Probing the chiral magnetic wave in pPb and PbPb collisions at
√
s
NN= 5.02 TeV
using charge-dependent azimuthal anisotropies
A. M. Sirunyan et al.∗ (CMS Collaboration)
(Received 29 August 2017; revised manuscript received 12 October 2018; published 18 December 2019) Charge-dependent anisotropy Fourier coefficients (vn) of particle azimuthal distributions are measured in pPb and PbPb collisions at √sNN= 5.02 TeV with the CMS detector at the LHC. The normalized difference in the second-order anisotropy coefficients (v2) between positively and negatively charged particles is found to depend
linearly on the observed event charge asymmetry with comparable slopes for both pPb and PbPb collisions over a wide range of charged particle multiplicity. In PbPb, the third-order anisotropy coefficientv3shows a similar
linear dependence with the same slope as seen forv2. The observed similarities between thev2slopes for pPb and
PbPb, as well as the similar slopes forv2andv3in PbPb, are compatible with expectations based on local charge
conservation in the decay of clusters or resonances, and constitute a challenge to the hypothesis that, at LHC ener-gies, the observed charge asymmetry dependence ofv2in heavy ion collisions arises from a chiral magnetic wave.
DOI:10.1103/PhysRevC.100.064908
I. INTRODUCTION
Observing macroscopic phenomena arising from quantum anomalies is a subject of interest for a wide range of physics communities, from magnetized relativistic matter in three-dimensional Dirac and Weyl materials [1–3] to hot plasma in the early universe or formed in relativistic heavy ion collisions [4–6]. In quantum chromodynamics, gluon fields within a localized region of space-time can form nontrivial topologi-cal configurations [7–10]. If approximate chiral symmetry is restored, the interactions of chiral quarks with these gluon fields can produce a chirality imbalance, violating the local P and CP symmetries [9,10]. This anomalous chiral effect can manifest itself as an electric current along or opposite to a strong magnetic field [11–13]. The electric charge separation produced by these currents is known as the chiral magnetic effect (CME) [11]. The chiral separation effect (CSE) is a similar process, where the separation of the chiral charges along the magnetic field will be induced by a finite density of the net electric charges [14]. The coupling of electric and chiral charge densities and currents leads to a long-wavelength collective excitation, known as the chiral magnetic wave (CMW) [14–17].
In relativistic heavy ion (AA) collisions, a strong magnetic field and the restoration of the approximate chiral symme-try, both necessary conditions for creating a CMW, may be present. The magnetic field is produced by the spectator protons and is, on average, perpendicular to the reaction plane
∗Full author list given at the end of the article.
Published by the American Physical Society under the terms of the
Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
defined by the impact parameter and beam directions. The propagation of the CMW leads to an electric quadrupole moment, where additional positive (negative) charges are accumulated away from (close to) the reaction plane [14]. Following a hydrodynamic evolution of the medium formed in AA collisions, this electric quadruple moment is expected to result in a charge-dependent variation of the second-order anisotropy coefficient (v2) in the Fourier expansion of the final-state particle azimuthal distribution. More specif-ically, the v2 coefficient will exhibit a linear dependence on the observed event charge asymmetry [14], Ach≡ (N+−
N−)/(N++ N−), where N+ and N− denote the number of positively and negatively charged hadrons in each event,
v2,±= vbase2,± ∓ rAch. (1) Here vbase
2,± represents the value in the absence of a charge
quadrupole moment from the CMW for positively (+) and
negatively (−) charged particles, and r denotes the slope
parameter. In the presence of a CMW, the difference of v2
values between positively and negatively charged particles will be proportional to Ach. Similar charge-dependent effects from the CMW are not expected for the third-order anisotropy coefficient (v3) [13].
Recent observations of the Ach dependence of v2,± in
AA collisions at RHIC at BNL and the CERN LHC are
qualitatively consistent with expectations of the CMW mech-anism [5,18,19]. However, the interpretation of the results remains inconclusive since alternative mechanisms have been proposed to generate charge-dependentv2coefficients without a CMW [20,21]. For example, it has been shown that local charge conservation (LCC) in the decay of clusters or reso-nances can qualitatively describe the charge-dependentv2data [20]. Decay particles from a lower transverse momentum (pT) resonance tend to have a larger rapidity separation, resulting in
a daughter more likely to fall outside the detector acceptance, leading to a nonzero Ach. Hence, this process generates a cor-relation between Achand the average pTof charged particles, and therefore also between Ach and the v2 coefficient, since
v2 depends on pT. The LCC mechanism also applies to all
higher-order anisotropy Fourier coefficients (vn).
This paper presents measurements of the Achdependence
of the pT and of the pT-averaged vn coefficients in pPb and PbPb collisions at√sNN= 5.02 TeV, using data collected
with the CMS experiment at the LHC. It has been shown that pp and pPb collisions with high charged-particle multi-plicities can generate large final-state azimuthal anisotropies, comparable to those in AA collisions at similar event mul-tiplicities [22–35]. However, the CMW contribution to any
Ach-dependent v2 signal is expected to be negligible in pPb collisions: the induced magnetic field is smaller than in PbPb collisions (albeit of the same order of magnitude) and, more importantly, its correlation with the harmonic event planes is vanishingly small [6,36]. The recent observation of nearly identical charge-dependent azimuthal correlations in
pPb and PbPb suggested significant contamination of
back-ground sources (e.g., LCC) to any CME induced signal [6,37]. Therefore, a comparison between pPb and PbPb systems and their Ach dependence of the pT and the v3 coefficient can differentiate between the CMW and LCC mechanisms. It is worth noting that a lack of experimental evidence for the CME [6,37] does not necessarily imply the absence of the CMW, as the CME requires an initial chirality imbalance from topological QCD charges (which may be too weak to be observed), whereas the CMW only requires an initial net electric charge density [14,16]. Therefore, the CME and CMW deserve independent experimental investigations.
