Progress on the experimental search for the chiral magnetic effect, the chiral vortical effect, and the chiral magnetic wave

Shou Qi-Ye; Zhao Jie; Xu Hao-Jie; Li Wei; Wang Gang; Tang Ai-Hong; Wang Fu-Qiang

doi:10.7498/aps.72.20230109

Abstract

In quantum chromodynamics, the interactions of quarks with the topological gluon field can lead to nonconservation of local parity (P) and conjugated parity (CP) , which provides a solution to the strong CP problem and a possibility to explain the asymmetry of matter-antimatter in the current universe. Under the action of a strong magnetic field, the nonconservation of P and CP can lead to the separation of particles according to their electric charges, which is called the chiral magnetic effect (CME). An observation of the CME-induced charge separation will confirm several fundamental properties of quantum chromodynamics (QCD), namely, approximate chiral symmetry restoration, topological charge fluctuation, and local parity violation. In relativistic heavy-ion collisions, there are other chiral anomalous effects similar to the CME, such as the chiral vortical effect (CVE) and the chiral magnetic wave (CMW). This review briefly summarizes the current progress of experimental research on the CME, CVE, and CMW in relativistic heavy-ion collisions.

Keywords:

Authors and contacts

1.
Key Laboratory of Nuclear Physics and Ion-beam Application, Ministry of Education, Institute of Modern Physics, Fudan University, Shanghai 200433, China
2.
Shanghai Research Center for Theoretical Nuclear Physics, National Natural Science Foundion of China, Fudan University, Shanghai 200438, China
3.
School of Science, Huzhou University, Huzhou 313000, China
4.
Department of Physics and Astronomy, Rice University, Houston 77005, USA
5.
Department of Physics and Astronomy, University of California, Los Angeles 90095, USA
6.
Department of Physics, Brookhaven National Laboratory, New York 11973, USA
7.
Department of Physics and Astronomy, Purdue University, West Lafayette IN 47907, USA

Corresponding author: Zhao Jie, jie_zhao@fudan.edu.cn ; Xu Hao-Jie, haojiexu@zjhu.edu.cn ; Li Wei, wl33@rice.edu ; Wang Gang, gwang@physics.ucla.edu ; Tang Ai-Hong, aihong@bnl.gov ; Wang Fu-Qiang, fqwang@purdue.edu

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12275053, 11975078, 12275082, 12035006, 12075085, 12147219), the Shanghai Rising-Star Program, China (Grant No. 20QA1401500), the National Key R&D Program of China (Grant No. 2022YFA1604900), and the U.S. Department of Energy (Grant Nos. DE-FG02-88ER40424, DE-AC02-98CH10886, DE-FG02-89ER40531, DE-SC0012910)

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Cited By

图 1 RHIC-STAR合作组于2009年左右对$ \gamma_{112} $关联函数的首次测量结果^[20,21]. 粗实线和虚线表示HIJING模型计算的三粒子关联背景贡献. 碰撞中心度从左到右增加; 0%对应于中心碰撞

Figure 1. First measurement of the $ \gamma_{112} $ correlator from RHIC-STAR experiment around 2009^[20,21]. The thick solid (Au+Au) and dashed (Cu+Cu) lines represent HIJING calculations of the contributions from three-particle correlations. Collision centrality increases from left to right. 0% corresponds to the most central collisions

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图 2 RHIC-STAR 7.7—200 GeV Au+Au以及LHC-ALICE 2.76 TeV Pb+Pb碰撞中$ \gamma_{112} $关联函数的中心度依赖性^[20-23]. 灰色线是MEVSIM模型估计的与电荷无关的背景贡献

Figure 2. $ \gamma_{112} $ correlator as a function of centrality for Au+Au collisions at 7.7–200 GeV from RHIC-STAR, and for Pb+Pb collisions at 2.76 TeV from LHC-ALICE^[20-23]. Gray curves are the charge-independent results from MEVSIM calculations

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图 3 RHIC-STAR 7.7—200 GeV Au+Au以及LHC-ALICE 2.76 TeV Pb+Pb碰撞中$ \kappa_{112} $关联函数的中心度依赖性^[20-23]. 灰色粗实线是AMPT模型估计的与CME无关的背景贡献^[28-30]

Figure 3. $ \kappa_{112} $ correlator as a function of centrality for Au+Au collisions at 7.7–200 GeV from RHIC-STAR, and for Pb+Pb collisions at 2.76 TeV from LHC-ALICE^[20-23]. Gray curves are the non-CME background estimations from AMPT^[28-30]

