Electromagnetic field effects and anomalous chiral phenomena in heavy-ion collisions at intermediate and high energy

Zhao Xin-Li; Ma Guo-Liang; Ma Yu-Gang

doi:10.7498/aps.72.20230245

Abstract

Heavy-ion collisions can produce high-temperature and high-density quantum chromodynamics (QCD) matter under extremely strong electromagnetic fields, which triggers off many important anomalous chiral phenomena, such as the chiral magnetic effect and chiral magnetic wave. The anomalous chiral phenomena can help to find the evidence of $\cal{CP}$ symmetry breaking in the strong interaction, deepen the understanding of the QCD vacuum fluctuations, and disclose the mystery of asymmetry of antimatter-matter in the universe. In this paper, firstly, the magnetic fields are investigated for small and large colliding systems at relativistic heavy ion collider (RHIC) and large hadron collider (LHC). These studies indicate that collision energy and initial nucleon structure have significant effects on magnetic fields. And, the lifetimes of magnetic field in different media are very different in heavy-ion collisions. Then, in order to study the chiral magnetic effect, some experimental observables are studied by using a multi-phase transport model without or with different strengths of the chiral magnetic effect. For small systems, if QGP exists, the chiral magnetic effect could be observed in the peripheral collisions. For isobaric collisions, the correlators with respect to the spectator plane can imply a much cleaner signal of chiral magnetic effect than that with respect to the participant plane. Our results support that the strength of chiral magnetic effect may be absent or small in isobaric collisions. Next, some new strategies are applied to study the chiral magnetic wave. Moreover, a novel mechanism for the electric quadrupole moment can also explain the charge-dependent elliptic flow of pions generated by the chiral magnetic wave. In addition, some interesting phenomena also occur, owing to the magnetic field in heavy-ion collisions at intermediate energy. The directed flow and elliptic flow of photons have no effect on magnetic field at $p_{\rm T}<25$ GeV. However, because of the magnetic field, the directed flow of photons decreases and the elliptic flow of photons increases at $p_{\rm T}>25$ GeV. Besides, the magnetic field has a significant effect on giant dipole resonance, i.e. the magnetic field increases the angular momentum and enhances some observables of the giant dipole resonance spectrum. In conclusion, magnetic field plays a key role in heavy-ion collisions at both high energy and intermediate energy. It provides an unprecedented opportunity for studying the microscopic laws of nuclear physics. However, there are still many unsolved problems that need further studying in the future.

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 Foundation of China, Fudan University, Shanghai 200438, China

Corresponding author: Ma Guo-Liang, glma@fudan.edu.cn ; Ma Yu-Gang, mayugang@fudan.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1604900), the National Natural Science Foundation of China (Grant Nos. 12147101, 11890714, 11835002, 11961131011, 11421505, 12105054), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB34030000), and the Major Project of Basic and Applied Basic Research of Guangdong Province, China (Grant No. 2020B0301030008)

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Cited By

图 1 自然界中的磁场强度

Figure 1. Magnetic field strengths in nature

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图 2 LHC能量下(a) $ \rm Pb+Pb $碰撞和(b) ${\rm{p}}\rm+Pb$碰撞中的电磁场与碰撞参数b的关系

Figure 2. Dependences of electromagnetic field on the impact parameter b for (a) $ \rm Pb+Pb $ collisions and (b) ${\rm{p}}\rm+Pb$ collisions at LHC energies

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图 3 RHIC能量下形变old case1情况下(a) ${\rm{Ru}}+{\rm{Ru}}$碰撞和(b)$ \rm Zr+Zr $碰撞中的电磁场与碰撞参数b的依赖关系; (c)两个同质异位素碰撞中磁场的相对差异与碰撞参数b的依赖关系

Figure 3. Dependences of electromagnetic fields on the impact parameter b for (a) $ \rm Ru+Ru $ collisions and (b) $ \rm Zr+Zr $ collisions at RHIC energy. (c) Dependence of the relative ratio between the magnetic fields in the two isobaric collisions on the impact parameter b

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图 4 RHIC能量下不对称碰撞系统中磁场对碰撞参数b的依赖性

Figure 4. Dependences of the magnetic field on impact parameter b for the asymmetric collisions at RHIC energy

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图 5 扩展的KMW模型给出的$ \rm Au+Au $碰撞中磁场强度随时间的演化

Figure 5. Evolution of the magnetic fields in $ \rm Au+Au $ collisions using the extended KMW model

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图 6 CME示意图, 图片来自文献[35]

Figure 6. Schematic diagram of CME, which is taken from Ref. [35]

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图 7 RHIC能量下$ \rm Au+Au $碰撞中, (a)不同初始电荷分离强度下电荷方位角关联与碰撞中心度的依赖关系, (b) 10%的初始电荷分离强度下, AMPT模型不同碰撞阶段的电荷分离百分比与碰撞中心度的依赖关系