II. THE CMS DETECTOR
The central feature of the CMS apparatus is a super-conducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume, there are silicon pixel and strip tracker detectors, a lead tungstate crys-tal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter. The silicon tracker measures charged par-ticles within the pseudorapidity range|η| < 2.5. For charged particles with 1< pT< 10 GeV/c and |η| < 1.4, the track resolutions are typically 1.5% in pTand 25−90 (45−150) μm in the transverse (longitudinal) impact parameter [38]. Iron and quartz-fiber Cherenkov hadron forward (HF) calorimeters cover the range 2.9 < |η| < 5.2. A detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [39].
III. EVENT AND TRACK SELECTIONS
The pPb data at√sNN= 5.02 TeV, collected in 2013 using
the CMS detector, correspond to an integrated luminosity of 35 nb−1. A subset of peripheral PbPb data at√sNN = 5.02 TeV
collected in 2015 (30–90% centrality, where centrality is defined as the fraction of the total inelastic cross section, with 0% denoting the most central collisions [40]), is also
ch
Observed A
0.2
−
−
0.1
0
0.1
0.2
0.05
0.1
CMS PbPb 5.02 TeV Cent. 30-40% < 3.0 GeV/c T p ≤ 0.3 | < 2.4 η |FIG. 1. The event-by-event probability distribution observed in the charge asymmetry, Ach, for PbPb collisions at √sNN= 5.02 TeV within the 30–40% centrality range. The particles are selected be-tween 0.3 and 3.0 GeV/c and having pseudorapidity |η| < 2.4.
used. The sample is reconstructed with the same algorithm as the pPb data, in order to compare directly the two sys-tems at similar multiplicities. The event reconstruction, event selection and the trigger, including the dedicated triggers to collect a large sample of high-multiplicity pPb events, are identical to those used in previous CMS particle correlation measurements [6,22,32]. In the offline analysis of pPb (PbPb) collisions, hadronic events are selected by requiring the pres-ence of at least one (three) energy deposit(s) greater than 3 GeV in each of the two HF calorimeters. Events are also required to contain a primary vertex within 15 cm of the nominal interaction point along the beam axis and 0.15 cm in the transverse direction. In the pPb data sample, there is a 3% probability to have at least one additional interaction in the same bunch crossing (pileup). After the procedure used to reject pileup events is applied, the remaining sample has a purity of 99.8% for single collision events [32]. The pileup in PbPb data is negligible.
Primary tracks, i.e., tracks that originate at the primary vertex and satisfy the high-purity criteria of Ref. [38], are used to define the event charged-particle multiplicity (Noffline
trk )
and to perform correlation measurements. In addition, the impact parameter significance of the tracks with respect to the primary vertex in the beam and transverse direction is required to be less than 3. The relative uncertainty in pT must be less than 10%. To ensure high tracking efficiency, only tracks with |η| < 2.4 and pT> 0.3 GeV/c are used for Ach andvn mea-surements in this analysis. The pPb and PbPb data are com-pared in ranges of Noffline
trk , where primary tracks with|η| < 2.4 and pT > 0.4 GeV/c are counted, in order to match the trigger selection criterion implemented at the HLT in pPb collisions.
ch true A 0.05 − 0 0.05 ) + 2 + v 2 − )/(v + 2 - v 2 − (v−0.01 0 0.01 < 220 N ≤ 185 < 3.0 GeV/c 0.3 < p CMS < 220 N ≤ 185 < 3.0 GeV/c 0.3 < p 0.005 ± PbPb 0.108 0.008 ± pPb 0.149 2 norm r ch true A 0.05 − 0 0.05 ) + 〉 T p〈 + - 〉 T p〈 )/( + 〉 T p〈 - - 〉 T p〈( 0.01 − 0 0.01 0.001 ± PbPb 0.058 0.001 ± pPb 0.062 〉 p 〈 norm r < 220 N ≤ 185 < 3.0 GeV/c 0.3 < p CMS ch true A 0.05 − 0 0.05 2 v 0.096 0.098 PbPb 5.02 TeV ch true A 0.05 − 0 0.05 (GeV/c)〉 T p〈 0.76 0.765 0.77 PbPb 5.02 TeV 2 v 0.07 0.072 < 220 N ≤ 185 < 3.0 GeV/c 0.3 < p + h − h CMS pPb 5.02 TeV (GeV/c)〉 T p〈 0.87 0.88 CMS pPb 5.02 TeV h+ − h < 220 N ≤ 185 < 3.0 GeV/c 0.3 < p
FIG. 2. The elliptic anisotropyv2 (top left) and event-averaged
pT (top right) for positively (h+) and negatively (h−) charged
particles, and their normalized differences (bottom row), as functions of Atrue
ch for the multiplicity range 185 Ntrkoffline< 220 of pPb and
PbPb collisions at √sNN= 5.02 TeV. Statistical uncertainties are smaller than the marker size, while systematic uncertainties are not displayed.
