Coherent photons induced high energy reactions in ultraperipheral heavy ion collisions

Pu Shi; Xiao Bo-Wen; Zhou Jian; Zhou Ya-Jin

doi:10.7498/aps.72.20230074

Abstract

We review the recent progress in the studies of coherent photons induced high energy reactions in ultraperipheral heavy ion collisions. The strong electromagnetic field created by a fast moving charged heavy ion can be effectively viewed as a flux of quasi-real coherent photons. In this paper, we mainly discuss two different type processes that coherent photons take part in: lepton pair production via photon fusion and diffractive vector meson production in UPCs. We focus on investigating the impact parameter dependent effect and the final state soft radiation effect. On the other hand, a series of recent work have revealed that coherent photons are highly linearly polarized with its polarization vector being parallel to its transverse momentum. It has been shown that the linearly polarized photons can lead to $\cos 4\phi$ azimuthal asymmetries in di-lepton production. This theoretical predication soon has been confirmed by the STAR measurement. With this new development from both theory and experiment sides, the linearly polarized photons provide a new experimental avenue to explore novel QCD phenomenology. For example, the linearly polarized photons can give rise to various different azimuthal asymmetries in diffractive vector meson production. These observables provide us unique chance to study two source interference effect in high energy scatterings, Coulomb-Nuclear interference effect as well as extracting gluon Wigner distribution. We will discuss these novel phenomenology studies and the possible future developments.

Keywords:

Authors and contacts

1.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
2.
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
3.
Key Laboratory of Particle Physics and Particle Irradiation, Ministry of Education, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China

Corresponding author: Pu Shi, shipu@ustc.edu.cn ; Xiao Bo-Wen, xiaobowen@cuhk.edu.cn ; Zhou Jian, jzhou@sdu.edu.cn ; Zhou Ya-Jin, zhouyj@sdu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175118, 12075235, 12135011) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2020MA098)