Figure 7. (a) Centrality dependence of $ \rm cos(\phi_{\alpha}+\phi_{\beta}) $ with the different fractions of charge separation in $ \rm Au+Au $ collisions at 200 GeV; (b) centrality dependence of charge separation percentage for different evolution stages in $ \rm Au+Au $ collisions at the RHIC energy, for 10% initial charge separation

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图 8 在RHIC能量下$ \rm Au+Au $碰撞中部分子相末态中CME粒子的分布, 其中(a) $ \sigma = 0 $ mb; (b)$ \sigma = 10 $ mb. (c) 10%的初始局域电荷分离强度下关联$ \rm cos(\phi_{\alpha}+\phi_{\beta}) $对碰撞中心度的依赖性

Figure 8. Transverse spatial distribution of CME particles in the final partonic state in $ \rm Au+Au $ collisions at the RHIC energy, (a) for 0 mb and (b) for 10 mb. (c) Centrality dependence of the azimuthal correlation $ \rm cos(\phi_{\alpha}+\phi_{\beta}) $ with 10% of the initial local charge separation

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图 9 LHC能量下$ \rm Pb+Pb $碰撞中, (a)电荷方位角关联γ与碰撞中心度的依赖关系, 以及(b)30%—50%中心度下, 电荷方位角关联γ与横动量$ p_{\rm T} $的依赖关系

Figure 9. (a) Centrality dependence of the charge azimuthal correlation γ in $ \rm Pb+Pb $ collisions at LHC energy; (b) transverse momentum $ p_{\rm T} $ dependence of the charge azimuthal correlation γ for 30%–50% centrality bin in $ \rm Pb+Pb $ collisions at the LHC energy

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图 10 RHIC能量下$ \rm Au+Au $碰撞30%—50%中心度中, 关联γ和$ \Delta\gamma $对初始电荷分离强度的依赖性

Figure 10. Dependences of the correlations γ and $ \Delta\gamma $ on the initial charge separation percentage in the 30%–50% centrality bin of $ \rm Au+Au $ collisions at the RHIC energy

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图 11 (a) CMS合作组测量的在LHC能量下${\rm{p}}\rm+Pb$和$ \rm Pb+Pb $碰撞中三粒子方位角关联对$ N_{\rm track} $的依赖性^[61]; (b)不同能量和小系统碰撞下磁场方位角关联对$ N_{\rm track} $的依赖性

Figure 11. (a) $ N_{\rm track} $ dependences of the three-particle azimuthal correlations in ${\rm{p}}\rm+Pb$ and $ \rm Pb+Pb $ collisions at the LHC energy measured by the CMS Collaboration; (b) $ N_{\rm track} $ dependences of correlation between the magnetic field and the event plane for small collisions at different energies

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图 12 RHIC能量的同质异位素碰撞中, (a) old case1的同质异位素碰撞中粒子分布比; (b)$ S=N_{\rm part}\times\Delta\gamma $与中心度的依赖关系; (c) S的相对比值与中心度的依赖关系

Figure 12. (a) Ratio of multiplicity distribution between two isobar collisions for the deformation old case1; (b) centrality dependence of $ S=N_{\rm part}\times\Delta\gamma $; (c) centrality dependence of the relative ratio of S

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图 13 RHIC能量的同质异位素碰撞中, (a)方位角关联及其相对比值与中心度的依赖关系; (b)$ H=\gamma^{\rm CME}-\gamma^{\rm no\; CME} $及其相对比值与中心度的依赖关系; (c)初始电荷分离强度和末态电荷分离强度及其相对比值对碰撞参数b的依赖关系

Figure 13. In isobar collisions at the RHIC energy: (a) The centrality dependence of azimuthal correlation and its relative ratio; (b) the centrality dependence of $ H=\gamma^{\rm CME}-\gamma^{\rm no\; CME} $ and its relative ratio; (c) the impact parameter b dependence of initial charge separation strength and final state charge separation strength and its relative ratios

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图 14 RHIC能量的同质异位素碰撞中, (a)与$ \varPsi_{2}^{\rm PP} $有关的关联的相对比值与中心度的依赖关系; (b)与$ \varPsi_{2}^{\rm SP} $有关的关联的相对比值与中心度的依赖关系

Figure 14. In isobar collisions at the RHIC energy, (a) centrality dependence of the relative ratios of the correlations related to $ \varPsi_{2}^{\rm PP} $; (b) centrality dependence of the relative ratios of the correlations related to $ \varPsi_{2}^{\rm SP} $

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图 15 RHIC能量的同质异位素碰撞中不同电荷分离强度下, (a)带电粒子分布比值, (b)平均带电粒子比值与中心度的依赖关系以及(c)$ v_2 $比值与中心度的依赖关系与实验结果的对比

Figure 15. (a) The charged particle multiplicity distribution ratio, (b) the centrality dependence of average charged particle ratio, and (c) the centrality dependence of $ v_2 $ ratio in isotopic collisions for different charge separation strengths at the RHIC energy, in comparison with the STAR data

