling scheme is Gray labelling that generates bit levels that are
independent from each other.

MLPC is the combination of multilevel coding (MLC) with polar coding [13]. In
contrast with BIPCM, MLPC consists of _multiple levels_ ; the number of levels
corresponds to the number of bits in each symbol. At each level, each bit of
the signal constellation is protected by an individual binary code. The total
number of encoders and decoders in MLPC is equal to the number of bit levels.
Each SCMA symbol depends on one bit from each encoder. In MLC, set
partitioning (SP) labelling is known to perform better than other labelling
scheme like Gray labelling [14], as it establishes larger variance in the
reliability of each bit level. At the receiver, MLPC decodes the bit levels
_sequentially_ , with information gained when decoding earlier levels used to
make decisions at later levels. This is in contrast to BIPCM, where a single
polar decoder is used to jointly decode the bits.

In this paper, we design and compare BIPCM and MLPC for SCMA systems that
operate over block and fast fading channels. We employ multiuser detection and
decoding separately in a concatenated manner as in [1] based on the non-binary
message passing algorithm (MPA) detection, and both successive cancellation
(SC) and successive cancellation list (SCL) decoding techniques. Simulation
results show that, with either decoder, BIPCM performs better than its MLPC
counterpart. Also, when the SCL technique is used for decoding, both BIPCM and
MLPC exhibit a performance advantage over SCMA systems employing either the
LTE turbo code or the WiMAX LDPC code.

The rest of the paper is organized as follows. We introduce the system model
in Section II, and we present MPA detection for coded SCMA systems in Section
III. In Section IV, we provide an overview on BIPCM and MLPC for SCMA systems.
Section V presents the simulation results, and Section VI concludes the paper.

Figure 1: The system model for uplink transmission of a coded SCMA system with
$K$ users multiplexed over $N$ resources with an overloading factor of $K/N$.

##  II System Model

The system model is shown in Fig. 1. We assume there are $K$ users multiplexed
over $N$ ($N<K$) orthogonal resources. In an $M$-ary signal constellation,
each signal point represents $L_{M}=\log_{2}M$ bits. Let $K_{c}$ and $N_{c}$
denote the length of message words input to the encoder and the length of
codewords output from the encoder, respectively. The codewords are in turn
partitioned into $N_{c}/L_{M}$ digital symbols of $L_{M}$ bits each. Let
$c_{k}=\left(c_{k,1},\dots,c_{k,L_{M}}\right)$, $c_{k,m}\in\left(0,1\right)$,
denote one symbol for user $k$, $k\in\left\\{1,\dots,K\right\\}$. Each symbol
is mapped to an $N$-dimensional sparse complex codeword
$\bm{x}_{k}=\left(x_{1,k},\dots,x_{N,k}\right)^{\textrm{T}}$ selected from an
$N$-dimensional complex codebook $\bm{V}_{k}$ of size $M$. That is,
$x_{n,k}=V_{n,k}\left(c_{k}\right)$.

The receiver observes

$\displaystyle\bm{r}=\sum\limits_{k=1}^{K}{\textrm{diag}}\left(\bm{h}_{k}\right)\bm{x}_{k}+\bm{w},$
(1)

where $\bm{h}_{k}=\left(h_{1,k},\dots,h_{N,k}\right)^{\textrm{T}}$ denotes the
fading channel coefficient vector for user $k$, and
$\bm{w}~{}\thicksim\mathcal{CN}\left(0,\sigma^{2}\mathbf{I}\right)$ is an
$N$-dimensional complex Gaussian ambient noise sample with zero mean and a
covariance matrix of $\sigma^{2}\mathbf{I}$.

Due to the sparse nature of SCMA codewords, the near optimal MPA, which is
discussed in Section III, is used to detect the SCMA codewords that will then
be fed to the polar decoders to retrieve the message transmitted by each user.

##  III Message Passing Algorithm

Figure 2: An example of the factor graph for $K=4$ users and $N=6$ resources.

The structure of an SCMA code can be represented by an $N\times K$ binary
mapping matrix $\bm{S}$ with its corresponding bipartite graph
$\mathcal{G}\left(K,N\right)$ that contains $K$ variable nodes. and $N$ check
nodes. The variable nodes and check nodes represent $K$ users and $N$
resources, respectively. Fig. 2 shows an example of
$\mathcal{G}\left(K,N\right)$ with $K=6$, $N=4$, for the mapping matrix

$\displaystyle\bm{S}=\left[{\begin{array}[]{*{20}c}0&1&1&0&1&0\\\
1&0&1&0&0&1\\\ 0&1&0&1&0&1\\\ 1&0&0&1&1&0\\\ \end{array}}\right].$

There is an edge between variable node $k$ and check node $n$ if and only if
$s_{n,k}=1$. The set of check nodes connected to variable node $k$ is
specified by the positions of the $1$’s in the $k$th column of the mapping
matrix and is represented by $\mathcal{D}_{k}=\left\\{n|s_{n,k}=1\right\\}$.
In a similar vein, the set of variable nodes connected to check node $n$ is
identified by the positions of the $1$’s in the $n$th row of $\bm{S}$ and is
denoted by $\mathcal{C}_{n}=\left\\{k|s_{n,k}=1\right\\}$.

Let $\bm{\mu}_{k\rightarrow n}$ and $\bm{\tilde{\mu}}_{n\rightarrow k}$ be
vectors of length $M$ that represent the message passed from user node $k$ to
resource node $n$, and the message from resource node $n$ to user node $k$ at
each iteration, respectively. Element $i$ of $\bm{\mu}_{k\rightarrow n}$ is
given by

$\displaystyle\bm{\mu}_{k\rightarrow
n}\left(i\right)=\prod_{m\in\mathcal{D}_{k}\backslash n}\bm{\mu}_{m\rightarrow
k}\left(i\right),$ (3)

where $i=1,\dots,M$. Each element of the message conveyed from resource node
$n$ to user node $k$ is

$\displaystyle\bm{\tilde{\mu}}_{n\rightarrow
k}\left(i\right)=\sum_{\bm{c}\in\mathcal{M}^{K}|c_{k}=i}f\left\\{r_{n}|\bm{c}\right\\}\prod_{l\in\mathcal{C}_{n}\backslash
k}\bm{\mu}_{l\rightarrow n}\left(c_{l}\right),$ (4)

where $\bm{c}=\left(c_{1},\dots,c_{K}\right)$ with elements
$c_{k}\in\mathcal{M}=\left\\{1,\dots,M\right\\}$, and $r_{n}$ is the $n$th
element of received vector $\bm{r}$. The likelihood function is given by

$\displaystyle
f\left(r_{n}|\bm{c}\right)=\frac{1}{2\pi\sigma^{2}}\exp\left\\{-\frac{1}{2\sigma^{2}}\left|r_{n}-\sum_{k=1}^{K}h_{n,k}V_{n,k}\left(c_{k}\right)\right|^{2}\right\\}.$
(5)

The _a posteriori_ probability distribution at each variable node is then

$\textrm{Pr}\left\\{c_{k}=i|\bm{r}\right\\}=\beta_{k}\prod_{m\in\mathcal{D}_{k}}\bm{\tilde{\mu}}_{m\rightarrow
k}\left(i\right),$ (6)

where $\beta_{k}$ is chosen such that
$\sum\nolimits_{i=1}^{M}\textrm{Pr}\left\\{c_{k}=i|\bm{r}\right\\}=1$.

##  IV Polar codes for SCMA Systems

As mentioned earlier, we design and compare both BIPCM and MLPC for SCMA
systems. In this section, we provide our design method with an overview on
BIPCM and MLPC for SCMA systems.

###  IV-A Monte-Carlo Simulation-based Polar Code Design

In general, the best polar code for one application is unlikely to be the best
for another application, but it is possible to design good polar codes
specifically for a certain application with a certain channel model. In
contrast, turbo codes and LDPC codes cannot be specifically designed for each
individual application, but turbo codes and LDPC codes designed for one
application tends to be good for a wide variety of other applications.

There are several different polar code design methods in the literature e.g.,
[6, 15, 16]. In this paper, we employ a Monte-Carlo simulation-based method,
proposed in [6], that can be applied to different channels. However, instead
of calculating the Bhattacharyya parameters of bit channels as in [6], the BER
is directly estimated [8]. At a specific design SNR, we simulate the
transmission of a large number of message words, and store the positions of
the bits where the first error events occur111 The position of the first error
event is the first message bit to be decoded incorrectly given that all
previous bits are either decoded correctly or frozen. To speed up the design
process, when an error occurs the position of the error is recorded, but a
correct decision is fed back to the decoder, so that multiple first error
events can be recorded with each simulated codeword.. To achieve a required
code rate of $K_{c}/N_{c}$, the $K_{c}$ bit positions with the fewest recorded
first error events are selected to carry the information bits. As will be
discussed in Section V, the performance of the system depends on the design
SNR.

###  IV-B Bit-interleaved Polar Coded Modulation (BIPCM)

In BIPCM, the message words for each user of length $K_{c}$ are encoded using
a single polar encoder with a rate of $R$ to produce codewords of length
$N_{c}$. The codewords are then interleaved using random interleaving, and
partitioned into $L_{M}$-tuples to be mapped to complex codewords,
$\bm{x}_{k}$.