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References

[1]	Skokov V, Illarionov A Y, Toneev V 2009 Int. J. Mod. Phys. A 24 5925 Google Scholar
[2]	Bzdak A, Skokov V 2012 Phys. Lett. B 710 171 Google Scholar
[3]	Deng W T, Huang X G 2012 Phys. Rev. C 85 044907 Google Scholar
[4]	Roy V, Pu S 2015 Phys. Rev. C 92 064902 Google Scholar
[5]	Pu S, Roy V, Rezzolla L, Rischke D H 2016 Phys. Rev. D 93 074022 Google Scholar
[6]	ATLAS Collaboration 2017 Nature Phys. 13 852 Google Scholar
[7]	STAR Collaboration 2021 Phys. Rev. Lett. 127 052302 Google Scholar
[8]	Zha W M, Brandenburg J D, Tang Z B, Xu Z B 2020 Phys. Lett. B 800 135089 Google Scholar
[9]	Breit G, Wheeler J A 1934 Phys. Rev. 46 1087 Google Scholar
[10]	Hattori K, Itakura K 2013 Annals Phys. 330 23 Google Scholar
[11]	Hattori K, Itakura K 2013 Annals Phys. 334 58 Google Scholar
[12]	Hattori K, Taya H, Yoshida S 2021 JHEP 01 093
[13]	Hattori K, Itakura K 2022 Annals Phys. 446 169114 Google Scholar
[14]	Adler S L 1971 Annals Phys. 67 599 Google Scholar
[15]	Jackiw R, Kabat D N, Ortiz M 1992 Phys. Lett. B 277 148 Google Scholar
[16]	Bethe H A, Maximon L C 1954 Phys. Rev. 93 768 Google Scholar
[17]	Ivanov D, Melnikov K 1998 Phys. Rev. D 57 4025 Google Scholar
[18]	Tuchin K 2009 Phys. Rev. D 80 093006 Google Scholar
[19]	Baltz A J, McLerran L D 1998 Phys. Rev. C 58 1679 Google Scholar
[20]	Baltz A J 2003 Phys. Rev. C 68 034906 Google Scholar
[21]	Lee R N, Milstein A I 2000 Phys. Rev. A 61 032103 Google Scholar
[22]	Baltz A J 2008 Phys. Rev. Lett. 100 062302 Google Scholar
[23]	Zha W M, Tang Z B 2021 JHEP 08 083
[24]	Knapen S, Lin T Y and Lou H K, Melia T 2017 Phys. Rev. Lett. 118 171801 Google Scholar
[25]	Xu I, Lewis N, Wang X F, Brandenburg J D, Ruan L J 2022 arXiv: 2211.02132[hep-ex]
[26]	The DELPHI Collaboration 2004 Eur. Phys. J. C 35 159 Google Scholar
[27]	ATLAS Collaboration 2022 arXiv: 2204.13478[hep-ex]
[28]	The CMS Collaboration 2019 Phys. Lett. B 797 134826 Google Scholar
[29]	Ellis J, Mavromatos N E, You T 2017 Phys. Rev. Lett. 118 261802 Google Scholar
[30]	STAR Collaboration 2018 Phys. Rev. Lett. 121 132301 Google Scholar
[31]	ATLAS Collaboration 2018 Phys. Rev. Lett. 121 212301 Google Scholar
[32]	CMS Collaboration 2021 Phys. Rev. Lett. 127 122001 Google Scholar
[33]	Klein S R, Nystrand J, Seger J, Gorbunov Y, Butterworth J 2017 Comput. Phys. Commun. 212 258 Google Scholar
[34]	Vidovic M, Greiner M, Best C, Soff G 1993 Phys. Rev. C 47 2308