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图 16 RHIC能量的同质异位素碰撞中$ \Delta\gamma $及其比值与中心度的依赖关系

Figure 16. Centrality dependence of $ \Delta\gamma $ and its ratio in isobar collisions at the RHIC energy

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图 17 RHIC能量的同质异位素碰撞中, 0—5%中心度中(a)$v_2\{2\}$及(b)其比值和20%—50%中心度中(c) $ v_{2}\{2\} $及(d)其比值与碰撞能量$ \sqrt{s} $的依赖关系

Figure 17. Collision energy $ \sqrt{s} $ dependence of (a) $ v_{2}\{2\} $ and (b) its ratio in 0–5% centrality bin, and collision energy $ \sqrt {s} $ dependence of (c) $v_2\{2\}$ and (d) its ratio in 20%–50% centrality bin (lower panel) in isobar collisions at the RHIC energy

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图 18 手征磁波(CMW)示意图, 图片来自文献[35]

Figure 18. Schematic diagram of chiral magnetic wave (CMW), which is taken from Ref. [35]

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图 19 RHIC能量30%—40%中心度$ \rm Au+Au $碰撞中, (a)初态部分子态的3%初始四极矩强度在横平面的净电荷密度分布; (b)不同初态部分子四极矩强度下斜率参数对中心度的依赖性

Figure 19. (a) Net charge density distribution in the transverse plane for the 3% initial quadrupole charge separation for 30%–40% centrality bin in $ \rm Au + Au $ collisions at the RHIC energy; (b) centrality dependence of the slope parameter for different strengths of initial quadrupole charge separation

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图 20 (a) RHIC能量碰撞参数$ b = 10 $ fm下$ \rm Au+Au $碰撞中$e^2\langle {\boldsymbol{E}} \cdot {\boldsymbol{B}}\rangle$在横平面上的分布; (b)不同计算方法得出的$ \langle {\boldsymbol{E}}\cdot{\boldsymbol{ B}}\rangle $在$ t = 0 $时在$ y < 0 $ fm的横向平面内的分区平均密度和斜率参数的碰撞中心度依赖性

Figure 20. (a) Spatial distributions of $ e^2\langle {\boldsymbol{E}} \cdot {\boldsymbol{B}}\rangle $ in the transverse plane at $ t = 0 $ for $ b = 10 $ fm in $ \rm Au+Au $ collisions at the RHIC energy, where the unit is $ m_\pi^4 $; (b) zone-averaged density of $ \langle {\boldsymbol{E}} \cdot {\boldsymbol{B}}\rangle $ from different calculation methods (open symbols) at $ t = 0 $ in the transverse plane of $ y < 0 $ fm and the slope parameter (red filled symbol) as functions of $ N_{{\rm{part}}} $ in $ \rm Au+Au $ collisions at the RHIC energy

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图 21 (a)$ A_{\rm ch}-\Delta v_2 $的斜率与$ \left < v_2 \right > $的依赖关系; (b)积分的三粒子关联的差与$ \left < v_2 \right > $的依赖关系

Figure 21. (a)$ \left < v_2 \right > $ dependence of the slope of $ A_{\rm ch}-\Delta v_2 $; (b)$ \left < v_2 \right > $ dependence of the difference of the integrated three-particle correlator

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图 22 关联$ W_{2(3)} $与$ \Delta v_2 $的依赖关系, (a)四极矩为零的情况; (b)10%的四极矩; (c)不同类型的5%的四极矩

Figure 22. $ \Delta v_2 $ dependence of the correlation $ W_{2(3)} $, (a) the case of zero quadrupole; (b) the case of quadrupole of 10%; (c) different types of cases of quadrupole of 5%

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图 23 40 MeV的$ \rm N+Pb $碰撞中光子的定向流$ v_1 $和椭圆流$ v_2 $与光子的横动量$ p_{\rm T} $的关系

Figure 23. Direct flow $ v_1 $ and elliptical flow $ v_2 $ as functions of $ p_{\rm T} $ of photons for $ \rm N+Pb $ collisions at 40 MeV

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图 24 $\rm {}^{16}O+{}^{40}Ca$碰撞在无磁场和有磁场的情况下, GDR光谱的(a)峰值能量, (b)峰值强度和(c)光谱宽度与入射能量的关系

Figure 24. (a) Peak energy, (b) peak intensity, and (c) spectral width of the GDR spectrum as functions of incident energy for $\rm {}^{16}O+ {}^{40}Ca$ collisions in the absence and presence of the magnetic field

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图 25 $ \rm ^{16}O+^{40}Ca $碰撞在无磁场和有磁场的情况下, (a)温度和(b)角动量$ J_y $与入射能量的关系

Figure 25. (a) Temperature and (b) angular momentum $ J_y $ as functions of the incident energy for $ \rm ^{16}O+^{40}Ca $ collisions in the absence and presence of the magnetic field

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