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Evidence for Effects of the Chiral Anomaly: Status and Future
Available online at www.sciencedirect.com
Nuclear Physics A 967 (2017) 129–136 www.elsevier.com/locate/nuclphysa
Evidence for Effects of the Chiral Anomaly: Status and Future Paul Sorensen Brookhaven National Laboratory, Upton, New York Department of Energy, Germantown, MD
Abstract The unique identification of effects of the chiral anomaly in heavy ion collisions has been a challenge because alternative scenarios can often be constructed to explain the relevant findings. For this reason, the measurements remain open to interpretation. Because the unambiguous identification of effects caused by the chiral anomaly would represent one of the most profound discoveries from heavy ions, resolving these questions of interpretation is a priority for the field. Several new analyses were presented at Quark Matter 2017 and in this paper as in the summary talk, I attempt to present a clear picture of the most pressing questions and ideas on how to reach a clear conclusion. Keywords: chiral anomaly, QGP, heavy-ions, CME, CMW
1. Introduction When a classic theory possesses a symmetry that is violated by the introduction of quantum corrections, the symmetry violation is called a quantum anomaly. The chiral anomaly refers to the anomalous nonconservation of chiral current and explains the decay of the neutral pion into two photons. The quantum chiral anomaly also leads to baryon non-conservation in the electroweak theory and can therefore explain the prevalence of matter over antimatter in the universe. While it is not feasible to recreate the electroweak phase transition in the laboratory setting, the QCD phase transition can be created in heavy ion collisions, providing an environment where it is possible to study the non-Abelian chiral anomaly in a laboratory setting. The unambiguous identification of the effects related to the chiral anomaly will therefore contribute to our understanding of nature at it’s deepest level and would provide direct evidence for a process that, in electroweak theory, would explain the matter-antimatter asymmetry of our universe. In this talk, I reviewed the status of the search for direct experimental evidence of the effects of the chiral anomaly in heavy ion collisions [1, 2, 3]. It has proven difficult to isolate these effects but several new analyses have shed light on the topic [4, 5, 6, 7, 8]. The first proposed signal for the chiral anomaly in heavy ion collisions was the chiral magnetic effect (CME) [1, 2, 3]. In the presence of a magnetic field, a prevalence of either right or left-handed fermions Email address: [email protected] (Paul Sorensen)
http://dx.doi.org/10.1016/j.nuclphysa.2017.05.100 0375-9474/© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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would lead to a current flow along the direction of the magnetic field with positive charges moving in one direction and negative in the other. This effect has been observed in Weyl semimetals which have approximately massless fermions as quasi-particles [9]. The effect has also been observed in lattice QCD simulations [10]. Heavy ion collisions are thought to create a quark gluon plasma (QGP) where chiral symmetry is restored and quarks and gluons become deconfined from their hadronic bound states. These collisions also create some of the largest magnetic fields known in the universe [11]. It is thought that the simultaneous presence of 1) nearly massless fermions in the QGP, 2) the strong magnetic field from the passing nuclei, and 3) local parity violation caused by the chiral anomaly could lead to charge separation along the direction of the magnetic field. If that charge separation is observed and unambiguously linked to CME, it would at once demonstrate that chiral symmetry has been restored and would be the first observation of the chiral anomaly of QCD in action. By way of comparison, the charge separation expected from CME in heavy ion collisions is roughly 24 orders of magnitude larger than the charge separation modern neutron electric dipole moment searches are sensitive to.
Fig. 1. Top left: A simplistic sketch of charge separation driven by the strong magnetic field (1018 Gauss) generated in heavy ion collisions. Top right: A hydrodynamic calculation of charge separation as expressed by the variable H (see text) compared to data [12]. Bottom left: a schematic illustration of how a decaying clusters boosted more in the in-plane direction than the out-of-plane direction can mimic the charge separation anticipated from CME. Bottom right: a model calculation of the background effects that can be tuned to reproduce most of the observed charge separation signal.
Even though the charge separation is expected to be relatively large, it has been a challenge to separate that effect from other background sources that mimic CME. It’s important to note that the interaction region of each collision may contain a number of regions with more right handed quarks and a number of regions with more left handed quarks. For that reason the signal for CME will not necessarily be a global charge separation as illustrated in the figure but will be reflected in fluctuations. This makes the observation more challenging and a number of effects can mimic the signal. The most important effect is illustrated in the bottom panels of the figure which show that a background model based on flowing clusters can reproduce
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early measurements of fluctuations thought to be driven by charge separation [13]. 2. Results The observable most frequently used to search for CME is γS S ,OS ≡ cos(φα + φβ − 2ΨRP ) where charge separation would show up as a difference between cases where particle α and β are either of the samesign OS or opposite signs S S (Δγ) [14]. One can attempt to subtract off the largest known background 2 δ−γ source to γ by assuming factorization and taking H = κv1+κv where δ = cos(Δφ) is the raw two-particle 2 correlations, v2 is the elliptic flow anisotropy and κ is an unknown factor that in simulations has been shown √ to be somewhere between one and two [15]. Fig. 2 shows data from sNN = 7.7 GeV to 2.76 TeV for Δγ in the top panel and ΔH in the bottom panel [16]. We note that even after attempting to subtract off the v2 related background, a signal is still present. The signal is consistent with zero at 7.7 GeV, reaches a maximum near 20 GeV and then decreases as energy increases, becoming marginal or consistent with zero at 2.76 TeV.