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图 4 (a) LHC-CMS合作组在5.02 TeV p+Pb和 Pb+Pb碰撞中测量的$ \gamma_{112} $关联函数随多重数的依赖性^[32]; (b) RHIC-STAR合作组测量的小系统p+Au, d+Au碰撞中$ \gamma_{112} $关联函数与Au+Au碰撞结果的对比^[33]. 图中的灰色标记代表实验测量的系统误差

Figure 4. (a) $ \gamma_{112} $ as a function of N in p+Pb and Pb+Pb collisions at 5.02 TeV from LHC-CMS collaboration^[32]; (b)$ \gamma_{112} $ as a function of N in p+Au, d+Au and Au+Au collisions at 200 GeV from RHIC-STAR collaboration^[33]. Systematic uncertainties are indicated by the shaded regions

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图 5 RHIC-STAR合作组通过事件形状筛选方法在200 GeV Au+Au碰撞中测量Δ关联函数与每个事件椭球形状观测量$ v_2^{\rm obs} $的关系^[35]

Figure 5. Charge multiplicity asymmetry correlations (Δ) as a function of event-by-event $ v_2^{\rm obs} $ from 200 GeV Au+Au collisions^[35]

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图 6 LHC-ALICE合作组(a)通过事件形状筛选方法在2.76 TeV Pb+Pb碰撞中测量的按粒子多重数缩放的$ \Delta\gamma_{112} $关联函数($\Delta\gamma_{112} \cdot {\rm{d}}N_{\rm ch}/{\rm{d}}\eta$)在不同中心度下随$ v_{2} $的关系, (b)通过事件形状筛选方法比较关联函数以及不同模型下磁场强度和$ v_{2} $的关系, 提取的手征磁效应的贡献^[37]

Figure 6. (a) Charge-particle density scaled correlator ($\Delta\gamma_{112} \cdot {\rm{d}}N_{\rm ch}/{\rm{d}}\eta$) as a function of $ v_{2} $ for shape selected events in 2.76 TeV Pb+Pb collisions from LHC-ALICE; (b) extracted CME fraction ($ f_{\rm CME} $) by comparing the correlator and magnetic field dependence on $ v_{2} $ with different models^[37]

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图 7 LHC-CMS合作组(a)通过事件形状筛选方法在5.02 TeV Pb+Pb碰撞中测量的按$ \Delta\delta $缩放的关联函数($ \Delta\gamma_{112}/\Delta\delta $)在不同中心度下随$ v_{2} $的关系, (b)通过事件形状筛选方法研究关联函数在$ v_{2}=0 $的结果, 提取的Pb+Pb以及p+Pb碰撞中手征磁效应的贡献^[38]

Figure 7. (a) Scaled correlator, $ \Delta\gamma_{112}/\Delta\delta $, as a function of $ v_{2} $ evaluated with the ESE method, for different multiplicity ranges in Pb+Pb collisions from LHC-CMS; (b) extracted CME contributions, $ v_{2} $-independent component, in Pb+Pb and p+Pb collisions^[38]

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图 8 RHIC-STAR合作组(a)通过事件形状筛选方法选择的不同$ q_{2} $事件(A: large $ q_{2} $, B: small $ q_{2} $)中$ \Delta\gamma_{112} $关联函数与不变质量的关系, (b) A-B与无事件形状筛选的测量结果的比较^[41]

Figure 8. (a) $ \Delta\gamma_{112} $ as functions of mass in different $ q_{2} $ events (A: large $ q_{2} $, B: small $ q_{2} $) using the event shape selection method; (b) inclusive measurement compared with the A-B^[41]

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图 9 RHIC-STAR合作组200 GeV Au+Au实验中通过比较旁观者平面和参与者平面测量结果而提取的手征磁效应信号百分比(a), 以及其信号大小(b)^[43]

Figure 9. (a) Extracted CME fraction ($ f_{\rm CME} $) and (b) CME signal ($ \Delta\gamma_{\rm CME} $) using the spectator and participant planes method from RHIC-STAR^[43]

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图 10 RHIC-STAR合作组200 GeV 同位异素核Ru+Ru和Zr+Zr实验中的关联函数结果的比较^[44]

Figure 10. Ratio of different observables between 200 GeV isobar Ru+Ru and Zr+Zr collisions from RHIC-STAR^[44]

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图 11 玩具模型显示$ r_{\mathrm{rest}} $和$R_{\rm{B}}$在不同CME强度下($ a_1 $)和共振态粒子椭圆流的关系^[55]

Figure 11. $ r_{\mathrm{rest}} $ (Upper) and $ R_{\rm{B}} $ (Bottom) as functions of resonance $ v_{2} $ with different CME strength ($ a_1 $) using the Toy model simulation^[55]

