Probing the chiral magnetic wave in pPb and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV using charge-dependent azimuthal anisotropies

Charge-dependent anisotropy Fourier coefficients ($v_n$) of particle azimuthal distributions are measured in pPb and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{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 pPb 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 pPb 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 energies, the observed charge asymmetry dependence of $v_2$ in heavy ion collisions arises from a chiral magnetic wave.


1
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][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]. This electric quadruple moment is expected to induce a charge-dependent variation of the second-order 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, as follows; 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 (+r) and negatively (−r) 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 the quantitative predictions of the CMW models still have large uncertainties and alternative mechanisms have been proposed to generate charge-dependent v 2 coefficients without a CMW [20,21]. For example, it has been shown that models of the impact of 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, hence leading to a nonzero A ch . Thus, 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 . No A ch dependence of the event-averaged particle p T , p T , is expected from the CMW. The LCC mechanism also applies to all higher-order anisotropy Fourier coefficients (v n ).
This Letter 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 chargedparticle 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, as compared to PbPb collisions with similar event multiplicity. This is because the induced magnetic field in pPb collisions is expected to be smaller and, more importantly, oriented randomly with respect to the harmonic event planes [6]. The recent observation of nearly identical charge-dependent azimuthal correlations in pPb and PbPb suggested significant contribution of background sources (e.g., LCC) to any CME induced signal [6]. Similarly, the LCC background is expected to produce A ch -dependent v 2,± in both pPb and PbPb collision systems. Therefore, a comparison between pPb and PbPb systems provides a way to disentangle the CMW and LCC effects. Furthermore, as discussed above, a measurement of the A ch dependence of the p T and the v 3 coefficient can also differentiate between the CMW and LCC mechanisms.
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 four primary subdetectors, including silicon pixel and strip tracker detectors, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter. Each calorimeter is composed of a barrel and two endcap sections. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. 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 [36]. 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. [37].
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 . The beam energies are 1.58 TeV per nucleon for the lead nuclei and 4 TeV for the protons. 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 [38]) 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. [36], 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 direction is required to be less than 3, as is the corresponding impact parameter significance in the transverse plane. 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.
The definition of the event classes in terms of N offline trk in pPb and PbPb collisions is identical to the previous measurement in Ref. [6]. The PbPb data are also presented as a function of event centrality.
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 reported in Appendix A. 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 [39] with a pseudorapidity gap of at least 1 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 2 units typically used in other CMS correlation measurements. Therefore, 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 main physics observable of interest in this analysis is the slope parameter (r norm ) extracted by fitting a linear function to the normalized v n differences, , as a function of the true event charge asymmetry value, A true ch , obtained by correcting A obs ch for the detector acceptance and tracking efficiency. Based on Monte Carlo (MC) simulations, detector effects can be modeled as a Gaussian response of the A true ch distribution within |η| < 2.4, with a width determined from the simulated A obs ch distribution at a given A true ch value. Combining the A obs ch distribution in data with the response function from MC simulations, the predicted correlation between A obs ch and A true ch in data is calculated. The slope of a linear fit to this correlation is used to obtain the average A true ch value in each selected A obs ch 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 A ch correction factors, based on the difference between EPOS LHC [40] and HYDJET++ [41] 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 two or five, 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.    and PbPb [19] systems at lower collision energies (a direct comparison to the lower-energy result [19] is reported in Appendix A 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 0.15 ± 0.01 for pPb and 0.11 ± 0.01 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. As discussed previously, the CMW effect is expected to be negligible in high-multiplicity pPb events because of the smaller induced magnetic field and weak correlation between the event plane and magnetic field directions. Therefore, the observation of significant linear slopes in both pPb and PbPb systems may indicate a common physics origin that is not related to the CMW.
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. 1 (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. As shown, a similar linear charge asymmetry dependence of the p T value to that of v 2 is observed. As argued earlier, this behavior is qualitatively consistent with the expectation of the LCC effect from resonance decays [20]. 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. 1 (left), can be also 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. 2. The two highest multiplicity ranges of PbPb data are selected based on the centrality class 30-40% and 40-50%, plotted at their average N offline trk values, while the other data points are obtained from selecting on N offline trk in order to compare directly with pPb data. 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. In the overlapping multiplicity range between pPb and PbPb systems, similar slope parameters are observed, which suggests a common underlying correlation between v ± 2 or p T with A ch for all multiplicities. The slope parameters for p T are approximately half of those for v 2 . This suggests that the p T slope can account for about 50% of the observed slope for p T -averaged v 2 values with 0.3 < p T < 3 GeV/c, as v 2 linearly increases with p T in this low-p T region. The measured values of normalized slope parameters, as well as values of absolute slope parameters, are reported in Tables of Appendix A.
The charge asymmetry dependence of the v 3 coefficient for positively and negatively charged particles is also studied in PbPb collisions at √ s NN = 5.02 TeV, as shown in Fig. 3 , is derived as a function of A true ch in PbPb collisions and compared with that for v 2 in Fig. 3 (bottom). The normalized slope parameter of v 3 , r norm 3 , agrees well with r norm 2 within statistical uncertainties. In the CME and CSE, which are the necessary conditions for the CMW effect, the electric or chiral charges are expected to separate with respect to the reaction plane, which is approximated by the secondorder event plane in AA collisions. The CMW effect is expected to be highly suppressed with respect to the third-order event plane, leading to a vanishing slope parameter r norm 3 [13]. Similar values of the r norm 2 and r norm 3 parameters as observed in the data indicate an underlying physics mechanism that is not related to the CMW effect. As discussed earlier, this observation of the A ch dependence for higher-order Fourier coefficients 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 . If, instead, the A true ch and v n values are determined for the same events as shown in Fig. 3, but for two distinct groups of randomly selected particles from each event, the slope parameter for each subgroup is found to be reduced by about a factor of three compared to that for the full particle sample. This suggests that the observed correlations are not of a collective nature as expected in the CMW, but are more suggestive of a local effect, e.g., the LCC mechanism.
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. 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 is expected from the chiral magnetic wave mechanism, but they are qualitatively consistent with predictions based on local charge conservation. New measurements presented here on the charge-dependent azimuthal anisotropy in pPb and PbPb collisions pose challenges to the chiral magnetic wave as its origin.  [32] CMS Collaboration, "Multiplicity and transverse momentum dependence of two-and four-particle correlations in pPb and PbPb collisions", Phys.

A Supplemental information: additional figures and tabular information
The normalized difference in elliptic flow v 2 between positively and negatively charged particles as a function of charge asymmetry is shown in Fig. 1, in centrality range 30-40% with particles within |η| < 0.8 and 0.2 ≤ p T < 5.0 GeV, and are compared between the ALICE [19] and the CMS experiment in PbPb collisions at √ s NN = 2.76 TeV and 5.02 TeV, respectively.
The A obs ch in centrality range 30-40% is shown in Fig. 2, with particles selected between 0.3 to 3.0 GeV/c and pseudorapidity range |η| < 2.4.
, 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 ≤ p T < 5.0 GeV, and are compared between the ALICE [19] and the CMS experiment in PbPb collisions at √ s NN = 2.76 TeV and 5.02 TeV, respectively. The bars represent statistical point-by-point uncertainties.
From Table 1 to 3, the values of slope parameter and normalized slope parameter for v 2 and p T are shown in pPb and PbPb collisions.