At the receiver, the output symbol probabilities of the MPA i.e.,
$\textrm{Pr}\left\\{c_{k}=i|\bm{r}\right\\}$ given by (6), are passed to the
BIPCM decoder. Since $c_{k}$ can be expressed as $L_{M}$ bits,
$c_{k}=\left(c_{k,1},\dots,c_{k,L_{M}}\right)$, we have
$\textrm{Pr}\left\\{c_{k}|\bm{r}\right\\}=\textrm{Pr}\left\\{c_{k,1}\dots
c_{k,L_{M}}|\bm{r}\right\\}$. The BIPCM decoder computes the log likelihood
ratio (LLR) of each code bit as

$\displaystyle\lambda_{k,m}=\log\frac{\textrm{Pr}\left\\{c_{k,m}=0|\bm{r}\right\\}}{\textrm{Pr}\left\\{c_{k,m}=1|\bm{r}\right\\}},$
(7)

where $\lambda_{k,m}$ denotes the LLR corresponding to bit $m$,
$m\in\left\\{1,\ldots,L_{M}\right\\}$, of user $k$, and

$\textrm{Pr}\left\\{c_{k,m}=l|\bm{r}\right\\}=\mathop{\sum_{c_{k,1}}\dots\sum_{c_{k,L_{M}}}}_{c_{k,m}=l}\textrm{Pr}\left\\{c_{k,1}\dots
c_{k,L_{M}}|\bm{r}\right\\}$ (8)

###  IV-C Multilevel Polar Coding (MLPC)

In the following, we describe the multilevel polar encoder and decoder schemes
[13] for SCMA systems.

####  IV-C1 Multilevel Polar Encoder

As mentioned earlier, for a signal constellation of $M$ points, there are
$L_{M}=\log_{2}M$ polar encoders, one for each bit. Each polar encoder output
has a length of $N_{c}/L_{M}$, so for each SCMA user we have a total of
$N_{c}$ code bits. The code bits are fed to the mapper so that each symbol
carries exactly one bit from each polar encoder.

In the design process of MLPC, all the constituent polar codes are designed
simultaneously. That is, the first error event probabilities of all the
possible $N_{c}$ message bits are calculated via Monte Carlo simulation, and
then the best $K_{c}$ positions are selected, without regard to which
constituent polar encoder they are associated with. As a result, the code
rates of the constituent codes are determined automatically, and reflect the
reliability of each bit level. In particular, those bit levels with lower
reliability end up being assigned a higher rate code and vice versa. In
keeping with polarization principle [6], we use set partitioning labelling to
polarize the bit level reliabilities [13].

####  IV-C2 Multilevel Polar Decoder

The symbol probabilities $\textrm{Pr}\left\\{c_{k}=i|\bm{r}\right\\}$ produced
by the MPA given by (6) are passed to the multilevel polar decoder. Unlike
BIPCM, with MLPC, the bit levels are decoded consecutively, with information
gained when decoding earlier levels used to direct decision making at later
levels. The probability distribution at the $m$th bit, given perfect knowledge
of the bits at lower levels, $c_{k,1},\dots,c_{k,m-1}$, but no knowledge of
the higher levels, $c_{k,m+1},\dots,c_{k,L_{M}}$, can be calculated as

$\displaystyle\textrm{Pr}\left\\{c_{k,m}|\bm{r},c_{k,1},\dots,c_{k,m-1}\right\\}=\hskip
85.35826pt$ $\displaystyle\hskip
71.13188pt\sum_{c_{k,m+1}}\dots\sum_{c_{k,L_{M}}}\frac{\textrm{Pr}\left\\{c_{k,1},\dots,c_{k,L_{M}}|\bm{r}\right\\}}{\textrm{Pr}\left\\{c_{k,1},\dots,c_{k,m-1}|\bm{r}\right\\}},$
(9)

and the corresponding LLR is

$\lambda_{k,m}=\log\frac{\textrm{Pr}\left\\{c_{k,m}=0|\bm{r},c_{k,1},\dots,c_{k,m-1}\right\\}}{\textrm{Pr}\left\\{c_{k,m}=1|\bm{r},c_{k,1},\dots,c_{k,m-1}\right\\}}.$
(10)

Multilevel decoding is carried out by calculating the LLRs for the first
level, $\lambda_{k,1}$, for all $N_{c}$ symbols for user $k$ and passing these
LLRs to a polar decoder for the first-level polar code. This decoder provides
an estimate of the transmitted polar codeword, which is used as $c_{k,1}$ when
calculating the LLRs at the second level, $\lambda_{k,2}$. The process is
repeated until all levels have been decoded.

In this paper, we use both SC and SCL techniques for decoding BIPCM and MLPC.
Note that the encoding complexity is in the order of
$\mathcal{O}(N_{c}\log{}N_{c})$ for BIPCM, and in the order of
$\mathcal{O}(N_{c}\log{}N_{c}/L_{M})$ for MLPC. In addition, to calculate the
LLR corresponding to each bit level, (7) suggests that BIPCM requires $N_{c}$
summations. On the other hand, according to (10), the number of summations
involved in the LLR calculation of level $m$ of MLPC is
$N_{c}/\left(L_{M}\>2^{m-1}\right)$, which results in a total of at most
$2N_{c}/L_{M}$ summations. As such, MLPC is computationally less complex
compared with BIPCM.

##  V Simulation Results

Figure 3: The comparison among an SC-decoded MLPC system, an SC-decoded BIPCM
system, an SCL-decoded MLPC system, and an SCL-decoded BIPCM system, with
$N_{c}=2048$, at two different design SNRs. The overall code rate for all
cases is $R=2/3$. All systems operate in fast fading.

In this section, we evaluate the frame error rate (FER) performance of an
uplink SCMA system with $K=6$ users and $N=4$ orthogonal resources with the
widely used 4-dimensional complex codebooks of size $M=4$, $L_{M}=2$, given in
[17]. We use Gray labelling for the BIPCM case and SP labelling for the MLPC
case. Each user operates over a fading channel that is contaminated by AWGN,
and transmits on only two of the four resources. We consider two fading
scenarios: fast fading and block fading. In the fast fading scenario, the
channel coefficients for each user vary independently in every use of the
channel, while in the block fading case, the channel coefficients for each
user are constant over a block of 18 channel uses as in [3]. In both channel
models, we assume that each user uses the same channel coefficients over the
$\left|\mathcal{D}_{k}\right|$ resources. Both BIPCM and MLPC when used by the
SCL decoder, have a cyclic redundancy check (CRC) length of 16 bits and a list
size of 32. The turbo codes are from the 3GPP LTE standard [18] and the LDPC
code is chosen from the WiMAX standard [19].

Figure 4: The comparison among an SC-decoded MLPC system, an SC-decoded BIPCM
system, both with $N_{c}=2048$, LTE turbo coded system with $N_{c}=2070$,
WiMAX LDPC system with $N_{c}=2016$, an SCL-decoded MLPC system, and an SCL-
decoded BIPCM system, both with $N_{c}=2048$. The overall code rate for all
cases is $R=2/3$. All systems operate in fast fading.

Fig. 3 compares the performance of length 2048 SC-decoded and SCL-decoded
BIPCM SCMA systems, length 2048 SC-decoded and SCL-decoded MLPC222The length
of the constituent polar code with MLPC for each level is 1024. SCMA systems
at two design SNRs, $E_{mb}/N_{0}=8$ dB and $E_{mb}/N_{0}=10$ dB. The net rate
of all codes is $2/3$, and all systems operate in fast fading channel. We
observe that it is important to choose the right design SNR depending on the
target FER. In particular, to achieve a target FER of $10^{-2}$, a design SNR
of $E_{mb}/N_{0}=10$ dB is a better choice for both BIPCM and MLPC with the SC
decoder, while a design SNR of $E_{mb}/N_{0}=8$ dB is a better choice for both
BIPCM and MLPC with the SCL decoder.

In Fig. 4 we show the performance of length 2048 SC-decoded and SCL-decoded
BIPCM SCMA systems designed at $E_{mb}/N_{0}=8$ dB, length 2048 SC-decoded and
SCL-decoded MLPC systems designed at $E_{mb}/N_{0}=10$ dB, a length 2070 LTE
turbo coded system, and a length 2016 WiMAX LDPC system. The net rate of all
codes is $2/3$, and all systems operate in fast fading channel. As we see,
BIPCM outperforms MLPC by about 0.2 dB with SC decoding, while it behaves
marginally better than MLPC with SCL decoding. Moreover, to achieve a target
FER of $10^{-2}$, both BIPCM and MLPC with the SCL decoder outperform the LTE
turbo coded system by about 1 dB, and outperform the WiMAX LDPC system by
about 0.8 dB with a comparable decoding complexity. On the other hand, the LTE
turbo and the WiMAX LDPC offer a gain of 0.5 dB and 0.7 dB compared with SC-
decoded BIPCM system, respectively, but at a cost of much more decoding
complexity.

Figure 5: The comparison among an SC-decoded MLPC system, an SC-decoded BIPCM
system, both with $N_{c}=2048$, LTE turbo coded system with $N_{c}=2028$, an
SCL-decoded MLPC system, and an SCL-decoded BIPCM system, both with
$N_{c}=2048$. The overall code rate for all cases is $R=1/3$. All systems
operate in fast fading.

We depict the performance comparison of rate $1/3$ coded SCMA systems that
operate over fast fading and block fading channels in Fig. 5 and Fig. 6,
respectively. All polar codes are designed at $E_{mb}/N_{0}=6$ dB. We see that
MLPC is not an ideal candidate for SCMA systems. This is, however, in contrast
with results previously reported in [13] for single-user AWGN channels.
Particularly, we see that to achieve a target FER of around $10^{-2}$, the SC-
decoded BIPCM system performs better than the SC-decoded MLPC system by about
0.2 dB in the fast fading case, and about 0.1 dB in the block fading scenario.
The SCL-decoded MLPC results in a gain of about 0.25 dB in the case of fast
fading and 0.15 dB in the case of block fading. Moreover, Fig. 5 and Fig. 6
confirm that the performance of turbo coded system with $N_{c}=2028$ falls
between BIPCM and MLPC with both SC decoding and SCL decoding. More precisely,
the SCL-decoded BIPCM system performs better than the LTE turbo coded system
by about 0.8 dB, in both fading scenarios, while the SC-decoded BIPCM system
falls behind the LTE turbo coded system by about 0.9 dB in fast fading and
about 0.5 dB in block fading.

##  VI Conclusion

We have designed and compared two polar-coded signalling schemes, MLPC and
BIPCM, for uplink SCMA systems that operate over fast and block fading
channels. The two polar-coded signalling schemes are designed with both SC and
SCL decoding techniques. Simulation results show that, with either decoder,
BIPCM performs better than MLPC. Moreover, both BIPCM and MLPC when decoded
using SCL outperform the LTE turbo codes and the WiMAX LDPC.