Fig. 2. The energy dependence of charge separation corrected for v2 backgrounds (bottom) and uncorrected (top).
While the bottom right panel of Fig. 1 seems to suggest that the measurements are dominated by v2 related backgrounds, the bottom panel of Fig. 2 seems to suggest that v2 related backgrounds can’t explain the energy dependence of the signal. It would be interesting to see model calculations of the v2 related background at all of the energies available at RHIC and the LHC. Other ways to distinguish v2 related backgrounds have been explored including grouping events within a given centrality class by their estimated v2 (event-shape engineering) [7], selecting ultra-central collisions where any magnetic field is randomly oriented relative to the v2 axis [5], and by looking in p + A collisions where it is also thought that if a magnetic field exists, it will not be aligned with the v2 axis [4, 5, 6, 8]. Event-shape engineering has been carried out at the LHC [7]. The idea is that the magnetic field will not change within a given centrality class but the v2 can due to fluctuations; this naive expectation isn’t borne
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out in model calculations but a model to data comparison can be used to estimate how much of the signal is driven by v2 and how much by the magnetic field. This analysis finds that at least 80% of the signal at the LHC is from v2 related backgrounds and that when scaled by multiplicity, the signal is linear in v2 with a slope of approximately 0.8, pointing to zero signal at zero v2 . It will be interesting to see this analysis carried out on data at RHIC where the H variable seems to suggest the signal is strongest.
Fig. 3. Top panels: Event shape engineering from the LHC. Middle panels: p+Pb results from LHC compared to Pb+Pb and Au+Au from RHIC. Bottom panels: Model calculations (left) and data (right) from ultra-central U+U collisions.
The middle panels of Fig. 3 show data on p+Pb collisions at 5.02 TeV compared to Pb+Pb [4] collisions and Au+Au collisions from RHIC. The naive expectation is that any signal observed in p+Pb collisions must be driven by backgrounds. The observation is that the signal in p+Pb is as large as that in Pb+Pb and Au+Au. This similarity seems to suggest that perhaps all the data is driven by background. On the other hand, there is no known background model that would predict a similarity between Au+Au collisions at RHIC and p+Pb or Pb+Pb collisions at the LHC. This is because as multiplicity goes up, the measurement of the background should drop as one over the multiplicity. It appears that the data challenge both the CME based expectations and the background model based expectations. The bottom panels show data from ultra-central U+U collisions [5]. These collisions possess an appre-
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ciable v2 but since models show that the magnetic field becomes oriented randomly with respect to the v2 axis [17], no CME signal is expected. In a v2 driven background scenario, we expect Δγ to only reach zero when v2 reaches zero. The data however contradicts this scenario and drops to zero while a large v2 still persists. This is consistent with CME and contradicts the background models. This is the opposite of the conclusion one would naturally draw from the LHC data where the eventshape engineering data is consistent with a v2 driven background and contradicts CME. Although much new data has appeared, the situation remains murky.
Fig. 4. Charge separation data from RHIC including new p+Au measurements and model calculations. Δγ on the left has been scaled by N part and plotted vs N part while the data plotted on the right is equivalent to Δγ scaled by multiplicity and divided by v2 . This latter quantity is expected to be approximately flat as a function of centrality for v2 dominated background. The LHC slope of 0.8 refers to the slope inferred from eventshape engineering where Δγ at the LHC was found to exhibit a linear dependence on v2 pointing to zero at zero v2 , as would be expected purely from background. The Δγ results from p+Au and d+Au are strongly dependent on how the analysis is carried out, especially when scaling by v2 where the interpretation of v2 is still very unclear and the result can depend strongly on assumptions and analysis details.