IV. ANALYSIS TECHNIQUE
In each multiplicity or centrality class, events are further divided into several ranges of the observed event charge asymmetry Aobs
ch, calculated based on the number of positively and negatively charged particles from primary tracks. An example of the Aobsch distribution for PbPb data in the 30–40% centrality range is shown in Fig.1. Within each Aobsch range, the
vncoefficients are obtained separately for tracks with positive (vn+) and negative (vn−) charge, and with|η| < 2.4 and 0.3 < pT < 3 GeV/c, using the two-particle cumulant method [41] with a pseudorapidity gap of at least one unit between the two particles to suppress the short-range correlations. Because of statistical limitations, the pseudorapidity gap chosen in this analysis is smaller than the value of two units typically used in other CMS correlation measurements, but results are found to be consistent between one and two units of pseudorapidity gap. Residual effects of short-range correlations may still contribute to the sum of thevn,v−n + v+n, but not the difference
since the effect is largely canceled out. However, this effect contributes to the pPb and PbPb systems similarly [32], so it has little impact on the comparison of the two systems.
The main physics observable of interest in this analysis is the slope parameter (rnorm) extracted by fitting a linear func-tion to the normalizedvndifferences, (vn−− vn+)/(vn−+ v+n),
as a function of the true event charge asymmetry value, Atrue ch , obtained by correcting Aobs
ch for the detector acceptance and
ch
Corrected A
0.1 − −0.05 0 0.05 0.1 + n+ v
- nv
+ n- v
- nv
0.02 − 0 0.02 0.002 ± (CMS) = 0.131 norm r 0.013 ± (ALICE) = 0.137 norm r CMS, PbPb 5.02 TeV ALICE, PbPb 2.76 TeV CMS Cent. 30-40% < 5.0 GeV/c T p ≤ 0.2 | < 0.8 η |FIG. 3. The normalized difference in elliptic flow v2 between
positive- and negative-charged particles, (v−2 − v2+)/(v2−+ v+2), as a function of charge asymmetry, is presented. The results are selected in centrality range 30–40% with particles within |η| < 0.8 and 0.2 pT < 5.0 GeV, and are compared between the ALICE [19]
and the CMS experiment in PbPb collisions at √sNN= 2.76 and 5.02 TeV, respectively. The bars represent statistical point-by-point uncertainties.
tracking efficiency. Based on Monte Carlo (MC) simulations, detector effects can be modeled as a Gaussian response of the
Atrue
ch distribution within |η| < 2.4, with a width determined from the simulated Aobs
ch distribution at a given Atruech value. Combining the Aobsch distribution in data with the response function from MC simulations, the predicted correlation be-tween Aobs
ch and Atruech in data is calculated. The slope of a linear fit to this correlation is used to obtain the average Atrue ch trk offline N 0 100 200 300 400 500 〉 p〈 norm , r normr 0.1 0.2 CMS r2norm pPb 5.02 TeV PbPb 5.02 TeV 〉 p 〈 norm r < 3.0 GeV/c T 0.3 < p
FIG. 4. The linear slope parameters rnormforv
2 (filled symbols)
andpT (open symbols) as functions of event multiplicity in pPb
and PbPb collisions at √sNN= 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
TABLE I. The table summarizes the absolute and normalized slope parameters (r) fromv2andpT in ranges of multiplicity class, Ntrkoffline,
in pPb collisions at √sNN= 5.02 TeV. The first uncertainty associated with the central values denotes statistical errors, while the second uncertainty represents the systematic uncertainty.
Noffline trk rv2 r norm v2 rpT r norm pT [120,150) 0.022 ± 0.001 ± 0.002 0.163 ± 0.01 ± 0.011 0.103 ± 0.001 ± 0.007 0.06 ± 0 ± 0.004 [150,185) 0.02 ± 0.001 ± 0.001 0.145 ± 0.008 ± 0.009 0.105 ± 0.001 ± 0.007 0.06 ± 0 ± 0.004 [185,220) 0.02 ± 0.001 ± 0.001 0.143 ± 0.008 ± 0.009 0.108 ± 0.001 ± 0.007 0.062 ± 0.001 ± 0.004 [220,260) 0.022 ± 0.002 ± 0.001 0.153 ± 0.012 ± 0.009 0.111 ± 0.002 ± 0.007 0.063 ± 0.001 ± 0.004
value in each selected Aobsch range in data. The slope, which ranges from 0.6 to 0.8, is fit separately for each multiplicity or centrality selection. This procedure is validated using different MC generators, which give similar correction factors.
The systematic uncertainty related to the Ach correction factors, based on the difference between EPOS LHC[42] and
HYDJET++ [43] event generators, is estimated to be 1–7%
ranging from high- to low-multiplicity events. To evaluate the systematic uncertainty related to thevnmeasurement, the sensitivity of the results to different track selection criteria is studied. Varying the longitudinal and transverse track impact parameter selection criteria from the default three standard deviations to 2 or 5, and the relative pTuncertainty selection criterion from the default 10% to 5%, yields a systematic uncertainty of less than 2%. The longitudinal primary vertex position (zvtx) has been varied, using ranges |zvtx| < 3 cm and 3< |zvtx| < 15 cm, where the difference with respect to the default range |zvtx| < 15 cm is less than 2%. All of the systematic uncertainty sources are uncorrelated and were found to be similar for pPb and PbPb collisions. Therefore, the total systematic uncertainty is taken as the quadratic sum, and the same values are quoted for both pPb and PbPb systems.