Figure 6: The performance comparison of an SC-decoded MLPC system, an SC-
decoded BIPCM system, both with $N_{c}=2048$, LTE turbo coded system with
$N_{c}=2028$, an SCL-decoded MLPC system, and an SCL-decoded BIPCM system,
both with $N_{c}=2048$. The net code rate for all scenarios is $R=1/3$. All
systems operate in block fading.

## ACKNOWLEDGMENT

This work is supported in part by an Ontario Trillium Scholarship, in part by
Huawei Canada Co., Ltd., and in part by the Ontario Ministry of Economic
Development and Innovations Ontario Research Fund - Research Excellence (ORF-
RE) program.

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  * [19] IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1, “ IEEE Std. 802.16e-2005 and 802.16-2004/Cor 1-2005,” pp. 1–822, Feb. 2006.


2017 241 12 September

Constraining the Chiral Magnetic Effect at the LHC

ALICE CollaborationALICE Collaboration

In ultrarelativistic heavy-ion collisions, the event-by-event variation of the
elliptic flow $v_{2}$ reflects fluctuations in the shape of the initial state
of the system. This allows to select events with the same centrality but
different initial geometry. This selection technique, Event Shape Engineering,
has been used in the analysis of charge-dependent two- and three-particle
correlations in Pb–Pb collisions at $\mbox{$\sqrt{s_{{}_{\rm NN}}}$}=2.76$
TeV. The two-particle correlator
$\langle\cos(\varphi_{\alpha}-\varphi_{\beta})\rangle$, calculated for
different combinations of charges $\alpha$ and $\beta$, is almost independent
of $v_{2}$ (for a given centrality), while the three-particle correlator
$\langle\cos(\varphi_{\alpha}+\varphi_{\beta}-2\Psi_{\rm 2})\rangle$ scales
almost linearly both with the event $v_{2}$ and charged-particle
pseudorapidity density. The charge dependence of the three-particle correlator
is often interpreted as evidence for the Chiral Magnetic Effect (CME), a
parity violating effect of the strong interaction. However, its measured
dependence on $v_{2}$ points to a large non-CME contribution to the
correlator. Comparing the results with Monte Carlo calculations including a
magnetic field due to the spectators, the upper limit of the CME signal
contribution to the three-particle correlator in the 10–50% centrality
interval is found to be 26–33% at 95% confidence level.

Parity symmetry is conserved in electromagnetism and is maximally violated in
weak interactions. In strong interactions, global parity violation is not
observed even though it is allowed by quantum chromodynamics. Local parity
violation in strong interactions might occur in microscopic domains under
conditions of finite temperature [1, 2, 3, 4] due to the existence of the
topologically non-trivial configurations of the gluonic field, instantons and
sphalerons. The interactions between quarks and gluonic fields with non-zero
topological charge [5] change the quark chirality. A local imbalance of
chirality, coupled with the strong magnetic field produced in heavy-ion
collisions ($B\sim 10^{15}$ T) [6, 7, 8], would lead to charge separation
along the direction of the magnetic field, which is on average perpendicular
to the reaction plane (the plane of symmetry defined by the impact parameter
vector and the beam direction), a phenomenon called Chiral Magnetic Effect
(CME) [9, 10, 11, 12]. Since the sign of the topological charge is equally
probable to be positive or negative, the charge separation averaged over many
events is zero. This makes the observation of the CME experimentally difficult
and possible only via correlation techniques.

Azimuthal anisotropies in particle production relative to the reaction plane,
often referred to as anisotropic flow, are an important observable to study
the system created in heavy-ion collisions [13, 14]. Anisotropic flow arises
from the asymmetry in the initial geometry of the collision. Its magnitude is
quantified via the coefficients $v_{n}$ in a Fourier decomposition of the
charged particle azimuthal distribution [15, 16]. Local parity violation would
result in an additional sine term [17]

$\frac{{\rm d}N}{{\rm d}\Delta\varphi_{\alpha}}\sim
1+2v_{1,\alpha}\cos(\Delta\varphi_{\alpha})+2a_{1,\alpha}\sin(\Delta\varphi_{\alpha})+2v_{2,\alpha}\cos(2\Delta\varphi_{\alpha})+...,$
(1)

where $\Delta\varphi_{\alpha}=\varphi_{\alpha}-\Psi_{\rm RP}$,
$\varphi_{\alpha}$ is the azimuthal angle of the particle of charge $\alpha$
(+, $-$) and $\Psi_{\rm RP}$ is the reaction-plane angle. The first
($v_{1,\alpha}$) and the second ($v_{2,\alpha}$) coefficients are called
directed and elliptic flow, respectively. The $a_{1,\alpha}$ coefficient
quantifies the effects from local parity violation. Since the average $\langle
a_{1,\alpha}\rangle=0$ over many events, one can only measure $\langle
a_{1,\alpha}^{2}\rangle$ or $\langle a_{1,+}\,a_{1,-}\rangle$. The charge-
dependent two-particle correlator

$\displaystyle\delta_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}-\varphi_{\beta})\rangle=\langle\cos(\Delta\varphi_{\alpha})\cos(\Delta\varphi_{\beta})\rangle+\langle\sin(\Delta\varphi_{\alpha})\sin(\Delta\varphi_{\beta})\rangle$
(2)

is not convenient for such a study, because along with the signal $\langle
a_{1,\alpha}\,a_{1,\beta}\rangle$ ($\beta$ denotes the charge) there is a much
stronger contribution from correlations unrelated to the azimuthal asymmetry
in the initial geometry (“non-flow”). These correlations largely come from the
inter-jet correlations and resonance decays. To increase the CME contribution
it was proposed to use the following correlator [17]

$\displaystyle\gamma_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}+\varphi_{\beta}-2\Psi_{\rm
RP})\rangle=\langle\cos(\Delta\varphi_{\alpha})\cos(\Delta\varphi_{\beta})\rangle-\langle\sin(\Delta\varphi_{\alpha})\sin(\Delta\varphi_{\beta})\rangle$
(3)

that measures the difference between the correlation projected onto the
reaction plane and perpendicular to it. In practice, the reaction-plane angle
is estimated by constructing the event plane angle $\Psi_{\rm 2}$ using
azimuthal particle distributions, which is why this correlator is often
described as a three-particle correlator. This correlator suppresses
background contributions at the level of $v_{2}$, the difference between the
particle production in-plane and out-of-plane. Examples of such background
sources are the local charge conservation (LCC) coupled with elliptic flow
[18, 19], momentum conservation [19, 20, 21], and directed-flow fluctuations
[22]. The most significant background source for CME measurements is the LCC.

The measurements of charge-dependent azimuthal correlations performed at the
Relativistic Heavy Ion Collider (RHIC) [23, 24, 25, 26] and the Large Hadron
Collider (LHC) [27, 28] are in qualitative agreement with the expectations for
the CME. However, the interpretation of these experimental results is
complicated due to possible background contributions. The Event Shape
Engineering (ESE) technique was proposed to disentangle background
contributions from the potential CME signal [29]. This method makes it
possible to select events with eccentricity values significantly larger or
smaller than the average in a given centrality class [30, 31] since $v_{2}$
scales approximately linearly with eccentricity [32]. Centrality estimates the
degree of overlap between the two colliding nuclei, with low percentage values
corresponding to head-on collisions. The CME contribution is expected to
mainly scale with the magnetic field strength and to not have a strong
dependence on the eccentricity [33], while the background varies
significantly. Therefore ESE provides a unique tool to separate the CME signal
from the background for the three-particle correlator.

The CMS Collaboration has recently reported the measurement of the three-
particle correlator $\gamma_{\alpha\beta}$ in p–Pb collisions at
$\sqrt{s_{{}_{\rm NN}}}=5.02$ TeV [34], where the direction of the magnetic
field is expected to be uncorrelated to the reaction plane [35]. The magnitude
of the correlator in p–Pb and Pb–Pb collisions is comparable for similar
final-state charged-particle multiplicities. This measurement indicates that
the contribution of the CME to this observable in this multiplicity range is
small.

In this paper we report the measurements of the two-particle correlator
$\delta_{\alpha\beta}$, the three-particle correlator $\gamma_{\alpha\beta}$,
and the elliptic flow $v_{2}$ of unidentified charged particles. These
measurements are performed for shape selected and unbiased events in Pb–Pb
collisions at $\mbox{$\sqrt{s_{{}_{\rm NN}}}$}=2.76$ TeV. An upper limit on
the CME contribution is deduced from comparisons of the observed dependence of
the correlations on the event $v_{2}$ to that estimated using Monte Carlo (MC)
simulations of the magnetic field of spectators with different initial
conditions. While this paper was in preparation, a paper employing a similar
approach to estimate the fraction of the CME signal in the three-particle
correlator was submitted by the CMS Collaboration [36].

The data sample recorded by ALICE during the 2010 LHC Pb–Pb run at
$\mbox{$\sqrt{s_{{}_{\rm NN}}}$}=2.76$ TeV is used for this analysis. General
information on the ALICE detector and its performance can be found in [37,
38]. The Time Projection Chamber (TPC) [37, 39] and Inner Tracking System
(ITS) [37, 40] are used to reconstruct charged-particle tracks and measure
their momenta with a track-momentum resolution better than 2% for the
transverse momentum interval $0.2<p_{\rm{T}}<5.0$ GeV/$c$ [38]. The two
innermost layers of the ITS, the Silicon Pixel Detector (SPD), are employed
for triggering and event selection. Two scintillator arrays (V0) [37, 41],
which cover the pseudorapidity ranges $-3.7<\eta<-1.7$ (V0C) and
$2.8<\eta<5.1$ (V0A), are used for triggering, event selection, and the
determination of centrality [42] and $\Psi_{\rm 2}$. The trigger conditions
and the event selection criteria are described in [38]. An offline event
selection is applied to remove beam induced background and pileup events.
Approximately $9.8\cdot 10^{6}$ minimum-bias Pb–Pb events with a reconstructed
primary vertex within $\pm 10$ cm from the nominal interaction point in the
beam direction belonging to the 0–60% centrality interval are used for this
analysis.