While the data from p+Pb collisions at the LHC can be interpreted as supporting a background interpretation of the data, the data presented from RHIC leave a less clear interpretation. In the left panel of Fig. 4, results from U+U and p+Au are shown where short-range correlations have been subtracted off [5, 6]. The subtraction assumes the correlations can be described in terms of a pedestal, a Gaussian, and a short-range background contribution which is assumed to be short-range in both Δη and Δφ so that it is required to contribute a positive contribution to γ. In more central collisions, the short-range subtraction picks out mostly HBT-like correlations and leads to a small correction. In peripheral and p+Au collisions, the subtracted peak is wider and is likely an admixture of HBT and correlations between jet fragments. After removing this contribution, RHIC data on p+Au collisions are consistent with zero. More work should be done however on understanding the systematic uncertainties of the analysis in p+Au collisions. In the right panel of Fig. 4, a compilation of Au+Au, d+Au, and p+Au data is shown where the plotted quantity is equivalent to Δγ scaled by the multiplicity and divided by v2 . If the data are dominated by a v2 driven background, we expect the data to be a single flat line for all systems. The AMPT background simulations shown in the figure confirm this expectation. No subtraction has been applied to the data leaving a large signal in p+Au, d+Au, and peripheral Au+Au collisions. The large value for p+Au and d+Au show that results in those systems can vary a lot depending on how the analysis has been carried out and how v2 has been calculated. The interpretation of v2 in small systems is still unclear. We note that approaching central Au+Au collisions, the data sharply deviate from background expectations and become consistent with zero as expected from the decorrelation of the v2 axis and the magnetic field. The data and simulations in the figure however still lend themselves to contradicting conclusions. For example, one can draw the following conclusions: 1) the AMPT simulations show that background can account for most if not all of the signal, 2) the background explains the flatness of the Au+Au results except in the most central collisions where perhaps v2 is less well understood, 3) the data in central collisions are consistent with CME and contradict expectations from v2 related backgrounds, and 4) data from small systems can either be well above background expectations or consistent with zero depending on how the analysis is carried out. It’s
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clear that questions of interpretation still persist even after the inclusion of the findings presented at this conference.
Fig. 5. Left: RHIC and LHC data on the chiral magnetic wave vs centrality interval. Right: v2 and the projected magnetic field each normalized to unity at their maxima and plotted vs N part .
New analyses related to a predicted chiral magnetic wave (CMW) [18] were also presented at this conference [6, 8]. Of particular note were data on the CMW in p+Pb collisions at the LHC and in p+Au collisions at RHIC. Fig. 5 shows measurements of the slope of v1 for charged particles as a function of the charge asymmetry observed in the event. CMW predicts a non-zero slope as indicated by the data. We note however that whereas RHIC data goes to zero in peripheral and central collisions (as expected from the projected magnetic field shown in the right figure), LHC data remains large and non-zero for central and peripheral collisions (as expected for background from v2 ). Note that for the figure on the left, most central is on the left and for the figure on the right, most central is on the right. These trends seem to suggest the slopes are dominated by background at higher energies but perhaps more consistent with a CMW at lower energies. 3. Discussion The relationship of the CMW findings at RHIC compared to the LHC mirrors those of CME with LHC results appearing to favor a background interpretation and RHIC results appearing to favor a CMW interpretation. Fig. 6 shows a schematic diagram of key findings related to CME. The vertical axis represents system size from p+A collisions at the top to ultra central U+U collisions at the bottom. The horizontal axis shows the energy from the lowest RHIC energies to LHC energies. At 7.7 GeV, data are consistent with no CME. The CME signals (H in particular) exhibit a maximum in mid-central collisions near 20 GeV. Since the duration of the magnetic field is longer at lower energies, it’s plausible that a maximum would occur at some lower energy. As the energy increases above 20 GeV, the CME signal decreases until at the LHC, data appear to be most consistent with background. At full RHIC energy, the centrality dependenc of the data seems to follow the projected magnetic field (as expected from CME) rather than v2 as expected from background models; consistent with zero in p+A and ultra-central U+U even when v2 is still significant. Based on Fig. 6, one may be tempted to conclude that data at RHIC are dominated by the effects of CME but that those effects decrease with energy until they are negligible at the LHC. One can imagine that the duration of the magnetic field becomes so short at the LHC that it is negligible by the time quarks appear in the overlap region. One might find this explanation unconvincing however given that the centrality dependence of the data at RHIC is so similar to that at the LHC. It has also been observed that the Δη width of the signal is also the same. Are these coincidences? The former might be explained by the simple observation that the centrality dependence expected for the background is very similar to the centrality dependence expected for the signal; they both have a maximum in the same centrality range. One could
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Fig. 6. A schematic diagram of experimental findings related to CME. Results related to the chiral magnetic wave follow the same pattern.