V. RESULTS
Figure2(left column) shows the Atrue
ch dependence ofv2 co-efficients, averaged over 0.3 < pT< 3 GeV/c, for positively and negatively charged particles in the multiplicity range 185 Noffline
trk < 220 of pPb and PbPb collisions at √sNN=
5.02 TeV. The normalized v2difference as a function of Atruech is also shown. A trend ofv+2 (v2−) decreasing (increasing) as
Atrue
ch increases is observed for both pPb and PbPb collisions
with an approximately linear dependence. A similar linear
trend of elliptic anisotropy as a function of Ach has been
observed in AuAu [18] and PbPb [19] systems at lower
collision energies, as shown in Fig.3 for 30–40% centrality PbPb events. The linear slope parameter, rnorm2 , is extracted by aχ2 fit to a linear function, which gives values of 0.149 ± 0.008 for pPb and 0.108 ± 0.005 for PbPb, in the multiplicity range 185 Noffline
trk < 220. A significant nonzero value of the linear slope parameter is observed in pPb collisions, even greater than that in PbPb collisions. Since the CMW effect is expected to be negligible in high-multiplicity pPb events, this observation might be caused, at LHC energies, by a mechanism unrelated to the CMW. The differences in the linear slope parameters observed in the pPb and PbPb systems remain to be understood.
ThepT for positively and negatively charged particles are also measured as functions of Atruech , in the multiplicity range 185 Noffline
trk < 220 of pPb and PbPb collisions at √sNN =
5.02 TeV, and shown in Fig.2(right column). The normalized pT difference as a function of Atruech is obtained for the two systems with the slope parameters displayed in the figure. A similar linear Atrue
ch dependence of thepT value to that of v2 is observed. This behavior is qualitatively consistent with the expectation of the LCC effect from resonance decays. Sincevn has a strong dependence on particle pT, a correlation between the pT-averagedvn and Ach, as observed in Fig.2(left), can also be induced by the LCC mechanism.
The extracted normalized slope parameters for v2 and
pT as functions of event multiplicity in pPb and PbPb
collisions are shown in Fig.4. The rnorm values for bothv 2 andpT are found to have a weak dependence on the event multiplicity for both pPb and PbPb collisions, with values for pT approximately half of those for v2. In the overlapping multiplicity range, normalized slope parameters are observed
TABLE II. The table summarizes the absolute and normalized slope parameters (r) fromv2andpT in ranges of multiplicity class, Ntrkoffline,
in PbPb collisions at √sNN= 5.02 TeV. The first uncertainty associated with the central values denotes statistical errors, while the second uncertainty represents the systematic uncertainty.
Noffline trk rv2 r norm v2 rpT r norm pT [90,120) 0.02 ± 0.001 ± 0.001 0.12 ± 0.007 ± 0.009 0.084 ± 0.001 ± 0.006 0.056 ± 0 ± 0.004 [120,150) 0.023 ± 0.001 ± 0.002 0.131 ± 0.006 ± 0.009 0.084 ± 0.001 ± 0.006 0.056 ± 0.001 ± 0.004 [150,185) 0.022 ± 0.001 ± 0.001 0.119 ± 0.005 ± 0.008 0.087 ± 0.001 ± 0.006 0.057 ± 0.001 ± 0.004 [185,220) 0.022 ± 0.001 ± 0.001 0.108 ± 0.005 ± 0.007 0.087 ± 0.001 ± 0.006 0.058 ± 0.001 ± 0.004 [220,260) 0.025 ± 0.001 ± 0.001 0.126 ± 0.004 ± 0.008 0.091 ± 0.001 ± 0.005 0.059 ± 0.001 ± 0.004 [260,300) 0.025 ± 0.001 ± 0.001 0.122 ± 0.004 ± 0.007 0.093 ± 0.001 ± 0.005 0.06 ± 0.001 ± 0.003 [300,400) 0.028 ± 0 ± 0.001 0.133 ± 0.002 ± 0.007 0.094 ± 0.001 ± 0.005 0.061 ± 0 ± 0.003 [400,500) 0.03 ± 0 ± 0.001 0.141 ± 0.002 ± 0.007 0.099 ± 0.001 ± 0.005 0.064 ± 0.001 ± 0.003
TABLE III. The table summarizes the absolute and normalized slope parameters (r) fromv2andv3in ranges of centrality class, in PbPb
collisions at √sNN= 5.02 TeV. The first uncertainty associated with the central values denotes statistical errors, while the second uncertainty represents the systematic uncertainty.