Charged particles reconstructed using the combined information from the ITS
and TPC in $|\eta|<0.8$ and $0.2<p_{\rm{T}}<5.0$ GeV/$c$ are selected with
full azimuthal coverage. Additional quality cuts are applied to reduce the
contamination from secondary charged particles (i.e. particles originating
from weak decays, conversions and secondary hadronic interactions in the
detector material) and fake tracks (with random associations of space points).
Only tracks with at least 70 space points in the TPC (out of a maximum of 159)
with an average $\chi^{2}$ per degree-of-freedom for the track fit lower than
2, a distance of closest approach (DCA) to the reconstructed event vertex
smaller than 2.4 cm in the transverse plane ($xy$) and 3.2 cm in the
longitudinal direction ($z$) are accepted. The charged particle track
reconstruction efficiency was estimated from HIJING simulations [43, 44]
combined with a GEANT3 [45] detector model, and found to be independent of the
collision centrality. The reconstruction efficiency of primary particles
defined in [46], which may bias the determination of the $p_{\rm{T}}$ averaged
charge-dependent correlations and flow, increases from 70% at $p_{\rm{T}}=0.2$
GeV/$c$ to 85% at $p_{\rm{T}}\sim 1.5$ GeV/$c$ where it has a maximum. It then
gradually decreases and is flat at 80% for $p_{\rm{T}}>3.0$ GeV/$c$. The
systematic uncertainty of the efficiency is about 5%.

The event shape selection is performed as in [30] based on the magnitude of
the second-order reduced flow vector, $q_{2}$ [47], defined as

$q_{2}=\frac{|\bf{Q}_{2}|}{\sqrt{M}},$ (4)

where $|{\bf Q}_{2}|=\sqrt{Q_{2,x}^{2}+Q_{2,y}^{2}}$ is the magnitude of the
second order harmonic flow vector and $M$ is the multiplicity. The vector
${\bf Q}_{2}$ is calculated from the azimuthal distribution of the energy
deposition measured in the V0C. Its $x$ and $y$ components and the
multiplicity are given by

$Q_{2,x}=\sum_{i}w_{i}\cos(2\varphi_{i}),\;Q_{2,y}=\sum_{i}w_{i}\sin(2\varphi_{i}),\;M=\sum_{i}w_{i},$
(5)

where the sum runs over all channels $i$ of the V0C detector ($i=1-32$),
$\varphi_{i}$ is the azimuthal angle of channel $i$ and $w_{i}$ is the
amplitude measured in channel $i$. The large gap in pseudorapidity
($|\Delta\eta|>0.9$) between the charged particles in the TPC used to
determine $v_{2}$, $\delta_{\alpha\beta}$ and $\gamma_{\alpha\beta}$ and those
in the V0C suppresses non-flow effects. Ten event-shape classes with the
lowest (highest) $q_{2}$ value corresponding to the 0–10% (90–100%) range are
investigated for each centrality interval.

The flow coefficient $v_{2}$ is measured using the event plane method [16].
The orientation of the event plane $\Psi_{\rm 2}$ is estimated from the
azimuthal distribution of the energy deposition measured by the V0A detector.
The event plane resolution is calculated from correlations between the event
planes determined in the TPC and the two V0 detectors separately [16]. The
non-flow contributions to the $v_{2}$ coefficient and charge-dependent
azimuthal correlations are greatly suppressed by the large rapidity separation
between the TPC and the V0A ($|\Delta\eta|>2.0$).

| Opposite charge | Same charge
---|---|---
$\delta_{\alpha\beta}$ | $(3.4-25)\times 10^{-5}$ | $(3.1-10)\times 10^{-5}$
$\gamma_{\alpha\beta}$ | $(2.6-34)\times 10^{-6}$ | $(4.1-74)\times 10^{-6}$
$v_{2}$ | $(1.2-4.7)\times 10^{-3}$
Table 1: Summary of absolute systematic uncertainties. The uncertainties
depend on centrality and shape selection, whose minimum and maximum values are
listed here. Figure 1: (Colour online) Unidentified charged particle $v_{2}$
for shape selected and unbiased events as a function of collision centrality.
The event selection is based on $q_{2}$ determined in the V0C with the lowest
(highest) value corresponding to 0–10% (90–100%) $q_{2}$. Points are slightly
shifted along the horizontal axis for better visibility. Error bars (shaded
boxes) represent the statistical (systematic) uncertainties. Figure 2: (Colour
online) Top: Centrality dependence of $\gamma_{\alpha\beta}$ for pairs of
particles with same and opposite charge for shape selected and unbiased
events. Bottom: Centrality dependence of $\delta_{\alpha\beta}$ for pairs of
particles with same and opposite charge for shape selected and unbiased
events.The event selection is based on $q_{2}$ determined in the V0C with the
lowest (highest) value corresponding to 0–10% (90–100%) $q_{2}$. Points are
slightly shifted along the horizontal axis for better visibility in both
panels. Error bars (shaded boxes) represent the statistical (systematic)
uncertainties.

The absolute systematic uncertainties are evaluated from the variation of the
results with different selection criteria on the reconstructed collision
vertex, different magnetic field polarities, as well as by estimating the
centrality from multiplicities measured by the TPC or the SPD rather than the
V0 detector. Changes of the results due to variations of the track-selection
criteria (e.g. changing the DCA $xy$ and $z$ ranges, number of the TPC space
points, using tracks reconstructed by the TPC only) are considered as part of
the systematic uncertainties. The effect of reconstruction efficiency on the
measurements is checked by randomly rejecting tracks to ensure a flat
acceptance in $p_{\rm{T}}$. The detector response is studied using HIJING and
AMPT [48] simulations, where the $v_{2}$ coefficients and the charge-dependent
azimuthal correlations obtained directly from the models are compared with
those from reconstructed tracks. The largest contribution to the systematic
uncertainties is given by the detector response. The checks related to the
reconstruction efficiency, magnetic field polarity and track-selection
criteria also yield significant deviations from the nominal values for
$v_{2}$, $\gamma_{\alpha\beta}$ and $\delta_{\alpha\beta}$, respectively. The
contributions from all sources are added in quadrature as an estimate of the
total systematic uncertainty. The resulting systematic uncertainties are
summarized in Table 1.

Figure 1 presents the unidentified charged particle $v_{2}$ averaged over
$0.2<p_{\rm{T}}<5.0$ GeV/$c$ for shape selected and unbiased samples as a
function of collision centrality. The measured $v_{2}$ for the shape selected
events differs from the average by up to 25%, which demonstrates that events
with the desired initial spatial anisotropy can be experimentally selected.
Sensitivity of the event shape selection deteriorates for peripheral
collisions (already visible for the 50–60% centrality class) due to the low
multiplicity and for central collisions due to the reduced magnitude of flow
[30].

Figure 3: (Colour online) Top: Difference between opposite and same charge
pair correlations for $\gamma_{\alpha\beta}$ as a function of $v_{2}$ for
shape selected events together with a linear fit (dashed lines) for various
centrality classes. Bottom: Difference between opposite and same charge pair
correlations for $\gamma_{\alpha\beta}$ multiplied by the charged-particle
density [49] as a function of $v_{2}$ for shape selected events for various
centrality classes. The event selection is based on $q_{2}$ determined in the
V0C with the lowest (highest) value corresponding to 0–10% (90–100%) $q_{2}$.
Error bars (shaded boxes) represent the statistical (systematic)
uncertainties.

The centrality dependence of $\gamma_{\alpha\beta}$ for pairs of particles
with same and opposite charge for shape selected and unbiased events is shown
in the top panel of Fig. 2. The same charge results denote the average between
pairs of particles with only positive and only negative charges since the two
combinations are found to be consistent within statistical uncertainties. The
correlation of pairs with the same charge is stronger than the correlation for
pairs of opposite charge for both shape selected and unbiased events. The
ordering of the correlations of pairs with same and opposite charge indicates
a charge separation with respect to the reaction plane. The magnitude of the
same and opposite charge pair correlations depends weakly on the event-shape
selection ($q_{2}$, i.e. $v_{2}$) in a given centrality bin.

The bottom panel of Fig. 2 shows the centrality dependence of
$\delta_{\alpha\beta}$ for pairs of particles with same and opposite charge
for shape selected and unbiased samples. As reported in [27], the magnitude of
the correlation for the same charge pairs is smaller than for the opposite
charge combinations. This is in contrast to the CME expectation, indicating
that background dominates the correlations. The same and opposite charge pair
correlations are insensitive to the event-shape selection in a given
centrality bin.

The difference between opposite and same charge pair correlations for
$\gamma_{\alpha\beta}$ can be used to study the charge separation effect. This
difference is presented as a function of $v_{2}$ for various centrality
classes in the top panel of Fig. 3. The difference is positive for all
centralities and its magnitude decreases for more central collisions and with
decreasing $v_{2}$ (in a given centrality bin). At least two effects could be
responsible for the centrality dependence: the reduction of the magnetic field
with decreasing centrality and the dilution of the correlation due to the
increase in the number of particles [24] in more central collisions. The
difference between opposite and same charge pair correlations multiplied by
the charged-particle density in a given centrality bin, ${\rm d}N_{\rm
ch}/{\rm d}\eta$ (taken from [49]), to compensate for the dilution effect, is
presented as a function of $v_{2}$ in the bottom panel of Fig. 3. All the data
points fall approximately onto the same line. This is qualitatively consistent
with expectations from LCC where an increase in $v_{2}$, which modulates the
correlation between balancing charges with respect to the reaction plane [50],
results in a strong effect. Therefore, the observed dependence on $v_{2}$
points to a large background contribution to $\gamma_{\alpha\beta}$.