also argue that the observed Δη width is a very natural width for many processes and that it is perhaps just coincidental. Given the success of the v2 related backgrounds to capture the general trends of the data and given the p+Pb findings from the LHC, one might also be tempted to conclude that the data at RHIC and the LHC is completely dominated by background and that any deviations between background models and data are just uninteresting details to be worked out. This conclusion however, neglects to explain why RHIC measurements in ultra-central A+A collisions are consistent with zero as expected from CME while LHC measurements are non-zero as expected from background. In addition, while background models seem to capture some of the centrality dependence, the observed energy dependence seems at odds with a background explanation. No known background model yet accounts for the wide range of observations. In addition, theoretical uncertainties allow orders-of-magnitude uncertainty in expectations for charge separation from CME. Given all of the above, what can be done to resolve these questions of interpretation? Fortunately there are steps that can be taken. An eventshape engineering analysis similar to the one carried out at the LHC needs to be done at RHIC. The v2 -background subtracted variable H needs to be analyzed in p+Pb collisions at the LHC. Charge separation should be analyzed in ultra-central collisions at the LHC. The energy dependence of background models should be analyzed and their predictions for ultra-central collisions should be scrutinized. Work needs to continue on refining predictions for CME. The most powerful way to distinguish between chiral effects and backgrounds, however, is to find a way to independently manipulate the magnetic field while keeping other variables fixed. This can be done by colliding isbaric nuclei. Simulations [19] indicate that collisions of 96 Zr+96 Zr and 96 Ru+96 Ru should lead to an approximately 20% difference in the component of the signal arising from CME. Such a program carried out at RHIC appears to have the potential to reduce the uncertainty on the portion of the charge separation arising from CME from 100% to plus or minus 7%. This appears to be the most unambigous way to resolve questions of interpretation.
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4. Conclusions A measurement of charge separation in heavy-ion collisions that can be unambiguously linked to the chiral magnetic effect would be of great interest to the wider physics community and would contribute significantly to the scientific impact and legacy of RHIC. Many measurements have been carried out to study charge separation in heavy-ion collisions that are generally in agreement with expectations from the CME while others, particularly at the LHC are in general agreement with expectations from background models and these models can also account for much of the RHIC data. In particular, at this conference results from p+A collisions, ultra-central collisions, and from event-shape-engineering were shown which followed this pattern. One must conclude therefore that based on our current understanding, backgrounds may account for all of the observed charge separation. Several experimental and theoretical steps can be take to try to improve our understanding of the contribution of the CME to charge separation in heavy-ion collisions. Some of these steps can be accomplished with exhisting data but the most unambiguous evidence linking the observed charge separation to the CME is likely to come from collisions of isobaric nuclei which should make it possible to ascertain the magnetic field dependence of the charge separation signal. It has been found that these collisions can reduce the uncertainty on the magnetic field dependent contribution from 100% to plus or minus 7%. Acknowledgements: The author would like to thank the conference organizers and the international advisory committee for the invitation to give this talk. The author is also indebted to those who presented talks and posters on this topic at this conference. The authors research is supported by the U.S. Department of Energy under contract DE-AC02-98CH10886. References [1] D. Kharzeev, R. D. Pisarski and M. H. G. Tytgat, Phys. Rev. Lett. 81, 512 (1998); D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A 803, 227 (2008); K. Fukushima, D. E. Kharzeev and H. J. Warringa, Phys. Rev. D 78, 074033 (2008). [2] D. E. Kharzeev, J. Liao, S. A. Voloshin and G. Wang, Prog. Part. Nucl. Phys. 88, 1 (2016); V. Skokov, P. Sorensen, V. Koch, S. Schlichting, J. Thomas, S. Voloshin, G. Wang and H. U. Yee, arXiv:1608.00982 [nucl-th]. [3] S. A. Voloshin, Phys. Rev. C 70, 057901 (2004). [4] V. Khachatryan et al. [CMS Collaboration], Phys. Rev. Lett. 118, 122301 (2017). [5] P. Tribedy [STAR Collaboration], arXiv:1704.03845 [nucl-ex]. [6] L. Wen [STAR Collaboration], these proceedings. [7] A. Dobrin [ALICE Collaboration], these proceedings. [8] Z. Tu [CMS Collaboration], these proceedings. [9] Q. Li et al., Nature Phys. 12, 550 (2016). [10] M. Mace, N. Mueller, S. Schlichting and S. Sharma, Phys. Rev. D 95, no. 3, 036023 (2017). [11] V. Skokov, A. Y. Illarionov and V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009). [12] S. Shi, Y. Jiang, E. Lilleskov, Y. Yin and J. Liao, arXiv:1704.05531 [nucl-th]; X. Guo, D. E. Kharzeev, X. G. Huang, W. T. Deng and Y. Hirono, arXiv:1704.05375 [nucl-th]. [13] S. Schlichting and S. Pratt, Phys. Rev. C 83, 014913 (2011). [14] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. 103, 251601 (2009). [15] A. Bzdak, V. Koch and J. Liao, Phys. Rev. C 83, 014905 (2011). [16] L. Adamczyk et al. [STAR Collaboration], Phys. Rev. Lett. 113, 052302 (2014); B. Abelev et al. [ALICE Collaboration], Phys. Rev. Lett. 110, no. 1, 012301 (2013). [17] S. Chatterjee and P. Tribedy, Phys. Rev. C 92, no. 1, 011902 (2015). [18] Y. Burnier, D. E. Kharzeev, J. Liao and H. U. Yee, Phys. Rev. Lett. 107, 052303 (2011). [19] X. G. Huang, W. T. Deng, G. L. Ma and G. Wang, arXiv:1704.04382 [nucl-th].