Centrality rv2 rnorm v2 rv3 r norm v3 30–40% 0.032 ± 0 ± 0.001 0.162 ± 0.001 ± 0.006 0.01 ± 0.0006 ± 0.0004 0.149 ± 0.008 ± 0.006 40–50% 0.032 ± 0 ± 0.001 0.151 ± 0.001 ± 0.006 0.0102 ± 0.0007 ± 0.0004 0.15 ± 0.01 ± 0.006 50–60% 0.028 ± 0 ± 0.001 0.135 ± 0.001 ± 0.007 0.0083 ± 0.001 ± 0.0004 0.131 ± 0.016 ± 0.007 60–70% 0.024 ± 0 ± 0.002 0.126 ± 0.002 ± 0.008 0.0054 ± 0.0016 ± 0.0003 0.102 ± 0.03 ± 0.006 70–80% 0.022 ± 0.001 ± 0.002 0.136 ± 0.004 ± 0.011 · · · · 80–90% 0.022 ± 0.002 ± 0.002 0.171 ± 0.012 ± 0.014 · · · ·
to be larger in pPb than PbPb collisions, which is not expected in the CMW context and may indicate a collision system dependence of the LCC or other mechanisms. The measured normalized slope parameters, as well as the absolute slope parameters, for each multiplicity or centrality range of pPb and PbPb collisions, are reported in TablesI–III.
The charge asymmetry dependence of the v3 coefficient
for positively and negatively charged particles is also studied in PbPb collisions at √sNN = 5.02 TeV, as shown in Fig. 5
(top) for the 30–40% centrality class. As found for the v2 values, thev+3 (v3−) values also decrease (increase) as Atruech
increases. No v3 results for pPb collisions are reported
ch true A 0.04 − −0.02 0 0.02 0.04 3
v
0.033 0.034 CMS 40% centrality − PbPb 5.02 TeV, 30 < 3.0 GeV/c T 0.3 < p + h − h ch true A 0.04 − −0.02 0 0.02 0.04)
+ n+ v
− n)/(v
+ n- v
− n(v
0.01 − 0 0.01 0.02 0.001 ± = 0.167 2 norm r 0.009 ± = 0.161 3 norm r 2 v 3 v CMS 40% centrality − PbPb 5.02 TeV, 30 < 3.0 GeV/c T 0.3 < pFIG. 5. Thev3coefficient for positively and negatively charged
particles (top) and the normalized difference invn, (vn−− vn+)/(v−n + v+
n) (bottom), for n= 2 and 3, as functions of true event charge asymmetry for the 30–40% centrality class in PbPb collisions at √s
NN= 5.02 TeV.
because of limited statistical precision. The normalized v3 difference, (v3−− v+3)/(v3−+ v+3), is derived as a function of
Atrue
ch in PbPb collisions and compared with that for v2 in
Fig.5(bottom). The normalized slope parameter ofv3, r3norm, agrees well with r2normwithin statistical uncertainties. Charge-dependent higher harmonicvn coefficients were measured in
PbPb collisions at 2.76 TeV [5] and their magnitude was
found to be smaller than that of the second order coefficient. We show in this paper that, once normalized, no difference is observed for the Atruech dependence between the charge-dependentv2andv3.
The rnorm
2 and r3norm values of PbPb collisions at √
sNN=
5.02 TeV are shown in Fig. 6, as functions of centrality in
the range 30–90%. As found for rnorm
2 , a moderate centrality
dependence of rnorm
3 is observed. Over the centrality range
studied in this analysis, the r2norm and r3norm slope parame-ters are consistent with each other within uncertainties. The CMW effect is expected with respect to the reaction plane, which is approximated by the second-order event plane in
AA collisions, but highly suppressed with respect to the
third-order event plane [13]. The observation of the harmonic order independence, reflected in the similar r2normand r3normvalues, indicates an underlying physics mechanism unrelated to the
Centrality (%) n normr 0.1 0.2 0 20 40 60 80 100 〉 trk offline N 〈 26 81 197 403 716 1139
CMS
PbPb 5.02 TeV < 3.0 GeV/c T 0.3 < p 2v
3v
FIG. 6. The linear slope parameters, rnorm
2 and rnorm3 as functions
of the centrality class in PbPb collisions. Average Noffline
trk values for
each centrality class are indicated on the top axis. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
CMW effect and, instead, can be qualitatively explained by the LCC effect [20].
Note that the results reported here and elsewhere [18,19] used the same population of particles to measure bothvnand
Atrue
ch . However, the slope parameters are found to be reduced by about a factor of 3, if the Atrue
ch andvnvalues are determined by two distinct groups of randomly selected particles. This suggests that the observed correlations are not of a collective nature.
VI. SUMMARY
In summary, the charge-dependent Fourier coefficients of the azimuthal anisotropy have been measured in pPb and PbPb collisions at√sNN= 5.02 TeV as functions of the charge
asymmetry of the produced hadrons. The normalized differ-ences in thev2coefficient between positively and negatively charged particles in pPb and PbPb, and that in the v3 coef-ficient in PbPb collisions, are found to depend linearly on the charge asymmetry. The normalized slope parameters of thev2 coefficient versus charge asymmetry in pPb collisions are found to be significant and similar to those in PbPb collisions over a wide range of charged particle multiplicities. The normalized slope parameters of thev2andv3coefficients in PbPb collisions show similar magnitudes for various cen-trality classes. A significant charged asymmetry dependence is also observed for the event-averaged transverse momenta of positively and negatively charged particles in both pPb and PbPb collisions. None of these observations, made at 5.02 TeV and within the CMS phase space window, are expected from the chiral magnetic wave as the dominant physics mechanism, while they are qualitatively consistent with predictions based on local charge conservation. The new measurements pre-sented here indicate that, at LHC energies, the chiral magnetic wave is not the cause of the charge-dependent azimuthal anisotropies seen in pPb and PbPb collisions.