Figure 4: (Colour online) The expected dependence of the CME signal on $v_{2}$
for various centrality classes from a MC-Glauber simulation [51] (see text for
details). No event shape selection is performed in the model, and therefore a
large range in $v_{2}$ is covered. The solid lines depict linear fits based on
the $v_{2}$ variation observed within each centrality interval.

The expected dependence of the CME signal on $v_{2}$ was evaluated with the
help of a Monte Carlo Glauber [51] calculation including a magnetic field. In
this simulation, the centrality classes are determined from the multiplicity
of charged particles in the acceptance of the V0 detector following the method
presented in [42]. The multiplicity is generated according to a negative
binomial distribution with parameters taken from [42] based on the number of
participant nucleons and binary collisions. The elliptic flow is assumed to be
proportional to the eccentricity of the participant nucleons and approximately
reproduces the measured $p_{\rm{T}}$-integrated $v_{2}$ values [52]. The
magnetic field is evaluated at the geometrical center of the overlap region
from the number of spectator nucleons following Eq. (A.6) from [11] with the
proper time $\tau=0.1$ fm/$c$. The magnetic field is calculated in 1%
centrality classes and averaged into the centrality intervals used for data
analysis. It is assumed that the CME signal is proportional to
$\langle|B|^{2}\cos(2(\Psi_{\rm B}-\Psi_{2}))\rangle$, where $|B|$ and
$\Psi_{\rm B}$ are the magnitude and direction of the magnetic field,
respectively. Figure 4 presents the expected dependence of the CME signal on
$v_{2}$ for various centrality classes. Similar results are found using MC-KLN
CGC [53, 54] and EKRT [55] initial conditions. The MC-KLN CGC simulation was
performed using version 32 of the Monte Carlo $k_{\rm T}$-factorization code
($mckt$) available at [56], while the TRENTO model [57] was employed for EKRT
initial conditions.

Figure 5: (Colour online) Centrality dependence of the $p_{1}$ parameter from
a linear fit to the difference between opposite and same charge pair
correlations for $\gamma_{\alpha\beta}$ and from linear fits to the CME signal
expectations from MC-Glauber [51], MC-KLN CGC [53, 54] and EKRT [55] models
(see text for details). Points from MC simulations are slightly shifted along
the horizontal axis for better visibility. Only statistical uncertainties are
shown.

To disentangle the potential CME signal from background, the dependence on
$v_{2}$ of the difference between opposite and same charge pair correlations
for $\gamma_{\alpha\beta}$ and the CME signal expectations are fitted with a
linear function (see lines in Figs. 3 (top panel) and 4, respectively):

$\displaystyle F_{1}(v_{2})=p_{0}(1+p_{1}(v_{2}-\langle v_{2}\rangle)/\langle
v_{2}\rangle),$ (6)

where $p_{0}$ accounts for the overall scale, which cannot be fixed in the MC
calculations, and $p_{1}$ reflects the slope normalised such that in a pure
background scenario, where the correlator is directly proportional to $v_{2}$,
it is equal to unity. The presence of a significant CME contribution, on the
other hand, would result in non-zero intercepts at $v_{2}=0$ of the linear
functions shown in Fig. 3. The ranges used in these fits are based on the
$v_{2}$ variation observed in data and the corresponding MC interval within
each centrality range. The centrality dependence of $p_{1}$ from fits to data
and to the signal expectations based on MC-Glauber, MC-KLN CGC and EKRT models
is reported in Fig. 5. The observed $p_{1}$ from data is a superposition of a
possible CME signal and background. Assuming a pure background case, $p_{1}$
from data and MC models can be related according to

$\displaystyle f_{\rm CME}\times p_{1,\rm{MC}}+(1-f_{\rm CME})\times
1=p_{1,\rm{data}},$ (7)

where $f_{\rm CME}$ denotes the CME fraction to the charge dependence of
$\gamma_{\alpha\beta}$ and is given by

$\displaystyle f_{\rm CME}=\frac{(\gamma_{\rm opp}-\gamma_{\rm same})^{\rm
CME}}{(\gamma_{\rm opp}-\gamma_{\rm same})^{\rm CME}+(\gamma_{\rm
opp}-\gamma_{\rm same})^{\rm Bkg}}.$ (8)

Figure 6 presents $f_{\rm CME}$ for the three models used in this study. The
CME fraction cannot be precisely extracted for central (0–10%) and peripheral
(50–60%) collisions due to the large statistical uncertainties on $p_{1}$
extracted from data. The negative values for the CME fraction obtained for the
40–50% centrality range (deviating from zero by one $\sigma$), if confirmed,
would indicate that our expectations for the background contribution to be
linearly proportional to $v_{2}$ are not accurate. Combining the points from
10–50% neglecting a possible centrality dependence gives $f_{\rm CME}=0.10\pm
0.13$, $f_{\rm CME}=0.08\pm 0.10$ and $f_{\rm CME}=0.08\pm 0.11$ for the MC-
Glauber, MC-KLN CGC and EKRT models, respectively. These results are
consistent with zero CME fraction and correspond to upper limits on $f_{\rm
CME}$ of 33%, 26% and 29%, respectively, at 95% confidence level for the
10–50% centrality interval. The CME fraction agrees with the observations in
[36] where the centrality intervals overlap.

Figure 6: (Colour online) Centrality dependence of the CME fraction extracted
from the slope parameter of fits to data and MC-Glauber [51], MC-KLN CGC [53,
54] and EKRT [55] models, respectively (see text for details). The dashed
lines indicate the physical parameter space of the CME fraction. Points are
slightly shifted along the horizontal axis for better visibility. Only
statistical uncertainties are shown.