Nuclear Physics A 967 (2017) 129–136 www.elsevier.com/locate/nuclphysa
Evidence for Effects of the Chiral Anomaly: Status and Future Paul Sorensen Brookhaven National Laboratory, Upton, New York Department of Energy, Germantown, MD
Abstract The unique identification of effects of the chiral anomaly in heavy ion collisions has been a challenge because alternative scenarios can often be constructed to explain the relevant findings. For this reason, the measurements remain open to interpretation. Because the unambiguous identification of effects caused by the chiral anomaly would represent one of the most profound discoveries from heavy ions, resolving these questions of interpretation is a priority for the field. Several new analyses were presented at Quark Matter 2017 and in this paper as in the summary talk, I attempt to present a clear picture of the most pressing questions and ideas on how to reach a clear conclusion. Keywords: chiral anomaly, QGP, heavy-ions, CME, CMW
1. Introduction When a classic theory possesses a symmetry that is violated by the introduction of quantum corrections, the symmetry violation is called a quantum anomaly. The chiral anomaly refers to the anomalous nonconservation of chiral current and explains the decay of the neutral pion into two photons. The quantum chiral anomaly also leads to baryon non-conservation in the electroweak theory and can therefore explain the prevalence of matter over antimatter in the universe. While it is not feasible to recreate the electroweak phase transition in the laboratory setting, the QCD phase transition can be created in heavy ion collisions, providing an environment where it is possible to study the non-Abelian chiral anomaly in a laboratory setting. The unambiguous identification of the effects related to the chiral anomaly will therefore contribute to our understanding of nature at it’s deepest level and would provide direct evidence for a process that, in electroweak theory, would explain the matter-antimatter asymmetry of our universe. In this talk, I reviewed the status of the search for direct experimental evidence of the effects of the chiral anomaly in heavy ion collisions [1, 2, 3]. It has proven difficult to isolate these effects but several new analyses have shed light on the topic [4, 5, 6, 7, 8]. The first proposed signal for the chiral anomaly in heavy ion collisions was the chiral magnetic effect (CME) [1, 2, 3]. In the presence of a magnetic field, a prevalence of either right or left-handed fermions Email address: [email protected] (Paul Sorensen)
http://dx.doi.org/10.1016/j.nuclphysa.2017.05.100 0375-9474/© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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would lead to a current flow along the direction of the magnetic field with positive charges moving in one direction and negative in the other. This effect has been observed in Weyl semimetals which have approximately massless fermions as quasi-particles [9]. The effect has also been observed in lattice QCD simulations [10]. Heavy ion collisions are thought to create a quark gluon plasma (QGP) where chiral symmetry is restored and quarks and gluons become deconfined from their hadronic bound states. These collisions also create some of the largest magnetic fields known in the universe [11]. It is thought that the simultaneous presence of 1) nearly massless fermions in the QGP, 2) the strong magnetic field from the passing nuclei, and 3) local parity violation caused by the chiral anomaly could lead to charge separation along the direction of the magnetic field. If that charge separation is observed and unambiguously linked to CME, it would at once demonstrate that chiral symmetry has been restored and would be the first observation of the chiral anomaly of QCD in action. By way of comparison, the charge separation expected from CME in heavy ion collisions is roughly 24 orders of magnitude larger than the charge separation modern neutron electric dipole moment searches are sensitive to.
Fig. 1. Top left: A simplistic sketch of charge separation driven by the strong magnetic field (1018 Gauss) generated in heavy ion collisions. Top right: A hydrodynamic calculation of charge separation as expressed by the variable H (see text) compared to data [12]. Bottom left: a schematic illustration of how a decaying clusters boosted more in the in-plane direction than the out-of-plane direction can mimic the charge separation anticipated from CME. Bottom right: a model calculation of the background effects that can be tuned to reproduce most of the observed charge separation signal.
Even though the charge separation is expected to be relatively large, it has been a challenge to separate that effect from other background sources that mimic CME. It’s important to note that the interaction region of each collision may contain a number of regions with more right handed quarks and a number of regions with more left handed quarks. For that reason the signal for CME will not necessarily be a global charge separation as illustrated in the figure but will be reflected in fluctuations. This makes the observation more challenging and a number of effects can mimic the signal. The most important effect is illustrated in the bottom panels of the figure which show that a background model based on flowing clusters can reproduce
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early measurements of fluctuations thought to be driven by charge separation [13]. 2. Results The observable most frequently used to search for CME is γS S ,OS ≡ cos(φα + φβ − 2ΨRP ) where charge separation would show up as a difference between cases where particle α and β are either of the samesign OS or opposite signs S S (Δγ) [14]. One can attempt to subtract off the largest known background 2 δ−γ source to γ by assuming factorization and taking H = κv1+κv where δ = cos(Δφ) is the raw two-particle 2 correlations, v2 is the elliptic flow anisotropy and κ is an unknown factor that in simulations has been shown √ to be somewhere between one and two [15]. Fig. 2 shows data from sNN = 7.7 GeV to 2.76 TeV for Δγ in the top panel and ΔH in the bottom panel [16]. We note that even after attempting to subtract off the v2 related background, a signal is still present. The signal is consistent with zero at 7.7 GeV, reaches a maximum near 20 GeV and then decreases as energy increases, becoming marginal or consistent with zero at 2.76 TeV.