[35]	Hencken K, Trautmann D, Baur G 1995 Phys. Rev. A 51 1874 Google Scholar
[36]	Hencken K, Baur G, Trautmann D 2004 Phys. Rev. C 69 054902 Google Scholar
[37]	Zha W, Ruan L, Tang Z, Xu Z, Yang S 2018 Phys. Lett. B 781 182 Google Scholar
[38]	Brandenburg J D, Li W, Ruan L J, Tang Z B, Xu Z B, Yang S, Zha W M 2020 arXiv: 2006.07365 [hep-ph]
[39]	Brandenburg J D, Zha W M, Xu Z B 2021 Eur. Phys. J. A 57 299 Google Scholar
[40]	Li C, Zhou J, Zhou, Y J 2020 Phys. Rev. D 101 034015 Google Scholar
[41]	Wang X F, Brandenburg J D, Ruan L J, Shao F L, Xu Z B, Yang C, Zha W M 2022 arXiv: 2207.05595 [nucl-th]
[42]	Wang R J, Pu S, Wang Q 2021 Phys. Rev. D 104 056011 Google Scholar
[43]	Wang R J, Lin S, Pu S, Zhang Y F, Wang Q 2022 Phys. Rev. D 106 034025 Google Scholar
[44]	Lin S, Wang R J, Wang J F, Xu H J, Pu S, Wang Q 2023 Phys. Rev. D 107 054004
[45]	Klein S, Mueller A H, Xiao B W, Yuan F 2019 Phys. Rev. Lett. 122 132301 Google Scholar
[46]	Klein S, Mueller A H, Xiao B W, Yuan F 2020 Phys. Rev. D 102 094013 Google Scholar
[47]	Li C, Zhou J, Zhou Y J 2019 Phys. Lett. B 795 576 Google Scholar
[48]	Xiao B W, Yuan F, Zhou J 2020 Phys. Rev. Lett. 125 232301 Google Scholar
[49]	Hatta Y, Xiao B W, Yuan F, Zhou J 2021 Phys. Rev. Lett. 126 142001 Google Scholar
[50]	Hatta Y, Xiao B W, Yuan F, Zhou J 2021 Phys. Rev. D 104 054037 Google Scholar
[51]	Brandenburg J D, Seger J, Xu Z B, Zha W M 2022 arXiv: 2208.14943 [hep-ph]
[52]	Heisenberg W, Euler H 1936 Z. Phys. 98 714 Google Scholar
[53]	Zhou J 2022 EPJ Web Conf. 259 13014 Google Scholar
[54]	STAR Collaboration 2022 Phys. Rev. C 105 014901 Google Scholar
[55]	STAR Collaboration 2023 Sci. Adv. 9 3903 Google Scholar
[56]	Xing H X, Zhang C, Zhou J, Zhou Y J 2020 JHEP 10 064
[57]	Hagiwara Y, Zhang C, Zhou J, Zhou Y J 2021 Phys. Rev. D 103 074013 Google Scholar
[58]	Hagiwara Y, Zhang C, Zhou J, Zhou Y J 2021 Phys. Rev. D 104 094021 Google Scholar
[59]	Brandenburg J D, Xu Z B, Zha W M, Zhang C, Zhou J, Zhou Y J 2022 Phys. Rev. D 106 074008 Google Scholar
[60]	Zha W M, Brandenburg J D, Ruan L J, Tang Z B, Xu Z B 2021 Phys. Rev. D 103 033007 Google Scholar
[61]	Wu X, Li X B, Tang Z B, Wang P F, Zha W M 2022 Phys. Rev. Res. 4 L042048 Google Scholar
[62]	Brodsky S J, Frankfurt L, Gunion J F, Mueller A H, Strikman M 1994 Phys. Rev. D 50 3134
[63]	Weizsäcker von C F 1934 Z. Phys. 88 612 Google Scholar
[64]	Williams E J 1934 Phys. Rev. 45 729 Google Scholar
[65]	Jackson J D 1998 Classical Electrodynamics (State of New Jersey: Wiley)
[66]	McLerran L D, Venugopalan R 1994 Phys. Rev. D 49 3352
[67]	Kovchegov Y V 1996 Phys. Rev. D 54 5463 Google Scholar
[68]	Aichelburg P C, Sexl R U 1971 Gen. Rel. Grav. 2 303 Google Scholar
[69]	Jackson J D 2008 Am. J. Phys 76 704 Google Scholar
[70]	Fermi E 1924 Z. Phys. 29 315 Google Scholar
[71]	Belitsky A V, Ji X D, Yuan F 2004 Phys. Rev. D 69 074014 Google Scholar
[72]	Mulders P J, Rodrigues J 2001 Phys. Rev. D 63 094021 Google Scholar
[73]	Metz A, Zhou J 2011 Phys. Rev. D 84 051503 Google Scholar
[74]	Dominguez F, Qiu J W, Xiao B W, Yuan F 2012 Phys. Rev. D 85 045003 Google Scholar
[75]	Boer D, Hagiwara Y, Zhou J, Zhou Y J 2022 Phys. Rev. D 105 096017 Google Scholar
[76]	Boer D, Mulders P J, Pisano C, Zhou J 2016 JHEP 08 001
[77]	Pisano C, Boer D, Brodsky S J, Buffing M G A, Mulders P J 2013 JHEP 10 024
[78]	Hencken Kai, Trautmann D, Baur G 1994 Phys. Rev. A 49 1584 Google Scholar
[79]	Catani S, Grazzini M, Torre A 2014 Nucl. Phys. B 890 518
[80]	Catani S, Grazzini M, Sargsyan H 2017 JHEP 06 017
[81]	Baur G, Hencken K, Trautmann D 1998 J. Phys. G 24 1657 Google Scholar
[82]	Mignani R P, Testa V, Caniulef D G, Taverna R, Turolla R, Zane S, Wu K 2017 Mon. Not. Roy. Astron. Soc. 465 492 Google Scholar
[83]	Sun Z H, Zheng D X, Zhou J, Zhou Y J 2020 Phys. Lett. B 808 135679 Google Scholar
[84]	Dilks C 2016 PoS DIS2016 212
[85]	PHENIX Collaboration 2019 Phys. Rev. Lett. 123 122001 Google Scholar
[86]	Lansberg J P, Massacrier L, Szymanowski L, Wagner J 2019 Phys. Lett. B 793 33 Google Scholar
[87]	Hatta Y, Rajan A, Yang D L 2019 Phys. Rev. D 100 014032 Google Scholar
[88]	ALICE, ATLAS, CMS, LHCb and STAR Collaborations 2021 Nucl. Phys. A 1005 122007
[89]	Ryskin M G 1993 Z. Phys. C 57 89 Google Scholar
[90]	Kopeliovich B Z, Nemchik J, Schafer A, Tarasov A V 2002 Phys. Rev. C 65 035201 Google Scholar
[91]	Lappi T, Mantysaari H 2011 Phys. Rev. C 83 065202 Google Scholar
[92]	Kowalski H, Teaney D 2003 Phys. Rev. D 68 114005 Google Scholar
[93]	Kowalski H, Motyka L, Watt G 2006 Phys. Rev. D 74 074016 Google Scholar
[94]	Bartels J, Golec-Biernat K J, Peters K 2003 Acta Phys. Polon. B 34 3051
[95]	Hatta Y, Xiao B W, Yuan F 2017 Phys. Rev. D 95 114026 Google Scholar
[96]	Ma Y G 2023 Nucl. Sci. Technol. 34 16 Google Scholar
[97]	STAR Collaboration 2017 Phys. Rev. C 96 054904 Google Scholar
[98]	Golec-Biernat K J, Wusthoff M 1998 Phys. Rev. D 59 014017 Google Scholar
[99]	Golec-Biernat K J, Wusthoff M 1999 Phys. Rev. D 60 114023 Google Scholar