In summary, the Event Shape Engineering technique has been applied to measure
the dependence on $v_{2}$ of the charge-dependent two- and three-particle
correlators $\delta_{\alpha\beta}$ and $\gamma_{\alpha\beta}$ in Pb–Pb
collisions at $\mbox{$\sqrt{s_{{}_{\rm NN}}}$}=2.76$ TeV. While for
$\delta_{\alpha\beta}$ we observe no significant $v_{2}$ dependence in a given
centrality bin, $\gamma_{\alpha\beta}$ is found to be almost linearly
dependent on $v_{2}$. When the charge dependence of $\gamma_{\alpha\beta}$ is
multiplied by the corresponding charged-particle density, to compensate for
the dilution effect, a linear dependence on $v_{2}$ is observed consistently
across all centrality classes. Using a Monte Carlo simulation with different
initial-state models, we have found that the CME signal is expected to exhibit
a weak dependence on $v_{2}$ in the measured range. The observations imply
that the dominant contribution to $\gamma_{\alpha\beta}$ is due to non-CME
effects. In order to get a quantitative estimate of the signal and background
contributions to the measurements, we fit both $\gamma_{\alpha\beta}$ and the
expected signal dependence on $v_{2}$ with a first order polynomial. This
procedure allows to estimate the fraction of the CME signal in the centrality
range 10–50%, but not for the most central (0–10%) and peripheral (50–60%)
collisions due to large statistical uncertainties. Averaging over the
centrality range 10–50% gives an upper limit of 26% to 33% (depending on the
initial-state model) at 95% confidence level for the CME contribution to the
difference between opposite and same charge pair correlations for
$\gamma_{\alpha\beta}$.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science, Education and Sport and Croatian Science Foundation,
Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech
Republic; The Danish Council for Independent Research — Natural Sciences, the
Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark;
Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie
Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des
Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS),
France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie
(BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany;
General Secretariat for Research and Technology, Ministry of Education,
Research and Religions, Greece; National Research, Development and Innovation
Office, Hungary; Department of Atomic Energy Government of India (DAE) and
Council of Scientific and Industrial Research (CSIR), New Delhi, India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y
Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología
(FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA),
Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO),
Netherlands; The Research Council of Norway, Norway; Commission on Science and
Technology for Sustainable Development in the South (COMSATS), Pakistan;
Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher
Education and National Science Centre, Poland; Korea Institute of Science and
Technology Information and National Research Foundation of Korea (NRF),
Republic of Korea; Ministry of Education and Scientific Research, Institute of
Atomic Physics and Romanian National Agency for Science, Technology and
Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of
Education and Science of the Russian Federation and National Research Centre
Kurchatov Institute, Russia; Ministry of Education, Science, Research and
Sport of the Slovak Republic, Slovakia; National Research Foundation of South
Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear
(CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain;
Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW),
Sweden; European Organization for Nuclear Research, Switzerland; National
Science and Technology Development Agency (NSDTA), Suranaree University of
Technology (SUT) and Office of the Higher Education Commission under NRU
project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey;
National Academy of Sciences of Ukraine, Ukraine; Science and Technology
Facilities Council (STFC), United Kingdom; National Science Foundation of the
United States of America (NSF) and United States Department of Energy, Office
of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg139&J. Adamorg98&D. Adamováorg95&J. Adolfssonorg34&M.M.
Aggarwalorg100&G. Aglieri Rinellaorg35&M. Agnelloorg31&N. Agrawalorg48&Z.
Ahammedorg139&N. Ahmadorg17&S.U. Ahnorg80&S. Aiolaorg143&A. Akindinovorg65&M.
Al-Turanyorg108&S.N. Alamorg139&D.S.D. Albuquerqueorg124&D.
Aleksandrovorg91&B. Alessandroorg59&R. Alfaro Molinaorg75&A.
Aliciorg27,org54,org12&A. Alkinorg3&J. Almeorg22&T. Altorg71&L.
Altenkamperorg22&I. Altsybeevorg138&C. Alves Garcia Pradoorg123&C.
Andreiorg88&D. Andreouorg35&H.A. Andrewsorg112&A. Andronicorg108&V.
Anguelovorg105&C. Ansonorg98&T. Antičićorg109&F. Antinoriorg57&P.
Antonioliorg54&R. Anwarorg126&L. Aphecetcheorg116&H. Appelshäuserorg71&S.
Arcelliorg27&R. Arnaldiorg59&O.W. Arnoldorg106,org36&I.C. Arseneorg21&M.
Arslandokorg105&B. Audurierorg116&A. Augustinusorg35&R. Averbeckorg108&M.D.
Azmiorg17&A. Badalàorg56&Y.W. Baekorg61,org79&S. Bagnascoorg59&R.
Bailhacheorg71&R. Balaorg102&A. Baldisseriorg76&M. Ballorg45&R.C.
Baralorg68,org89&A.M. Barbanoorg26&R. Barberaorg28&F. Barileorg53,org33&L.
Barioglioorg26&G.G. Barnaföldiorg142&L.S. Barnbyorg94&V. Barretorg133&P.
Bartaliniorg7&K. Barthorg35&E. Bartschorg71&M. Basileorg27&N. Bastidorg133&S.
Basuorg141&G. Batigneorg116&B. Batyunyaorg78&P.C. Batzingorg21&J.L. Bazo
Albaorg113&I.G. Beardenorg92&H. Beckorg105&C. Beddaorg64&N.K. Beheraorg61&I.
Belikovorg135&F. Belliniorg27,org35&H. Bello Martinezorg2&R.
Bellwiedorg126&L.G.E. Beltranorg122&V. Belyaevorg84&G. Bencediorg142&S.
Beoleorg26&A. Bercuciorg88&Y. Berdnikovorg97&D. Berenyiorg142&R.A.
Bertensorg129&D. Berzanoorg35&L. Betevorg35&A. Bhasinorg102&I.R.
Bhatorg102&A.K. Bhatiorg100&B. Bhattacharjeeorg44&J. Bhomorg120&A.
Bianchiorg26&L. Bianchiorg126&N. Bianchiorg51&C. Bianchinorg141&J.
Bielčíkorg39&J. Bielčíkováorg95&A. Bilandzicorg36,org106&G. Biroorg142&R.
Biswasorg4&S. Biswasorg4&J.T. Blairorg121&D. Blauorg91&C. Blumeorg71&G.
Bocaorg136&F. Bockorg83,org35,org105&A. Bogdanovorg84&L. Boldizsárorg142&M.
Bombaraorg40&G. Bonomiorg137&M. Bonoraorg35&J. Bookorg71&H. Borelorg76&A.
Borissovorg105,org19&M. Borriorg128&E. Bottaorg26&C. Bourjauorg92&L.
Bratrudorg71&P. Braun-Munzingerorg108&M. Bregantorg123&T.A. Brokerorg71&M.
Brozorg39&E.J. Bruckenorg46&E. Brunaorg59&G.E. Brunoorg35,org33&D.
Budnikovorg110&H. Bueschingorg71&S. Bufalinoorg31&P. Buhlerorg115&P.
Buncicorg35&O. Buschorg132&Z. Butheleziorg77&J.B. Buttorg15&J.T.
Buxtonorg18&J. Cabalaorg118&D. Caffarriorg35,org93&H. Cainesorg143&A.
Calivaorg64,org108&E. Calvo Villarorg113&P. Cameriniorg25&A.A. Caponorg115&F.
Carenaorg35&W. Carenaorg35&F. Carnesecchiorg27,org12&J. Castillo
Castellanosorg76&A.J. Castroorg129&E.A.R. Casulaorg55&C. Ceballos
Sanchezorg9&P. Cerelloorg59&S. Chandraorg139&B. Changorg127&S.
Chapelandorg35&M. Chartierorg128&S. Chattopadhyayorg139&S.
Chattopadhyayorg111&A. Chauvinorg36,org106&C. Cheshkovorg134&B.
Cheynisorg134&V. Chibante Barrosoorg35&D.D. Chinellatoorg124&S. Choorg61&P.
Chochulaorg35&M. Chojnackiorg92&S. Choudhuryorg139&T. Chowdhuryorg133&P.
Christakoglouorg93&C.H. Christensenorg92&P. Christiansenorg34&T.
Chujoorg132&S.U. Chungorg19&C. Cicaloorg55&L. Cifarelliorg12,org27&F.
Cindoloorg54&J. Cleymansorg101&F. Colamariaorg33&D.
Colellaorg35,org66,org53&A. Colluorg83&M. Colocciorg27&M. Concasorg59orgI&G.
Conesa Balbastreorg82&Z. Conesa del Valleorg62&M.E. Connorsorg143orgII&J.G.
Contrerasorg39&T.M. Cormierorg96&Y. Corrales Moralesorg59&I. Cortés
Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg125&F. Costaorg35&S.
Costanzaorg136&J. Crkovskáorg62&P. Crochetorg133&E. Cuautleorg73&L.
Cunqueiroorg72&T. Dahmsorg36,org106&A. Daineseorg57&M.C. Danischorg105&A.
Danuorg69&D. Dasorg111&I. Dasorg111&S. Dasorg4&A. Dashorg89&S. Dashorg48&S.
Deorg49,org123&A. De Caroorg30&G. de Cataldoorg53&C. de Contiorg123&J. de
Cuvelandorg42&A. De Falcoorg24&D. De Gruttolaorg30,org12&N. De Marcoorg59&S.
De Pasqualeorg30&R.D. De Souzaorg124&H.F. Degenhardtorg123&A.
Deistingorg108,org105&A. Delofforg87&C. Deplanoorg93&P. Dhankherorg48&D. Di
Bariorg33&A. Di Mauroorg35&P. Di Nezzaorg51&B. Di Ruzzaorg57&M.A. Diaz
Corcheroorg10&T. Dietelorg101&P. Dillensegerorg71&R. Diviàorg35&Ø.
Djuvslandorg22&A. Dobrinorg35&D. Domenicis Gimenezorg123&B. Dönigusorg71&O.
Dordicorg21&L.V.R. Doremalenorg64&A.K. Dubeyorg139&A. Dublaorg108&L.
Ducrouxorg134&A.K. Duggalorg100&M. Dukhishyamorg89&P. Dupieuxorg133&R.J.
Ehlersorg143&D. Eliaorg53&E. Endressorg113&H. Engelorg70&E. Eppleorg143&B.
Erazmusorg116&F. Erhardtorg99&B. Espagnonorg62&S. Esumiorg132&G.
Eulisseorg35&J. Eumorg19&D. Evansorg112&S. Evdokimovorg114&L.
Fabbiettiorg106,org36&J. Faivreorg82&A. Fantoniorg51&M. Faselorg96,org83&L.
Feldkamporg72&A. Felicielloorg59&G. Feofilovorg138&A. Fernández
Téllezorg2&E.G. Ferreiroorg16&A. Ferrettiorg26&A. Festantiorg29,org35&V.J.G.
Feuillardorg76,org133&J. Figielorg120&M.A.S. Figueredoorg123&S.
Filchaginorg110&D. Finogeevorg63&F.M. Fiondaorg22,org24&M. Florisorg35&S.
Foertschorg77&P. Fokaorg108&S. Fokinorg91&E. Fragiacomoorg60&A.
Francesconorg35&A. Franciscoorg116&U. Frankenfeldorg108&G.G. Fronzeorg26&U.
Fuchsorg35&C. Furgetorg82&A. Fursorg63&M. Fusco Girardorg30&J.J.
Gaardhøjeorg92&M. Gagliardiorg26&A.M. Gagoorg113&K. Gajdosovaorg92&M.
Gallioorg26&C.D. Galvanorg122&P. Ganotiorg86&C. Garabatosorg108&E. Garcia-
Solisorg13&K. Gargorg28&C. Gargiuloorg35&P. Gasikorg106,org36&E.F.
Gaugerorg121&M.B. Gay Ducatiorg74&M. Germainorg116&J. Ghoshorg111&P.
Ghoshorg139&S.K. Ghoshorg4&P. Gianottiorg51&P. Giubellinoorg35,org108,org59&P.
Giubilatoorg29&E. Gladysz-Dziadusorg120&P. Glässelorg105&D.M. Goméz
Coralorg75&A. Gomez Ramirezorg70&A.S. Gonzalezorg35&V. Gonzalezorg10&P.
González-Zamoraorg10,org2&S. Gorbunovorg42&L. Görlichorg120&S.
Gotovacorg119&V. Grabskiorg75&L.K. Graczykowskiorg140&K.L. Grahamorg112&L.
Greinerorg83&A. Grelliorg64&C. Grigorasorg35&V. Grigorievorg84&A.
Grigoryanorg1&S. Grigoryanorg78&J.M. Gronefeldorg108&F. Grosaorg31&J.F.
Grosse-Oetringhausorg35&R. Grossoorg108&L. Gruberorg115&F. Guberorg63&R.
Guernaneorg82&B. Guerzoniorg27&K. Gulbrandsenorg92&T. Gunjiorg131&A.
Guptaorg102&R. Guptaorg102&I.B. Guzmanorg2&R. Haakeorg35&C. Hadjidakisorg62&H.
Hamagakiorg85&G. Hamarorg142&J.C. Hamonorg135&M.R. Haqueorg64&J.W.
Harrisorg143&A. Hartonorg13&H. Hassanorg82&D. Hatzifotiadouorg12,org54&S.
Hayashiorg131&S.T. Heckelorg71&E. Hellbärorg71&H. Helstruporg37&A.
Herghelegiuorg88&E.G. Hernandezorg2&G. Herrera Corralorg11&F.
Herrmannorg72&B.A. Hessorg104&K.F. Hetlandorg37&H. Hillemannsorg35&C.
Hillsorg128&B. Hippolyteorg135&J. Hladkyorg67&B. Hohlwegerorg106&D.
Horakorg39&S. Hornungorg108&R. Hosokawaorg82,org132&P. Hristovorg35&C.