Fig. 2. The energy dependence of charge separation corrected for v2 backgrounds (bottom) and uncorrected (top).
While the bottom right panel of Fig. 1 seems to suggest that the measurements are dominated by v2 related backgrounds, the bottom panel of Fig. 2 seems to suggest that v2 related backgrounds can’t explain the energy dependence of the signal. It would be interesting to see model calculations of the v2 related background at all of the energies available at RHIC and the LHC. Other ways to distinguish v2 related backgrounds have been explored including grouping events within a given centrality class by their estimated v2 (event-shape engineering) [7], selecting ultra-central collisions where any magnetic field is randomly oriented relative to the v2 axis [5], and by looking in p + A collisions where it is also thought that if a magnetic field exists, it will not be aligned with the v2 axis [4, 5, 6, 8]. Event-shape engineering has been carried out at the LHC [7]. The idea is that the magnetic field will not change within a given centrality class but the v2 can due to fluctuations; this naive expectation isn’t borne
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out in model calculations but a model to data comparison can be used to estimate how much of the signal is driven by v2 and how much by the magnetic field. This analysis finds that at least 80% of the signal at the LHC is from v2 related backgrounds and that when scaled by multiplicity, the signal is linear in v2 with a slope of approximately 0.8, pointing to zero signal at zero v2 . It will be interesting to see this analysis carried out on data at RHIC where the H variable seems to suggest the signal is strongest.
Fig. 3. Top panels: Event shape engineering from the LHC. Middle panels: p+Pb results from LHC compared to Pb+Pb and Au+Au from RHIC. Bottom panels: Model calculations (left) and data (right) from ultra-central U+U collisions.
The middle panels of Fig. 3 show data on p+Pb collisions at 5.02 TeV compared to Pb+Pb [4] collisions and Au+Au collisions from RHIC. The naive expectation is that any signal observed in p+Pb collisions must be driven by backgrounds. The observation is that the signal in p+Pb is as large as that in Pb+Pb and Au+Au. This similarity seems to suggest that perhaps all the data is driven by background. On the other hand, there is no known background model that would predict a similarity between Au+Au collisions at RHIC and p+Pb or Pb+Pb collisions at the LHC. This is because as multiplicity goes up, the measurement of the background should drop as one over the multiplicity. It appears that the data challenge both the CME based expectations and the background model based expectations. The bottom panels show data from ultra-central U+U collisions [5]. These collisions possess an appre-
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ciable v2 but since models show that the magnetic field becomes oriented randomly with respect to the v2 axis [17], no CME signal is expected. In a v2 driven background scenario, we expect Δγ to only reach zero when v2 reaches zero. The data however contradicts this scenario and drops to zero while a large v2 still persists. This is consistent with CME and contradicts the background models. This is the opposite of the conclusion one would naturally draw from the LHC data where the eventshape engineering data is consistent with a v2 driven background and contradicts CME. Although much new data has appeared, the situation remains murky.
Fig. 4. Charge separation data from RHIC including new p+Au measurements and model calculations. Δγ on the left has been scaled by N part and plotted vs N part while the data plotted on the right is equivalent to Δγ scaled by multiplicity and divided by v2 . This latter quantity is expected to be approximately flat as a function of centrality for v2 dominated background. The LHC slope of 0.8 refers to the slope inferred from eventshape engineering where Δγ at the LHC was found to exhibit a linear dependence on v2 pointing to zero at zero v2 , as would be expected purely from background. The Δγ results from p+Au and d+Au are strongly dependent on how the analysis is carried out, especially when scaling by v2 where the interpretation of v2 is still very unclear and the result can depend strongly on assumptions and analysis details.