[100]	STAR Collaboration 2022 Phys. Rev. Lett. 128 122303 Google Scholar
[101]	Schmidke W 2021 talk presented in DIS 2021, NY, US
[102]	ALICE Collaboration 2021 Phys. Lett. B 817 136280 Google Scholar
[103]	Anderle P D, Bertone V, Cao X, Chang L, Chang N B, Chen G, Chen X R, Chen Z J, Cui Z F, Dai L Y, Deng W T, Ding M H, Feng X, Gong C, Gui L C, Guo F K, Han C D, He J, Hou T J, Huang H X, Huang Y, KumeričKi K, Kaptari L P, Li D M, Li H N, Li M X, Li X Q, Liang Y T, Liang Z T, Liu C, Liu C, Liu G M, Liu J, Liu L M, Liu X, Liu T B, Luo X F, Lyu Z, Ma B Q, Ma F, Ma J P, Ma Y G, Mao L J, Mezrag C, Moutarde H, Ping J L, Qin S X, Ren H, Roberts C D, Rojo J, Shen G D, Shi C, Song Q T, Sun H, Sznajder P, Wang E K, Wang F, Wang Q, Wang R, Wang R R, Wang T F, Wang W, Wang X Y, Wang X Y, Wu J J, Wu X G, Xia L, Xiao B W, Xiao G Q, Xie J J, Xie Y P, Xing H X, Xu H S, Xu N, Xu S H, Yan M S, Yan W B, Yan W C, Yan X H, Yang J C, Yang Y B, Yang Z, Yao D L, Ye Z H, Yin P L, Yuan C P, Zhan W L, Zhang J H, Zhang J L, Zhang P M, Zhang Y F, Chang C H, Zhang Z Y, Zhao H W, Chao K T, Zhao Q, Zhao Y X, Zhao Z G, Zheng L, Zhou J, Zhou X, Zhou X R, Zou B S, Zou L P 2021 Front. Phys. 16 64701 Google Scholar
[104]	曹须, 常雷, 畅宁波, 陈旭荣, 陈卓俊, 崔著钫, 戴凌云, 邓维天, 丁明慧, 龚畅, 桂龙成, 郭奉坤, 韩成栋, 何军, 黄虹霞, 黄银, Kaptari L P, 李德民, 李衡讷, 李民祥, 李学潜, 梁羽铁, 梁作堂, 刘国明, 刘杰, 刘柳明, 刘翔, 罗晓峰, 吕准, 马伯强, 马伏, 马建平, 马余刚, 冒立军, Mezrag C, 平加伦, 秦思学, 任航, Roberts C D, 申国栋, 史潮, 宋勤涛, 孙昊, 王恩科, 王凡, 王倩, 王荣, 王睿儒, 王涛峰, 王伟, 王晓玉, 王晓云, 吴佳俊, 吴兴刚, 肖博文, 肖国青, 谢聚军, 谢亚平, 邢宏喜, 徐瑚珊, 许怒, 徐书生, 鄢文标, 闫文成, 闫新虎, 杨建成, 杨一玻, 杨智, 姚德良, 尹佩林, 詹文龙, 张建辉, 张金龙, 张鹏鸣, 张肇西, 张振宇, 赵红卫, 赵光达, 赵强, 赵宇翔, 赵政国, 郑亮, 周剑, 周详, 周小蓉, 邹冰松, 邹丽平 2020 核技术 43 20001 Google Scholar Cao X, Chang L, Chang N B, Chen X R, Chen Z J, Cui Z F, Dai L Y, Deng W T, Ding M H, Gong C, Gui L C, Guo F K, Han C D, He J, Huang H X, Huang Y, Kaptari L P, Li D M, Li H N, Li M X, Li X Q, Liang Y T, Liang Z T, Liu G M, Liu J, Liu L M, Liu X, Luo X F, Lv Z, Ma B Q, Ma F, Ma J P, Ma Y G, Mao L J, Mezrag C, Ping J L, Qin S X, Ren H, Roberts C D, Shen G D, Shi C, Song Q T, Sun H, Wang E K, Wang F, Wang Q, Wang R, Wang R R, Wang T F, Wang W, Wang X Y, Wang X Y, Wu J J, Wu X G, Xiao B W, Xiao G Q, Xie J J, Xie Y P, Xing H X, Xu H S, Xu N, Xu S S, Yan W B, Yan W C, Yan X H, Yang J C, Yang Y B, Yang Z, Yao D L, Yin P L, Zhan W L, Zhang J H, Zhang J L, Zhang P M, Zhang Z X, Zhang Z Y, Zhao H W, Zhao G D, Zhao Q, Zhao Y X, Zhao Z G, Zheng L, Zhou J, Zhou X, Zhou X R, Zhou B S, Zhou L P 2020 Nucl. Sci. Tech. 43 20001 Google Scholar