Hughesorg129&T.J. Humanicorg18&N. Hussainorg44&T. Hussainorg17&D.
Hutterorg42&D.S. Hwangorg20&S.A. Iga Buitronorg73&R. Ilkaevorg110&M.
Inabaorg132&M. Ippolitovorg84,org91&M. Irfanorg17&M.S. Islamorg111&M.
Ivanovorg108&V. Ivanovorg97&V. Izucheevorg114&B. Jacakorg83&N.
Jacazioorg27&P.M. Jacobsorg83&M.B. Jadhavorg48&J. Jadlovskyorg118&S.
Jaelaniorg64&C. Jahnkeorg36&M.J. Jakubowskaorg140&M.A. Janikorg140&P.H.S.Y.
Jayarathnaorg126&C. Jenaorg89&S. Jenaorg126&M. Jercicorg99&R.T. Jimenez
Bustamanteorg108&P.G. Jonesorg112&A. Juskoorg112&P. Kalinakorg66&A.
Kalweitorg35&J.H. Kangorg144&V. Kaplinorg84&S. Karorg139&A. Karasu
Uysalorg81&O. Karavichevorg63&T. Karavichevaorg63&L. Karayanorg108,org105&P.
Karczmarczykorg35&E. Karpechevorg63&U. Kebschullorg70&R. Keidelorg145&D.L.D.
Keijdenerorg64&M. Keilorg35&B. Ketzerorg45&Z. Khabanovaorg93&P.
Khanorg111&S.A. Khanorg139&A. Khanzadeevorg97&Y. Kharlovorg114&A.
Khatunorg17&A. Khuntiaorg49&M.M. Kielbowiczorg120&B. Kilengorg37&B.
Kimorg132&D. Kimorg144&D.J. Kimorg127&H. Kimorg144&J.S. Kimorg43&J.
Kimorg105&M. Kimorg61&M. Kimorg144&S. Kimorg20&T. Kimorg144&S. Kirschorg42&I.
Kiselorg42&S. Kiselevorg65&A. Kisielorg140&G. Kissorg142&J.L. Klayorg6&C.
Kleinorg71&J. Kleinorg35&C. Klein-Bösingorg72&S. Klewinorg105&A.
Klugeorg35&M.L. Knichelorg35,org105&A.G. Knospeorg126&C. Kobdajorg117&M.
Kofaragoorg142&M.K. Köhlerorg105&T. Kolleggerorg108&V. Kondratievorg138&N.
Kondratyevaorg84&E. Kondratyukorg114&A. Konevskikhorg63&M.
Konyushikhinorg141&M. Kopcikorg118&M. Kourorg102&C. Kouzinopoulosorg35&O.
Kovalenkoorg87&V. Kovalenkoorg138&M. Kowalskiorg120&G. Koyithatta
Meethaleveeduorg48&I. Králikorg66&A. Kravčákováorg40&L. Kreisorg108&M.
Krivdaorg66,org112&F. Krizekorg95&E. Kryshenorg97&M. Krzewickiorg42&A.M.
Kuberaorg18&V. Kučeraorg95&C. Kuhnorg135&P.G. Kuijerorg93&A. Kumarorg102&J.
Kumarorg48&L. Kumarorg100&S. Kumarorg48&S. Kunduorg89&P. Kurashviliorg87&A.
Kurepinorg63&A.B. Kurepinorg63&A. Kuryakinorg110&S. Kushpilorg95&M.J.
Kweonorg61&Y. Kwonorg144&S.L. La Pointeorg42&P. La Roccaorg28&C. Lagana
Fernandesorg123&Y.S. Laiorg83&I. Lakomovorg35&R. Langoyorg41&K.
Lapidusorg143&C. Laraorg70&A. Lardeuxorg76,org21&A. Lattucaorg26&E.
Laudiorg35&R. Lavickaorg39&R. Leaorg25&L. Leardiniorg105&S. Leeorg144&F.
Lehasorg93&S. Lehnerorg115&J. Lehrbachorg42&R.C. Lemmonorg94&V. Lentiorg53&E.
Leograndeorg64&I. León Monzónorg122&P. Lévaiorg142&X. Liorg14&J. Lienorg41&R.
Lietavaorg112&B. Limorg19&S. Lindalorg21&V. Lindenstruthorg42&S.W.
Lindsayorg128&C. Lippmannorg108&M.A. Lisaorg18&V. Litichevskyiorg46&W.J.
Llopeorg141&D.F. Lodatoorg64&P.I. Loenneorg22&V. Loginovorg84&C.
Loizidesorg83&P. Loncarorg119&X. Lopezorg133&E. López Torresorg9&A.
Loweorg142&P. Luettigorg71&J.R. Luhderorg72&M. Lunardonorg29&G.
Luparelloorg60,org25&M. Lupiorg35&T.H. Lutzorg143&A. Maevskayaorg63&M.
Magerorg35&S. Mahajanorg102&S.M. Mahmoodorg21&A. Maireorg135&R.D.
Majkaorg143&M. Malaevorg97&L. Malininaorg78orgIII&D. Mal’Kevichorg65&P.
Malzacherorg108&A. Mamonovorg110&V. Mankoorg91&F. Mansoorg133&V.
Manzariorg53&Y. Maoorg7&M. Marchisoneorg77,org130&J. Marešorg67&G.V.
Margagliottiorg25&A. Margottiorg54&J. Marguttiorg64&A. Marínorg108&C.
Markertorg121&M. Marquardorg71&N.A. Martinorg108&P. Martinengoorg35&J.A.L.
Martinezorg70&M.I. Martínezorg2&G. Martínez Garcíaorg116&M. Martinez
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Massonorg116&A. Mastroserioorg53&A.M. Mathisorg106,org36&P.F.T.
Matuokaorg123&A. Matyjaorg129&C. Mayerorg120&J. Mazerorg129&M.
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Mhlangaorg101&Y. Miakeorg132&M.M. Mieskolainenorg46&D.L. Mihaylovorg106&K.
Mikhaylovorg65,org78&J. Milosevicorg21&A. Mischkeorg64&A.N. Mishraorg49&D.
Miśkowiecorg108&J. Mitraorg139&C.M. Mituorg69&N. Mohammadiorg64&B.
Mohantyorg89&M. Mohisin Khanorg17orgIV&E. Montesorg10&D.A. Moreira De
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Morschorg35&V. Mucciforaorg51&E. Mudnicorg119&D. Mühlheimorg72&S.
Muhuriorg139&M. Mukherjeeorg4&J.D. Mulliganorg143&M.G. Munhozorg123&K.
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Musinskyorg66&C.J. Myersorg126&J.W. Myrchaorg140&D. Nagorg4&B. Naikorg48&R.
Nairorg87&B.K. Nandiorg48&R. Naniaorg54,org12&E. Nappiorg53&A.
Narayanorg48&M.U. Naruorg15&H. Natal da Luzorg123&C. Nattrassorg129&S.R.
Navarroorg2&K. Nayakorg89&R. Nayakorg48&T.K. Nayakorg139&S. Nazarenkoorg110&A.
Nedosekinorg65&R.A. Negrao De Oliveiraorg35&L. Nellenorg73&S.V. Nesboorg37&F.
Ngorg126&M. Nicassioorg108&M. Niculescuorg69&J. Niedzielaorg140,org35&B.S.
Nielsenorg92&S. Nikolaevorg91&S. Nikulinorg91&V. Nikulinorg97&F.
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Normanorg128&A. Nyaninorg91&J. Nystrandorg22&H. Oeschlerorg19,org105org*&S.
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Velasquezorg73&A. Oskarssonorg34&J. Otwinowskiorg120&K. Oyamaorg85&Y.
Pachmayerorg105&V. Pacikorg92&D. Paganoorg137&P. Paganoorg30&G. Paićorg73&P.
Palniorg7&J. Panorg141&A.K. Pandeyorg48&S. Panebiancoorg76&V.
Papikyanorg1&G.S. Pappalardoorg56&P. Pareekorg49&J. Parkorg61&S.
Parmarorg100&A. Passfeldorg72&S.P. Pathakorg126&R.N. Patraorg139&B.
Paulorg59&H. Peiorg7&T. Peitzmannorg64&X. Pengorg7&L.G. Pereiraorg74&H.
Pereira Da Costaorg76&D. Peresunkoorg91,org84&E. Perez Lezamaorg71&V.
Peskovorg71&Y. Pestovorg5&V. Petráčekorg39&V. Petrovorg114&M.
Petroviciorg88&C. Pettaorg28&R.P. Pezziorg74&S. Pianoorg60&M. Piknaorg38&P.
Pillotorg116&L.O.D.L. Pimentelorg92&O. Pinazzaorg54,org35&L. Pinskyorg126&D.B.
Piyarathnaorg126&M. Płoskońorg83&M. Planinicorg99&F. Pliquettorg71&J.
Plutaorg140&S. Pochybovaorg142&P.L.M. Podesta-Lermaorg122&M.G.
Poghosyanorg96&B. Polichtchoukorg114&N. Poljakorg99&W. Poonsawatorg117&A.
Poporg88&H. Poppenborgorg72&S. Porteboeuf-Houssaisorg133&V.
Pozdniakovorg78&S.K. Prasadorg4&R. Preghenellaorg54&F. Prinoorg59&C.A.
Pruneauorg141&I. Pshenichnovorg63&M. Puccioorg26&G. Pudduorg24&P.
Pujahariorg141&V. Puninorg110&J. Putschkeorg141&S. Rahaorg4&S. Rajputorg102&J.
Rakorg127&A. Rakotozafindrabeorg76&L. Ramelloorg32&F. Ramiorg135&D.B.
Ranaorg126&R. Raniwalaorg103&S. Raniwalaorg103&S.S. Räsänenorg46&B.T.
Rascanuorg71&D. Ratheeorg100&V. Ratzaorg45&I. Ravasengaorg31&K.F.
Readorg129,org96&K. Redlichorg87orgV&A. Rehmanorg22&P. Reicheltorg71&F.
Reidtorg35&X. Renorg7&R. Renfordtorg71&A.R. Reolonorg51&A. Reshetinorg63&K.
Reygersorg105&V. Riabovorg97&R.A. Ricciorg52&T. Richertorg34&M.
Richterorg21&P. Riedlerorg35&W. Rieglerorg35&F. Riggiorg28&C. Risteaorg69&M.
Rodríguez Cahuantziorg2&K. Røedorg21&E. Rogochayaorg78&D. Rohrorg35,org42&D.
Röhrichorg22&P.S. Rokitaorg140&F. Ronchettiorg51&E.D. Rosasorg73&P.
Rosnetorg133&A. Rossiorg29,org57&A. Rotondiorg136&F. Roukoutakisorg86&A.
Royorg49&C. Royorg135&P. Royorg111&A.J. Rubio Monteroorg10&O.V. Ruedaorg73&R.
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Sadovskyorg114&K. Šafaříkorg35&S.K. Sahaorg139&B. Sahlmullerorg71&B.
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Sainiorg139&S. Sakaiorg132&M.A. Salehorg141&J. Salzwedelorg18&S.
Sambyalorg102&V. Samsonovorg97,org84&A. Sandovalorg75&D. Sarkarorg139&N.
Sarkarorg139&P. Sarmaorg44&M.H.P. Sasorg64&E. Scapparoneorg54&F.
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Schiauaorg88&R. Schickerorg105&C. Schmidtorg108&H.R. Schmidtorg104&M.O.
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Schutzorg135,org35&K. Schwarzorg108&K. Schwedaorg108&G. Scioliorg27&E.
Scomparinorg59&M. Šefčíkorg40&J.E. Segerorg98&Y. Sekiguchiorg131&D.
Sekihataorg47&I. Selyuzhenkovorg108,org84&K. Senosiorg77&S.
Senyukovorg3,org35,org135&E. Serradillaorg75,org10&P. Settorg48&A.
Sevcencoorg69&A. Shabanovorg63&A. Shabetaiorg116&R. Shahoyanorg35&W.
Shaikhorg111&A. Shangaraevorg114&A. Sharmaorg100&A. Sharmaorg102&M.
Sharmaorg102&M. Sharmaorg102&N. Sharmaorg129,org100&A.I. Sheikhorg139&K.
Shigakiorg47&Q. Shouorg7&K. Shtejerorg26,org9&Y. Sibiriakorg91&S.
Siddhantaorg55&K.M. Sielewiczorg35&T. Siemiarczukorg87&S. Silaevaorg91&D.
Silvermyrorg34&C. Silvestreorg82&G. Simatovicorg99&G. Simonettiorg35&R.
Singarajuorg139&R. Singhorg89&V. Singhalorg139&T. Sinhaorg111&B. Sitarorg38&M.
Sittaorg32&T.B. Skaaliorg21&M. Slupeckiorg127&N. Smirnovorg143&R.J.M.
Snellingsorg64&T.W. Snellmanorg127&J. Songorg19&M. Songorg144&F.
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Sputowskaorg120&B.K. Srivastavaorg107&J. Stachelorg105&I. Stanorg69&P.
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Strmenorg38&A.A.P. Suaideorg123&T. Sugitateorg47&C. Suireorg62&M.
Suleymanovorg15&M. Suljicorg25&R. Sultanovorg65&M. Šumberaorg95&S.
Sumowidagdoorg50&K. Suzukiorg115&S. Swainorg68&A. Szaboorg38&I. Szarkaorg38&U.
Tabassamorg15&J. Takahashiorg124&G.J. Tambaveorg22&N. Tanakaorg132&M.
Tarhiniorg62&M. Tariqorg17&M.G. Tarzilaorg88&A. Tauroorg35&G. Tejeda
Muñozorg2&A. Telescaorg35&K. Terasakiorg131&C. Terrevoliorg29&B.
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Thoresenorg92&R. Tieulentorg134&A. Tikhonovorg63&A.R. Timminsorg126&A.
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Trombettaorg33&L. Tropporg40&V. Trubnikovorg3&W.H. Trzaskaorg127&B.A.
Trzeciakorg64&T. Tsujiorg131&A. Tumkinorg110&R. Turrisiorg57&T.S.
Tveterorg21&K. Ullalandorg22&E.N. Umakaorg126&A. Urasorg134&G.L. Usaiorg24&A.
Utrobicicorg99&M. Valaorg118,org66&J. Van Der Maarelorg64&J.W. Van
Hoorneorg35&M. van Leeuwenorg64&T. Vanatorg95&P. Vande Vyvreorg35&D.
Vargaorg142&A. Vargasorg2&M. Vargyasorg127&R. Varmaorg48&M. Vasileiouorg86&A.
Vasilievorg91&A. Vauthierorg82&O. Vázquez Doceorg106,org36&V.
Vecherninorg138&A.M. Veenorg64&A. Velureorg22&E. Vercellinorg26&S. Vergara
Limónorg2&R. Vernetorg8&R. Vértesiorg142&L. Vickovicorg119&S. Vigoloorg64&J.
Viinikainenorg127&Z. Vilakaziorg130&O. Villalobos Baillieorg112&A. Villatoro
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Vislaviciusorg34&A. Vodopyanovorg78&M.A. Völklorg105,org104&K.
Voloshinorg65&S.A. Voloshinorg141&G. Volpeorg33&B. von Hallerorg35&I.
Vorobyevorg106,org36&D. Voscekorg118&D. Vranicorg35,org108&J. Vrlákováorg40&B.
Wagnerorg22&H. Wangorg64&M. Wangorg7&D. Watanabeorg132&Y.
Watanabeorg131,org132&M. Weberorg115&S.G. Weberorg108&D.F. Weiserorg105&S.C.
Wenzelorg35&J.P. Wesselsorg72&U. Westerhofforg72&A.M. Whiteheadorg101&J.
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Windelbandorg105&W.E. Wittorg129&S. Yalcinorg81&K. Yamakawaorg47&P.
Yangorg7&S. Yanoorg47&Z. Yinorg7&H. Yokoyamaorg132,org82&I.-K. Yooorg19&J.H.
Yoonorg61&V. Yurchenkoorg3&V. Zaccoloorg59&A. Zamanorg15&C.
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Zhangorg22,org7&X. Zhangorg7&Y. Zhangorg7&C. Zhangorg64&Z. Zhangorg7,org133&C.
Zhaoorg21&N. Zhigarevaorg65&D. Zhouorg7&Y. Zhouorg92&Z. Zhouorg22&H.
Zhuorg22&J. Zhuorg7&A. Zichichiorg27,org12&A. Zimmermannorg105&M.B.
Zimmermannorg35&G. Zinovjevorg3&J. Zmeskalorg115&S. Zouorg7&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIGeorgia State University, Atlanta, Georgia, United States

orgIIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIVDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org13Chicago State University, Chicago, Illinois, United States

org14China Institute of Atomic Energy, Beijing, China

org15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org16Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Ohio State University, Columbus, Ohio, United
States

org19Department of Physics, Pusan National University, Pusan, Republic of
Korea

org20Department of Physics, Sejong University, Seoul, Republic of Korea

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35European Organization for Nuclear Research (CERN), Geneva, Switzerland

org36Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org37Faculty of Engineering, Bergen University College, Bergen, Norway

org38Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org41Faculty of Technology, Buskerud and Vestfold University College,
Tonsberg, Norway

org42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org43Gangneung-Wonju National University, Gangneung, Republic of Korea

org44Gauhati University, Department of Physics, Guwahati, India

org45Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

org62Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org64Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org65Institute for Theoretical and Experimental Physics, Moscow, Russia

org66Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org67Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org68Institute of Physics, Bhubaneswar, India

org69Institute of Space Science (ISS), Bucharest, Romania

org70Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org71Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org72Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org73Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org74Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org75Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org76IRFU, CEA, Université Paris-Saclay, Saclay, France

org77iThemba LABS, National Research Foundation, Somerset West, South Africa

org78Joint Institute for Nuclear Research (JINR), Dubna, Russia

org79Konkuk University, Seoul, Republic of Korea

org80Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org81KTO Karatay University, Konya, Turkey

org82Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org83Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org84Moscow Engineering Physics Institute, Moscow, Russia

org85Nagasaki Institute of Applied Science, Nagasaki, Japan

org86National and Kapodistrian University of Athens, Physics Department,
Athens, Greece

org87National Centre for Nuclear Studies, Warsaw, Poland

org88National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org89National Institute of Science Education and Research, HBNI, Jatni, India

org90National Nuclear Research Center, Baku, Azerbaijan

org91National Research Centre Kurchatov Institute, Moscow, Russia

org92Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org93Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org94Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org95Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org96Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org97Petersburg Nuclear Physics Institute, Gatchina, Russia

org98Physics Department, Creighton University, Omaha, Nebraska, United States

org99Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org100Physics Department, Panjab University, Chandigarh, India

org101Physics Department, University of Cape Town, Cape Town, South Africa

org102Physics Department, University of Jammu, Jammu, India

org103Physics Department, University of Rajasthan, Jaipur, India

org104Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen,
Germany

org105Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org106Physik Department, Technische Universität München, Munich, Germany

org107Purdue University, West Lafayette, Indiana, United States

org108Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org109Rudjer Bošković Institute, Zagreb, Croatia

org110Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org111Saha Institute of Nuclear Physics, Kolkata, India

org112School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org113Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org114SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org115Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org116SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org117Suranaree University of Technology, Nakhon Ratchasima, Thailand

org118Technical University of Košice, Košice, Slovakia

org119Technical University of Split FESB, Split, Croatia

org120The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org121The University of Texas at Austin, Physics Department, Austin, Texas,
United States

org122Universidad Autónoma de Sinaloa, Culiacán, Mexico

org123Universidade de São Paulo (USP), São Paulo, Brazil

org124Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org125Universidade Federal do ABC, Santo Andre, Brazil

org126University of Houston, Houston, Texas, United States

org127University of Jyväskylä, Jyväskylä, Finland

org128University of Liverpool, Liverpool, United Kingdom

org129University of Tennessee, Knoxville, Tennessee, United States

org130University of the Witwatersrand, Johannesburg, South Africa

org131University of Tokyo, Tokyo, Japan

org132University of Tsukuba, Tsukuba, Japan

org133Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org136Università degli Studi di Pavia, Pavia, Italy

org137Università di Brescia, Brescia, Italy

org138V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org139Variable Energy Cyclotron Centre, Kolkata, India

org140Warsaw University of Technology, Warsaw, Poland

org141Wayne State University, Detroit, Michigan, United States

org142Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org143Yale University, New Haven, Connecticut, United States

org144Yonsei University, Seoul, Republic of Korea

org145Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany