Probing the chiral magnetic wave in p Pb and PbPb collisions at using charge-dependent azimuthal anisotropies

Charge-dependent anisotropy Fourier coefﬁcients ( v n ) of particle azimuthal distributions are measured in p Pb and PbPb collisions at √ s NN = 5 . 02 TeV with the CMS detector at the LHC. The normalized difference in the second-order anisotropy coefﬁcients ( v 2 ) between positively and negatively charged particles is found to depend linearly on the observed event charge asymmetry with comparable slopes for both p Pb and PbPb collisions over a wide range of charged particle multiplicity. In PbPb, the third-order anisotropy coefﬁcient v 3 shows a similar linear dependence with the same slope as seen for v 2 . The observed similarities between the v 2 slopes for p Pb and PbPb, as well as the similar slopes for v 2 and v 3 in 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 of v 2 in heavy ion collisions arises from a chiral magnetic wave.


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 threedimensional Dirac and Weyl materials [1][2][3] to hot plasma in the early universe or formed in relativistic heavy ion collisions [4][5][6]. In quantum chromodynamics, gluon fields within a localized region of space-time can form nontrivial topological configurations [7][8][9][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][12][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][15][16][17].
In relativistic heavy ion (AA) collisions, a strong magnetic field and the restoration of the approximate chiral symmetry, 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 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 secondorder anisotropy coefficient (v 2 ) in the Fourier expansion of the final-state particle azimuthal distribution. More specifically, the v 2 coefficient will exhibit a linear dependence on the observed event charge asymmetry [14], A ch ≡ (N + − N − )/(N + + N − ), where N + and N − denote the number of positively and negatively charged hadrons in each event, v 2,± = v base 2,± ∓ rA ch .
Here v base 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 v 2 values between positively and negatively charged particles will be proportional to A ch . Similar charge-dependent effects from the CMW are not expected for the third-order anisotropy coefficient (v 3 ) [13].
Recent observations of the A ch dependence of v 2,± in AA collisions at RHIC at BNL and the CERN LHC are qualitatively consistent with expectations of the CMW mechanism [5,18,19]. However, the interpretation of the results remains inconclusive since alternative mechanisms have been proposed to generate charge-dependent v 2 coefficients without a CMW [20,21]. For example, it has been shown that local charge conservation (LCC) in the decay of clusters or resonances can qualitatively describe the charge-dependent v 2 data [20]. Decay particles from a lower transverse momentum (p T ) resonance tend to have a larger rapidity separation, resulting in a daughter more likely to fall outside the detector acceptance, leading to a nonzero A ch . Hence, this process generates a correlation between A ch and the average p T of charged particles, and therefore also between A ch and the v 2 coefficient, since v 2 depends on p T . The LCC mechanism also applies to all higher-order anisotropy Fourier coefficients (v n ).
This paper presents measurements of the A ch dependence of the p T and of the p T -averaged v n coefficients in pPb and PbPb collisions at √ s NN = 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 multiplicities can generate large final-state azimuthal anisotropies, comparable to those in AA collisions at similar event multiplicities [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. However, the CMW contribution to any A ch -dependent v 2 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 background sources (e.g., LCC) to any CME induced signal [6,37]. Therefore, a comparison between pPb and PbPb systems and their A ch dependence of the p T and the v 3 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 superconducting 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 crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter. The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5. For charged particles with 1 < p T < 10 GeV/c and |η| < 1.4, the track resolutions are typically 1.5% in p T and 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 √ s NN = 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 √ s NN = 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 used. The sample is reconstructed with the same algorithm as the pPb data, in order to compare directly the two systems 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 presence 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 (N offline 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 p T must be less than 10%. To ensure high tracking efficiency, only tracks with |η| < 2.4 and p T > 0.3 GeV/c are used for A ch and v n measurements in this analysis. The pPb and PbPb data are compared in ranges of N offline trk , where primary tracks with |η| < 2.4 and p T > 0.4 GeV/c are counted, in order to match the trigger selection criterion implemented at the HLT in pPb collisions.

IV. ANALYSIS TECHNIQUE
In each multiplicity or centrality class, events are further divided into several ranges of the observed event charge asymmetry A obs ch , calculated based on the number of positively and negatively charged particles from primary tracks. An example of the A obs ch distribution for PbPb data in the 30-40% centrality range is shown in Fig. 1. Within each A obs ch range, the v n coefficients are obtained separately for tracks with positive (v + n ) and negative (v − n ) charge, and with |η| < 2.4 and 0.3 < p T < 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 the v n , 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 systematic uncertainty related to the A ch 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 the v n measurement, 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 p T uncertainty selection criterion from the default 10% to 5%, yields a systematic uncertainty of less than 2%. The longitudinal primary vertex position (z vtx ) has been varied, using ranges |z vtx | < 3 cm and 3 < |z vtx | < 15 cm, where the difference with respect to the default range |z vtx | < 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.   Fig. 3 for 30-40% centrality PbPb events. The linear slope parameter, r norm 2 , is extracted by a χ 2 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 N offline 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.

V. RESULTS
The p T for positively and negatively charged particles are also measured as functions of A true ch , in the multiplicity range 185 N offline trk < 220 of pPb and PbPb collisions at √ s NN = 5.02 TeV, and shown in Fig. 2 (right column). The normalized p T difference as a function of A true ch is obtained for the two systems with the slope parameters displayed in the figure. A similar linear A true ch dependence of the p T value to that of v 2 is observed. This behavior is qualitatively consistent with the expectation of the LCC effect from resonance decays. Since v n has a strong dependence on particle p T , a correlation between the p T -averaged v n and A ch , as observed in Fig. 2 (left), can also be induced by the LCC mechanism.
The extracted normalized slope parameters for v 2 and p T as functions of event multiplicity in pPb and PbPb collisions are shown in Fig. 4. The r norm values for both v 2 and p T are found to have a weak dependence on the event multiplicity for both pPb and PbPb collisions, with values for p T approximately half of those for v 2 . In the overlapping multiplicity range, normalized slope parameters are observed  Centrality 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 Tables I-III , is derived as a function of A true ch in PbPb collisions and compared with that for v 2 in Fig. 5 (bottom). The normalized slope parameter of v 3 , r norm 3 , agrees well with r norm 2 within statistical uncertainties. Chargedependent higher harmonic v n 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 A true ch dependence between the chargedependent v 2 and v 3 .
The r norm 2 and r norm 3 values of PbPb collisions at √ s NN = 5.02 TeV are shown in Fig. 6, as functions of centrality in the range 30-90%. As found for r norm 2 , a moderate centrality dependence of r norm 3 is observed. Over the centrality range studied in this analysis, the r norm 2 and r norm 3 slope parameters 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 thirdorder event plane [13]. The observation of the harmonic order independence, reflected in the similar r norm 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 both v n and A true ch . However, the slope parameters are found to be reduced by about a factor of 3, if the A true ch and v n values 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 √ s NN = 5.02 TeV as functions of the charge asymmetry of the produced hadrons. The normalized differences in the v 2 coefficient between positively and negatively charged particles in pPb and PbPb, and that in the v 3 coefficient in PbPb collisions, are found to depend linearly on the charge asymmetry. The normalized slope parameters of the v 2 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 the v 2 and v 3 coefficients in PbPb collisions show similar magnitudes for various centrality 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 presented 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 computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and