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图 1 重离子对撞中的光致双轻子产生示意图。图片取自文献[42]

Figure 1. Illustration for the dilepton photoproduction in the heavy ion collisions ^[42]

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图 2 $ \sqrt{s_{NN}} = 200\;{\rm{GeV}} $碰撞能量60%—80%中心度下金金碰撞中光致电子对产生过程　(a)截面关于横动量分布; (b)横动量关于不变质量的分布. 图片取自文献[43]

Figure 2. (a) Differential cross section as a function of transverse momentum; (b) transverse momentum distributions for dilepton photoproduction at 60%–80% centrality in $ \sqrt{s_{NN}} = 200\;{\rm{GeV}} $ Au-Au collisions ^[43]

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图 3 $ \sqrt{s_{NN}}=200\;\mathrm{GeV} $碰撞能量下Au-Au碰撞中光致电子对产生的辐角分布. 图片取自文献[43]

Figure 3. Azimuthal angle distribution for dilepton photoproduction in $ \sqrt{s_{NN}}=200\;\mathrm{GeV} $ Au-Au collisions^[43]

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图 4 (a) RHIC能区($ \sqrt {s}=200 $ GeV)金-金对撞中电子对产生的$ \cos 4\phi $方位角不对称度, 电子和反电子的快度和横动量积分区间分别为[–1, 1]和[0.2 GeV, 0.4 GeV]; (b) LHC能区($ \sqrt {s}=5.02 $ TeV)铅核-铅核对撞中缪子对产生中的$ \cos 4\phi $方位角不对称度. 缪子和反缪子的快度和横动量积分区间分别为[–1, 1]和[4 GeV, 45 GeV]. 两个图中的横轴都为轻子对的总横动量. 图片取自文献[47]

Figure 4. (a) $ \cos(4\phi) $ azimuthal asymmetry in dielectron production in Au-Au collisions at RHIC energy ($ \sqrt{s} = 200 $ GeV). The rapidity and transverse momentum integration regions for $ e^+e^- $ are [–1, 1] and [0.2 GeV, 0.4 GeV], respectively. (b) $ \cos(4\phi) $ azimuthal asymmetry in dimuon production in Pb-Pb collisions at LHC energy ($ \sqrt{s} = 5.02 $ TeV). The rapidity and transverse momentum integration regions for $ \mu^+\mu^- $ are [–1, 1] and [4 GeV, 45 GeV], respectively. The horizontal axis in both figures represents the total transverse momentum of the lepton pair. The figures are taken from Ref. [47].

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图 5 (a)金-金对撞中(质心能$ \sqrt {s}=200 $ GeV)轻子对产生过程中的$ b_\perp $与$ P_\perp $之间的$ \cos 4\phi $方位角关联, 横轴为$ b_\perp $; (b)铅-铅对撞中(质心能$ \sqrt {s}=5.02 $ TeV)的轻子对$ \cos 4\phi $方位角不对称, 轻子对快度的积分区间为[–1, 1]. 图片取自文献[48]

Figure 5. (a) $ \cos 4\phi $ azimuthal correlation between the impact parameter $ b_\perp $ and the transverse momentum $ P_\perp $ of the lepton pair produced in Au-Au collisions at $ \sqrt{s}=200 $ GeV. The horizontal axis represents $ b_\perp $. (b) $ \cos 4\phi $ azimuthal asymmetry of lepton pairs produced in Pb-Pb collisions at $ \sqrt{s}=5.02 $ TeV. The rapidity integration range is $ [-1, 1] $. The figures are taken from Ref. [48]

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图 6 偶极矩类型光子TMD与WW类型光子TMD之间的比值$ R = f_1^\gamma/f_{1, 0}^\gamma $　(a)点电荷源的光子TMD函数的比值, 横轴为$ \dfrac{k_\perp}{xM_{\rm{p}}} $; (b)铅核的相干光子TMD函数的比值, 横轴为$ k_\perp $. 图片取自文献[83]

Figure 6. Ratio $ R = f_1^\gamma/f_{1, 0}^\gamma $ between the dipole-type photon TMD $ f_1^\gamma $ and the WW-type photon TMD $ f_{1, 0}^\gamma $: (a) R as a function of $ \dfrac{k_\perp}{xM_{\rm{p}}} $ for a point like charged particle; (b) R as a funciton of $ k_\perp $ for lead. The figures are taken from Ref. [83]

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图 7 UPC过程中$ \rho^0 $介子衍射产生示意图

Figure 7. A shematic diagram for diffractive $ \rho^0 $ meson production in ultraperipheral heavy ion collisions

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图 8 方位角不对称性示意图　(a) $ \left\langle {+1 |-1} \right\rangle \sim \cos 2 \phi $; (b) $ \left\langle {+2 |\mp 1} \right\rangle \sim \cos 3\phi/\cos \phi $