ACKNOWLEDGMENTS
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the comput-ing infrastructure essential to our analyses. Finally, we ac-knowledge the enduring support for the construction and
operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Finland, MEC,
and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF,
DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVES-TAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR and RAEP (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI and FEDER (Spain); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie Curie program and the European Research Council and Horizon 2020 Grant, Contract No. 675440 (European Union); the Leventis Foundation; the A. P. Sloan Founda-tion; the Alexander von Humboldt FoundaFounda-tion; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofi-nanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland),
Contracts No. Harmonia 2014/14/M/ST2/00428, No. Opus
2014/13/B/ST2/02543, No. 2014/15/B/ST2/03998, and
No. 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/
01406; the National Priorities Research Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Thalis and Aristeia programs cofi-nanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); the Welch Foundation, contract C-1845; and the Weston Havens Foun-dation (USA).
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S. S. Chhibra,64a,64bG. Codispoti,64a,64bM. Cuffiani,64a,64bG. M. Dallavalle,64a,64bF. Fabbri,64a,64bA. Fanfani,64a,64b D. Fasanella,64a,64bP. Giacomelli,64a,64bC. Grandi,64a,64bL. Guiducci,64a,64bS. Marcellini,64a,64bG. Masetti,64a,64b
A. Montanari,64a,64bF. L. Navarria,64a,64bA. Perrotta,64a,64bA. M. Rossi,64a,64bT. Rovelli,64a,64bG. P. Siroli,64a,64bN. Tosi,64a,64b
S. Albergo,65a,65bS. Costa,65a,65bA. Di Mattia,65a,65bF. Giordano,65a,65bR. Potenza,65a,65bA. Tricomi,65a,65bC. Tuve,65a,65b
G. Barbagli,66a,66bK. Chatterjee,66a,66bV. Ciulli,66a,66bC. Civinini,66a,66bR. D’Alessandro,66a,66bE. Focardi,66a,66b
P. Lenzi,66a,66bM. Meschini,66a,66bS. Paoletti,66a,66bL. Russo,66a,66b,acG. Sguazzoni,66a,66bD. Strom,66a,66bL. Viliani,66a,66b,o L. Benussi,67S. Bianco,67F. Fabbri,67D. Piccolo,67F. Primavera,67,oV. Calvelli,68a,68bF. Ferro,68a,68bE. Robutti,68a,68b S. Tosi,68a,68bA. Benaglia,69a,69bL. Brianza,69a,69bF. Brivio,69a,69bV. Ciriolo,69a,69bM. E. Dinardo,69a,69bS. Fiorendi,69a,69b
S. Gennai,69aA. Ghezzi,69a,69bP. Govoni,69a,69bM. Malberti,69a,69bS. Malvezzi,69a,69bR. A. Manzoni,69a,69bD. Menasce,69a,69b
L. Moroni,69a,69bM. Paganoni,69a,69bK. Pauwels,69a,69bD. Pedrini,69a,69bS. Pigazzini,69a,69b,adS. Ragazzi,69a,69bT. Tabarelli de
Fatis,69a,69bS. Buontempo,70a,70b,70c,70dN. Cavallo,70a,70b,70c,70dS. Di Guida,70a,70b,70c,70d,oF. Fabozzi,70a,70b,70c,70d
F. Fienga,70a,70b,70c,70dA. O. M. Iorio,70a,70b,70c,70dW. A. Khan,70a,70b,70c,70dL. Lista,70a,70b,70c,70dS. Meola,70a,70b,70c,70d,o P. Paolucci,70a,70b,70c,70d,oC. Sciacca,70a,70b,70c,70dF. Thyssen,70a,70b,70c,70dP. Azzi,71a,71b,71c,oN. Bacchetta,71a,71b,71c
L. Benato,71a,71b,71cM. Biasotto,71a,71b,71c,aeA. Boletti,71a,71b,71cR. Carlin,71a,71b,71cP. Checchia,71a,71b,71c
M. Dall’Osso,71a,71b,71cP. De Castro Manzano,71a,71b,71cT. Dorigo,71a,71b,71cU. Dosselli,71a,71b,71cF. Gasparini,71a,71b,71c
U. Gasparini,71a,71b,71cA. Gozzelino,71a,71b,71cS. Lacaprara,71a,71b,71cM. Margoni,71a,71b,71cA. T. Meneguzzo,71a,71b,71c
M. Michelotto,71a,71b,71cN. Pozzobon,71a,71b,71cP. Ronchese,71a,71b,71cR. Rossin,71a,71b,71cF. Simonetto,71a,71b,71c E. Torassa,71a,71b,71cM. Zanetti,71a,71b,71cP. Zotto,71a,71b,71cG. Zumerle,71a,71b,71cA. Braghieri,72a,72bA. Magnani,72a,72b
P. Montagna,72a,72bS. P. Ratti,72a,72bV. Re,72a,72bM. Ressegotti,72a,72bC. Riccardi,72a,72bP. Salvini,72a,72bI. Vai,72a,72b
L. Fanò,73a,73bP. Lariccia,73a,73bR. Leonardi,73a,73bE. Manoni,73a,73bG. Mantovani,73a,73bV. Mariani,73a,73b M. Menichelli,73a,73bA. Rossi,73a,73bA. Santocchia,73a,73bD. Spiga,73a,73bK. Androsov,74a,74b,74cP. Azzurri,74a,74b,74c,o
G. Bagliesi,74a,74b,74cJ. Bernardini,74a,74b,74cT. Boccali,74a,74b,74cL. Borrello,74a,74b,74cR. Castaldi,74a,74b,74c
M. A. Ciocci,74a,74b,74cR. Dell’Orso,74a,74b,74cG. Fedi,74a,74b,74cL. Giannini,74a,74b,74cA. Giassi,74a,74b,74c
M. T. Grippo,74a,74b,74c,acF. Ligabue,74a,74b,74cT. Lomtadze,74a,74b,74cE. Manca,74a,74b,74cG. Mandorli,74a,74b,74c
L. Martini,74a,74b,74cA. Messineo,74a,74b,74cF. Palla,74a,74b,74cA. Rizzi,74a,74b,74cA. Savoy-Navarro,74a,74b,74c,af
P. Spagnolo,74a,74b,74cR. Tenchini,74a,74b,74cG. Tonelli,74a,74b,74cA. Venturi,74a,74b,74cP. G. Verdini,74a,74b,74cL. Barone,75a,75b F. Cavallari,75a,75bM. Cipriani,75a,75bN. Daci,75a,75bD. Del Re,75a,75b,oE. Di Marco,75a,75bM. Diemoz,75a,75bS. Gelli,75a,75b
E. Longo,75a,75bF. Margaroli,75a,75bB. Marzocchi,75a,75bP. Meridiani,75a,75bG. Organtini,75a,75bR. Paramatti,75a,75b
F. Preiato,75a,75bS. Rahatlou,75a,75bC. Rovelli,75a,75bF. Santanastasio,75a,75bN. Amapane,76a,76b,76cR. Arcidiacono,76a,76b,76c
S. Argiro,76a,76b,76cM. Arneodo,76a,76b,76cN. Bartosik,76a,76b,76cR. Bellan,76a,76b,76cC. Biino,76a,76b,76cN. Cartiglia,76a,76b,76c
F. Cenna,76a,76b,76cM. Costa,76a,76b,76cR. Covarelli,76a,76b,76cA. Degano,76a,76b,76cN. Demaria,76a,76b,76cB. Kiani,76a,76b,76c C. Mariotti,76a,76b,76cS. Maselli,76a,76b,76cE. Migliore,76a,76b,76cV. Monaco,76a,76b,76cE. Monteil,76a,76b,76cM. Monteno,76a,76b,76c
M. M. Obertino,76a,76b,76cL. Pacher,76a,76b,76cN. Pastrone,76a,76b,76cM. Pelliccioni,76a,76b,76cG. L. Pinna Angioni,76a,76b,76c
F. Ravera,76a,76b,76cA. Romero,76a,76b,76cM. Ruspa,76a,76b,76cR. Sacchi,76a,76b,76cK. Shchelina,76a,76b,76cV. Sola,76a,76b,76c
A. Solano,76a,76b,76cA. Staiano,76a,76b,76cP. Traczyk,76a,76b,76cS. Belforte,77a,77bM. Casarsa,77a,77bF. Cossutti,77a,77bG. Della
Ricca,77a,77bA. Zanetti,77a,77bD. H. Kim,78G. N. Kim,78M. S. Kim,78J. Lee,78S. Lee,78S. W. Lee,78C. S. Moon,78 Y. D. Oh,78S. Sekmen,78D. C. Son,78Y. C. Yang,78A. Lee,79H. Kim,80D. H. Moon,80G. Oh,80J. A. Brochero Cifuentes,81
J. Goh,81T. J. Kim,81S. Cho,82S. Choi,82Y. Go,82D. Gyun,82S. Ha,82B. Hong,82Y. Jo,82Y. Kim,82K. Lee,82K. S. Lee,82
S. Lee,82J. Lim,82S. K. Park,82Y. Roh,82J. Almond,83J. Kim,83J. S. Kim,83H. Lee,83K. Lee,83K. Nam,83S. B. Oh,83
B. C. Radburn-Smith,83S. h. Seo,83U. K. Yang,83H. D. Yoo,83G. B. Yu,83M. Choi,84H. Kim,84J. H. Kim,84J. S. H. Lee,84
I. C. Park,84Y. Choi,85C. Hwang,85J. Lee,85I. Yu,85V. Dudenas,86A. Juodagalvis,86J. Vaitkus,86I. Ahmed,87Z. A. Ibrahim,87
M. A. B. Md Ali,87,agF. Mohamad Idris,87,ahW. A. T. Wan Abdullah,87M. N. Yusli,87Z. Zolkapli,87M. C. Duran-Osuna,88 H. Castilla-Valdez,88E. De La Cruz-Burelo,88G. Ramirez-Sanchez,88I. Heredia-De La Cruz,88,aiR. I. Rabadan-Trejo,88
R. Lopez-Fernandez,88J. Mejia Guisao,88R. Reyes-Almanza,88A. Sanchez-Hernandez,88S. Carrillo Moreno,89C. Oropeza
Barrera,89F. Vazquez Valencia,89I. Pedraza,90H. A. Salazar Ibarguen,90C. Uribe Estrada,90A. Morelos Pineda,91
D. Krofcheck,92P. H. Butler,93A. Ahmad,94M. Ahmad,94Q. Hassan,94H. R. Hoorani,94A. Saddique,94M. A. Shah,94
M. Shoaib,94M. Waqas,94H. Bialkowska,95M. Bluj,95B. Boimska,95T. Frueboes,95M. Górski,95M. Kazana,95 K. Nawrocki,95M. Szleper,95P. Zalewski,95K. Bunkowski,96A. Byszuk,96,ajK. Doroba,96A. Kalinowski,96M. Konecki,96 J. Krolikowski,96M. Misiura,96M. Olszewski,96A. Pyskir,96M. Walczak,96P. Bargassa,97C. Beirão Da Cruz E. Silva,97A. Di
Francesco,97P. Faccioli,97B. Galinhas,97M. Gallinaro,97J. Hollar,97N. Leonardo,97L. Lloret Iglesias,97M. V. Nemallapudi,97
J. Seixas,97G. Strong,97O. Toldaiev,97D. Vadruccio,97J. Varela,97S. Afanasiev,98P. Bunin,98M. Gavrilenko,98I. Golutvin,98
I. Gorbunov,98A. Kamenev,98V. Karjavin,98A. Lanev,98A. Malakhov,98V. Matveev,98,akV. Palichik,98V. Perelygin,98 S. Shmatov,98S. Shulha,98N. Skatchkov,98V. Smirnov,98N. Voytishin,98A. Zarubin,98Y. Ivanov,99V. Kim,99,al E. Kuznetsova,99,amP. Levchenko,99V. Murzin,99V. Oreshkin,99I. Smirnov,99V. Sulimov,99L. Uvarov,99S. Vavilov,99
A. Vorobyev,99Yu. Andreev,100A. Dermenev,100S. Gninenko,100N. Golubev,100A. Karneyeu,100M. Kirsanov,100
N. Krasnikov,100A. Pashenkov,100D. Tlisov,100A. Toropin,100V. Epshteyn,101V. Gavrilov,101N. Lychkovskaya,101
V. Popov,101I. Pozdnyakov,101G. Safronov,101A. Spiridonov,101A. Stepennov,101M. Toms,101E. Vlasov,101A. Zhokin,101
T. Aushev,102A. Bylinkin,102,anM. Chadeeva,103,aoP. Parygin,103D. Philippov,103S. Polikarpov,103E. Popova,103 V. Rusinov,103V. Andreev,104M. Azarkin,104,anI. Dremin,104,anM. Kirakosyan,104,anA. Terkulov,104A. Baskakov,105
A. Belyaev,105E. Boos,105A. Demiyanov,105A. Ershov,105A. Gribushin,105O. Kodolova,105V. Korotkikh,105I. Lokhtin,105
I. Miagkov,105S. Obraztsov,105S. Petrushanko,105V. Savrin,105A. Snigirev,105I. Vardanyan,105V. Blinov,106,apD. Shtol,106,ap
Y. Skovpen,106,apI. Azhgirey,107I. Bayshev,107S. Bitioukov,107D. Elumakhov,107V. Kachanov,107A. Kalinin,107
D. Konstantinov,107V. Krychkine,107V. Petrov,107R. Ryutin,107A. Sobol,107S. Troshin,107N. Tyurin,107A. Uzunian,107 A. Volkov,107P. Adzic,108,aqP. Cirkovic,108D. Devetak,108M. Dordevic,108J. Milosevic,108V. Rekovic,108J. Alcaraz Maestre,109A. Álvarez Fernández,109M. Barrio Luna,109M. Cerrada,109N. Colino,109B. De La Cruz,109A. Delgado Peris,109
A. Escalante Del Valle,109C. Fernandez Bedoya,109J. P. Fernández Ramos,109J. Flix,109M. C. Fouz,109P. Garcia-Abia,109
O. Gonzalez Lopez,109S. Goy Lopez,109J. M. Hernandez,109M. I. Josa,109A. Pérez-Calero Yzquierdo,109J. Puerta Pelayo,109
A. Quintario Olmeda,109I. Redondo,109L. Romero,109M. S. Soares,109J. F. de Trocóniz,110M. Missiroli,110D. Moran,110
J. Cuevas,111C. Erice,111J. Fernandez Menendez,111I. Gonzalez Caballero,111J. R. González Fernández,111E. Palencia Cortezon,111S. Sanchez Cruz,111P. Vischia,111J. M. Vizan Garcia,111I. J. Cabrillo,112A. Calderon,112B. Chazin Quero,112
E. Curras,112J. Duarte Campderros,112M. Fernandez,112J. Garcia-Ferrero,112G. Gomez,112A. Lopez Virto,112J. Marco,112
C. Martinez Rivero,112P. Martinez Ruiz del Arbol,112F. Matorras,112J. Piedra Gomez,112T. Rodrigo,112A. Ruiz-Jimeno,112
L. Scodellaro,112N. Trevisani,112I. Vila,112R. Vilar Cortabitarte,112D. Abbaneo,113E. Auffray,113P. Baillon,113A. H. Ball,113
D. Barney,113M. Bianco,113P. Bloch,113A. Bocci,113C. Botta,113T. Camporesi,113R. Castello,113M. Cepeda,113 G. Cerminara,113E. Chapon,113Y. Chen,113D. d’Enterria,113A. Dabrowski,113V. Daponte,113A. David,113M. De Gruttola,113 A. De Roeck,113M. Dobson,113B. Dorney,113T. du Pree,113M. Dünser,113N. Dupont,113A. Elliott-Peisert,113P. Everaerts,113