While the data from p+Pb collisions at the LHC can be interpreted as supporting a background interpretation of the data, the data presented from RHIC leave a less clear interpretation. In the left panel of Fig. 4, results from U+U and p+Au are shown where short-range correlations have been subtracted off [5, 6]. The subtraction assumes the correlations can be described in terms of a pedestal, a Gaussian, and a short-range background contribution which is assumed to be short-range in both Δη and Δφ so that it is required to contribute a positive contribution to γ. In more central collisions, the short-range subtraction picks out mostly HBT-like correlations and leads to a small correction. In peripheral and p+Au collisions, the subtracted peak is wider and is likely an admixture of HBT and correlations between jet fragments. After removing this contribution, RHIC data on p+Au collisions are consistent with zero. More work should be done however on understanding the systematic uncertainties of the analysis in p+Au collisions. In the right panel of Fig. 4, a compilation of Au+Au, d+Au, and p+Au data is shown where the plotted quantity is equivalent to Δγ scaled by the multiplicity and divided by v2 . If the data are dominated by a v2 driven background, we expect the data to be a single flat line for all systems. The AMPT background simulations shown in the figure confirm this expectation. No subtraction has been applied to the data leaving a large signal in p+Au, d+Au, and peripheral Au+Au collisions. The large value for p+Au and d+Au show that results in those systems can vary a lot depending on how the analysis has been carried out and how v2 has been calculated. The interpretation of v2 in small systems is still unclear. We note that approaching central Au+Au collisions, the data sharply deviate from background expectations and become consistent with zero as expected from the decorrelation of the v2 axis and the magnetic field. The data and simulations in the figure however still lend themselves to contradicting conclusions. For example, one can draw the following conclusions: 1) the AMPT simulations show that background can account for most if not all of the signal, 2) the background explains the flatness of the Au+Au results except in the most central collisions where perhaps v2 is less well understood, 3) the data in central collisions are consistent with CME and contradict expectations from v2 related backgrounds, and 4) data from small systems can either be well above background expectations or consistent with zero depending on how the analysis is carried out. It’s
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clear that questions of interpretation still persist even after the inclusion of the findings presented at this conference.
Fig. 5. Left: RHIC and LHC data on the chiral magnetic wave vs centrality interval. Right: v2 and the projected magnetic field each normalized to unity at their maxima and plotted vs N part .
New analyses related to a predicted chiral magnetic wave (CMW) [18] were also presented at this conference [6, 8]. Of particular note were data on the CMW in p+Pb collisions at the LHC and in p+Au collisions at RHIC. Fig. 5 shows measurements of the slope of v1 for charged particles as a function of the charge asymmetry observed in the event. CMW predicts a non-zero slope as indicated by the data. We note however that whereas RHIC data goes to zero in peripheral and central collisions (as expected from the projected magnetic field shown in the right figure), LHC data remains large and non-zero for central and peripheral collisions (as expected for background from v2 ). Note that for the figure on the left, most central is on the left and for the figure on the right, most central is on the right. These trends seem to suggest the slopes are dominated by background at higher energies but perhaps more consistent with a CMW at lower energies. 3. Discussion The relationship of the CMW findings at RHIC compared to the LHC mirrors those of CME with LHC results appearing to favor a background interpretation and RHIC results appearing to favor a CMW interpretation. Fig. 6 shows a schematic diagram of key findings related to CME. The vertical axis represents system size from p+A collisions at the top to ultra central U+U collisions at the bottom. The horizontal axis shows the energy from the lowest RHIC energies to LHC energies. At 7.7 GeV, data are consistent with no CME. The CME signals (H in particular) exhibit a maximum in mid-central collisions near 20 GeV. Since the duration of the magnetic field is longer at lower energies, it’s plausible that a maximum would occur at some lower energy. As the energy increases above 20 GeV, the CME signal decreases until at the LHC, data appear to be most consistent with background. At full RHIC energy, the centrality dependenc of the data seems to follow the projected magnetic field (as expected from CME) rather than v2 as expected from background models; consistent with zero in p+A and ultra-central U+U even when v2 is still significant. Based on Fig. 6, one may be tempted to conclude that data at RHIC are dominated by the effects of CME but that those effects decrease with energy until they are negligible at the LHC. One can imagine that the duration of the magnetic field becomes so short at the LHC that it is negligible by the time quarks appear in the overlap region. One might find this explanation unconvincing however given that the centrality dependence of the data at RHIC is so similar to that at the LHC. It has also been observed that the Δη width of the signal is also the same. Are these coincidences? The former might be explained by the simple observation that the centrality dependence expected for the background is very similar to the centrality dependence expected for the signal; they both have a maximum in the same centrality range. One could
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Fig. 6. A schematic diagram of experimental findings related to CME. Results related to the chiral magnetic wave follow the same pattern.