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图 12 基于EBE-AVFD模拟数据计算的$ \Delta \gamma_{112} $ (a), $ \sigma^{-1}_{R2} $ ($ \sigma_{R2} $为R关联函数宽度) (c) 和 $ r_{\mathrm{lab}} $ (e) 关于$ n_{5}/s $的函数. $ n_{5}/s $在AVFD里表示原始植入的CME强度. 该计算是针对30%—40% 中心度同位异素$ \sqrt{s_{\rm NN}} = 200 $ GeV核核对撞. (b), (d), (f)观测量在Ru+Ru对Zr+Zr比值^[49]

Figure 12. $ \Delta \gamma_{112} $ (a), $ \sigma^{-1}_{R2} $ (c) and $ r_{\mathrm{lab}} $ (e) as functions of $ n_{5}/s $ in EBE-AVFD model simulation. (b), (d), (f) Corresponding ratios between Ru+Ru and Zr+Zr^[49]

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图 13 (a) STAR实验200 GeV Au+Au对撞中$ v_2^\pm $-$ A_{\rm ch} $的关系和(b)$ \Delta v_2 $-$ A_{\rm ch} $的关系^[73]; (c) ALICE实验2.76 TeV Pb+ Pb对撞中$ \Delta v_2 $-$ A_{\rm ch} $的关系 ^[74]

Figure 13. (a)$ v_2^\pm $, (b) $ \Delta v_2 $ as functions of $ A_{\rm ch} $ in 200 GeV Au+Au collisions from STAR ^[73]; (c) $ \Delta v_2 $ as functions of $ A_{\rm ch} $ in 2.76 TeV Pb+Pb collisions from ALICE^[74]

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图 14 RHIC和LHC不同碰撞系统和能量下$ \Delta v_2 $-$ A_{\rm ch} $斜率的中心度依赖^[73,74]

Figure 14. Slopes of the $ \Delta v_2 $-$ A_{\rm ch} $ as functions of centrality in different collisions systems and energies from RHIC and LHC^[73,74]

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图 15 (a) STAR实验200 GeVAu+Au对撞和(b) CMS实验5.02 TeV Pb+Pb对撞中观测到的$ r_2 $、$ r_3 $斜率, 在误差范围内基本一致^[76,77]

Figure 15. Measured $ r_2 $, $ r_3 $ slopes as functions of centrality in 200 GeV Au+Au collisions from STAR (a), and in 5.02 TeV Pb+Pb collisions from CMS (b), within the uncertainties, the slopes of $ r_2 $, $ r_3 $ are consistent with each other^[76,77]

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图 16 (a) STAR实验200 GeVAu+Au、U+U、p+Au和d+Au对撞和(b) CMS实验5.02 TeV Pb+Pb和p+Pb对撞中观测到的$ r_2 $斜率^[76,77]

Figure 16. Measured $ r_2 $ slopes as functions of multiplicity (a) in small system collisions of 200 GeV p+A, d+Au compared with Au+Au and U+U from STAR, and (b) in 5.02 TeV p+Pb and Pb+Pb collisions from CMS^[76,77]

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图 17 ALICE实验利用“事件形状筛选”方法得到(a)观测量和$ v_2 $显著的线性关联, 继而提取出(b) CMW信号在观测量中的占比^[84]

Figure 17. Covariance of $ \Delta v_2 $ and $ A_{\rm ch} $ ($ \Delta \rm{Int.\; Cov.} $) as functions of $ v_2 $ from the ESE method (a) and (b) the corresponding extracted CMW fraction^[84]

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图 18 (a) STAR实验200 GeVAu+Au对撞和(b) ALICE实验5.02 TeV Pb+Pb对撞中可鉴别强子π, K, p的$ r_2 $斜率, π和K的结果在误差范围内基本一致^[76,84]

Figure 18. Measured $ r_2 $ slopes of identified particles (π, K, p) as functions of centrality in (a) 200 GeV Au+Au collisions from STAR, and (b) in 5.02 TeV Pb+Pb collisions from ALICE^[76,84]