also argue that the observed Δη width is a very natural width for many processes and that it is perhaps just coincidental. Given the success of the v2 related backgrounds to capture the general trends of the data and given the p+Pb findings from the LHC, one might also be tempted to conclude that the data at RHIC and the LHC is completely dominated by background and that any deviations between background models and data are just uninteresting details to be worked out. This conclusion however, neglects to explain why RHIC measurements in ultra-central A+A collisions are consistent with zero as expected from CME while LHC measurements are non-zero as expected from background. In addition, while background models seem to capture some of the centrality dependence, the observed energy dependence seems at odds with a background explanation. No known background model yet accounts for the wide range of observations. In addition, theoretical uncertainties allow orders-of-magnitude uncertainty in expectations for charge separation from CME. Given all of the above, what can be done to resolve these questions of interpretation? Fortunately there are steps that can be taken. An eventshape engineering analysis similar to the one carried out at the LHC needs to be done at RHIC. The v2 -background subtracted variable H needs to be analyzed in p+Pb collisions at the LHC. Charge separation should be analyzed in ultra-central collisions at the LHC. The energy dependence of background models should be analyzed and their predictions for ultra-central collisions should be scrutinized. Work needs to continue on refining predictions for CME. The most powerful way to distinguish between chiral effects and backgrounds, however, is to find a way to independently manipulate the magnetic field while keeping other variables fixed. This can be done by colliding isbaric nuclei. Simulations [19] indicate that collisions of 96 Zr+96 Zr and 96 Ru+96 Ru should lead to an approximately 20% difference in the component of the signal arising from CME. Such a program carried out at RHIC appears to have the potential to reduce the uncertainty on the portion of the charge separation arising from CME from 100% to plus or minus 7%. This appears to be the most unambigous way to resolve questions of interpretation.
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4. Conclusions A measurement of charge separation in heavy-ion collisions that can be unambiguously linked to the chiral magnetic effect would be of great interest to the wider physics community and would contribute significantly to the scientific impact and legacy of RHIC. Many measurements have been carried out to study charge separation in heavy-ion collisions that are generally in agreement with expectations from the CME while others, particularly at the LHC are in general agreement with expectations from background models and these models can also account for much of the RHIC data. In particular, at this conference results from p+A collisions, ultra-central collisions, and from event-shape-engineering were shown which followed this pattern. One must conclude therefore that based on our current understanding, backgrounds may account for all of the observed charge separation. Several experimental and theoretical steps can be take to try to improve our understanding of the contribution of the CME to charge separation in heavy-ion collisions. Some of these steps can be accomplished with exhisting data but the most unambiguous evidence linking the observed charge separation to the CME is likely to come from collisions of isobaric nuclei which should make it possible to ascertain the magnetic field dependence of the charge separation signal. It has been found that these collisions can reduce the uncertainty on the magnetic field dependent contribution from 100% to plus or minus 7%. Acknowledgements: The author would like to thank the conference organizers and the international advisory committee for the invitation to give this talk. The author is also indebted to those who presented talks and posters on this topic at this conference. The authors research is supported by the U.S. Department of Energy under contract DE-AC02-98CH10886. References [1] D. Kharzeev, R. D. Pisarski and M. H. G. Tytgat, Phys. Rev. Lett. 81, 512 (1998); D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A 803, 227 (2008); K. Fukushima, D. E. Kharzeev and H. J. Warringa, Phys. Rev. D 78, 074033 (2008). [2] D. E. Kharzeev, J. Liao, S. A. Voloshin and G. Wang, Prog. Part. Nucl. Phys. 88, 1 (2016); V. Skokov, P. Sorensen, V. Koch, S. Schlichting, J. Thomas, S. Voloshin, G. Wang and H. U. Yee, arXiv:1608.00982 [nucl-th]. [3] S. A. Voloshin, Phys. Rev. C 70, 057901 (2004). [4] V. Khachatryan et al. [CMS Collaboration], Phys. Rev. Lett. 118, 122301 (2017). [5] P. Tribedy [STAR Collaboration], arXiv:1704.03845 [nucl-ex]. [6] L. Wen [STAR Collaboration], these proceedings. [7] A. Dobrin [ALICE Collaboration], these proceedings. [8] Z. Tu [CMS Collaboration], these proceedings. [9] Q. Li et al., Nature Phys. 12, 550 (2016). [10] M. Mace, N. Mueller, S. Schlichting and S. Sharma, Phys. Rev. D 95, no. 3, 036023 (2017). [11] V. Skokov, A. Y. Illarionov and V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009). [12] S. Shi, Y. Jiang, E. Lilleskov, Y. Yin and J. Liao, arXiv:1704.05531 [nucl-th]; X. Guo, D. E. Kharzeev, X. G. Huang, W. T. Deng and Y. Hirono, arXiv:1704.05375 [nucl-th]. [13] S. Schlichting and S. Pratt, Phys. Rev. C 83, 014913 (2011). [14] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. 103, 251601 (2009). [15] A. Bzdak, V. Koch and J. Liao, Phys. Rev. C 83, 014905 (2011). [16] L. Adamczyk et al. [STAR Collaboration], Phys. Rev. Lett. 113, 052302 (2014); B. Abelev et al. [ALICE Collaboration], Phys. Rev. Lett. 110, no. 1, 012301 (2013). [17] S. Chatterjee and P. Tribedy, Phys. Rev. C 92, no. 1, 011902 (2015). [18] Y. Burnier, D. E. Kharzeev, J. Liao and H. U. Yee, Phys. Rev. Lett. 107, 052303 (2011). [19] X. G. Huang, W. T. Deng, G. L. Ma and G. Wang, arXiv:1704.04382 [nucl-th].