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map

[1]	Belavin A A, Polyakov A M, Schwartz A S, Tyupkin Y S 1975 Phys. Lett. B 59 85 Google Scholar
[2]	Callan C G, Dashen R F, Gross D J 1976 Phys. Lett. B 63 334 Google Scholar
[3]	Hooft G T 1976 Phys. Rev. D 14 3432
[4]	Schäfer T, Shuryak E V 1998 Rev. Mod. Phys. 70 323 Google Scholar
[5]	Kharzeev D E, Levin E M. 2015 Phys. Rev. Lett. 114 242001 Google Scholar
[6]	Adler S L 1969 Phys. Rev. 177 2426 Google Scholar
[7]	Bell J S, Jackiw R 1969 Nuovo Cim. A 60 74
[8]	Kharzeev D E 2006 Phys. Lett. B 633 260 Google Scholar
[9]	Kharzeev D E, McLerran L D, Warringa H J 2008 Nucl. Phys. A2008 227
[10]	Li Q, Kharzeev D E, Zhang C, Huang Y, Pletikosic I, Fedorov A V, Zhong R D, Schneeloch J A, Gu G D, Valla T 2016 Nat. Phys. 12 550 Google Scholar
[11]	Xiong J, Kushwaha S K, Liang T, Krizan J W, Hirschberger M, Wang W, Cava R J, Ong N P 2015 Science 350 413 Google Scholar
[12]	Li C Z, Wang L X, Liu H W, Wang J, Liao Z M, Yu D P 2015 Nat. Commun. 6 10137 Google Scholar
[13]	Long Y J, Wang P P, Chen D, Yang Z H, Liang H, Xue M Q, Weng H M, Fang Z, Dai X, Chen G F, Huang X C, Zhao L X 2015 Phys. Rev. X 5 031023
[14]	Kharzeev D E, Liao J F, Voloshin S A, Wang G 2016 Prog. Part. Nucl. Phys. 88 1 Google Scholar
[15]	Zhao J 2018 Int. J. Mod. Phys. A 33 1830010 Google Scholar
[16]	Zhao J, Tu Z, Wang F Q 2018 Nucl. Phys. Rev. 35 225
[17]	Zhao J, Wang F Q 2019 Prog. Part. Nucl. Phys. 107 200 Google Scholar
[18]	Li W, Wang G 2020 Ann. Rev. Nucl. Part. Sci. 70 293 Google Scholar
[19]	Kharzeev D E, Liao J F 2021 Nat. Rev. Phys. 3 55
[20]	Abelev B I, Aggarwal M M, Ahammed Z, et al. 2009 Phys. Rev. Lett. 103 251601 Google Scholar
[21]	Abelev B I, Aggarwal M M, Ahammed Z, et al. 2010 Phys. Rev. C 81 054908 Google Scholar
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[23]	Abelev B I, Adam J , Adamova D, et al. 2013 Phys. Rev. Lett. 110 012301 Google Scholar
[24]	Voloshin S A 2004 Phys. Rev. C 70 057901 Google Scholar
[25]	Pratt S, Schlichting S, Gavin S 2011 Phys. Rev. C 84 024909 Google Scholar
[26]	Bzdak A, Koch V, Liao J F 2013 Lect. Notes Phys. 871 503
[27]	Schlichting S, Pratt S 2011 Phys. Rev. C 83 014913 Google Scholar
[28]	Lin Z W, Ko C M, Li B A, Zhang B, Pal S 2005 Phys. Rev. C 72 064901 Google Scholar
[29]	Lin Z W 2014 Phys. Rev. C 90 014904 Google Scholar
[30]	Lin Z W, Zheng L 2021 Nucl. Sci. Tech. 32 113 Google Scholar
[31]	Zhang H X, Xiao Y X, Kang J W, Zhang B W 2022 Nucl. Sci. Tech. 33 150 Google Scholar
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[34]	Zhao J, Feng Y C, Li H L, Wang F Q 2020 Phys. Rev. C 101 034912 Google Scholar
[35]	Adamczyk L, et al. 2014 Phys. Rev. C 89 044908 Google Scholar
[36]	Tu B In Poster Given at 25th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2015) Kobe, Japan, September 27-October 3, 2015
[37]	Acharya S, et al. 2018 Phys. Lett. B 777 151 Google Scholar
[38]	Sirunyan A M, et al. 2018 Phys. Rev. C 97 044912 Google Scholar
[39]	Wang F Q, Zhao J 2017 Phys. Rev. C 95 051901 (R Google Scholar
[40]	Zhao J, Li H L, Wang F Q 2019 Eur. Phys. J. C 79 168 Google Scholar
[41]	Abdallah M S, et al. 2022 Phys. Rev. C 106 034908 Google Scholar
[42]	Xu H J, Zhao J, Wang X B, Li H L, Lin Z W, Shen C W, Wang F Q 2018 Chin. Phys. C 42 084103 Google Scholar
[43]	Abdallah M S, et al. 2022 Phys. Rev. Lett. 128 092301 Google Scholar
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