Figure 8. Illustration diagrams for azimuthal asymmetry: (a) $ \left\langle {+1 |-1} \right\rangle \sim \cos 2 \phi $; (b) $ \left\langle {+2 |\mp 1} \right\rangle \sim \cos 3\phi/\cos \phi $

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图 9 $ \cos 4 \phi $方位角不对称性示意图, $ \left\langle {+3 |-1} \right\rangle \sim \cos 4 \phi $　(a)椭圆胶子Wigner分布的贡献; (b)末态软光子辐射的贡献

Figure 9. Illustration diagrams for $ \cos 4 \phi $ azimuthal asymmetry: (a) Contributions from elliptic gluon Wigner distribution; (b) contributions from final state soft photon radiation

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图 10 RHIC 能区非极化光致$ \rho^0 $相干产生过程的XnXn事例, 其中蓝色实线是数值计算结果, 红色的点取自文献[97]中图 8 的数据. 图片取自文献[56]

Figure 10. Unpolarized cross section for coherent $ \rho^0 $ photo-production in XnXn events at RHIC energy. The red dots are experimental data points taken from Ref. [97]. The blue line shows our numerical result for this unpolarized cross section. The figure is taken from Ref. [56]

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图 11 RHIC 能区光致$ \rho^0 $产生过程XnXn事例的$ \cos2\phi $方位角不对称性. 蓝色实线是数值计算结果, 红色点是STAR的实验结果[55], 这里误差没有画出

Figure 11. The $ \cos2\phi $ azimuthal asymmetry of the XnXn events for the photoproduction of $ \rho^0 $ at RHIC. The blue solid line represents the numerical calculation result, and the red dots represent the experimental result from STAR[55], where the errors are not shown here

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图 12 $ \pi^+\pi^- $非极化截面的不变质量分布. 其中蓝色虚线是$ \rho^0 $衰变的结果, 利用(72)式计算; 粉色点线是$ \pi^+\pi^- $直接产生, 由(80)式的幅度$ {\cal A}_{d} $计算得到; 蓝绿色点划线是他们的干涉项. 红色实线为总的结果

Figure 12. Invariant mass distribution of the unpolarized cross section for $ \pi^+\pi^- $ production. The blue dashed line represents the decay of $ \rho^0 $ mesons, which is calculated using formula (72). The magenta dotted line represents the direct production of $ \pi^+\pi^- $, which is calculated using the amplitude $ {\cal A}_{d} $ from equation (80). The cyan dash-dotted line represents the interference term between them. The red solid line is the total result

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图 13 (a) RHIC Au-Au 200 GeV 上$ \pi^+\pi^- $光致产生过程的$ \cos4\phi $不对称性随$ q_\perp $变化的曲线, 其中$ \pi^+ $, $ \pi^- $介子快度$ y_1,\; y_2 $的积分区间为$ [-1, 1] $, 它们的不变质量$ Q $的积分区间为$ [0.6 {\rm GeV}, 1{\rm GeV}] $; (b) EIC上质心能量100 GeV的电子-原子核对撞产生$ \pi^+\pi^- $过程的$ \cos4\phi $不对称性随$ q_\perp $变化的曲线, $ y_1, \;y_2 $的积分区间为$ [2, 3] $, $ Q $的积分区间为$[0.6\; {\rm GeV}, 1\;{\rm GeV}]$. 图中蓝色的实线为总的结果, 黑色的虚线来自末态软光子辐射的贡献, 红色的点线为椭圆胶子Wigner分布的贡献. 图片取自文献[58]

Figure 13. (a) $ \cos4\phi $ asymmetry as a function of $ q_\perp $ for the $ \pi^+\pi^- $ photoproduction process for RHIC Au-Au collision at 200 GeV, where the integration range of the rapidity $ y_1,\; y_2 $ of $ \pi^+ $ and $ \pi^- $ mesons is $ [-1, 1] $, and the integration range of the invariant mass $ Q $ is $[0.6\; \rm{ GeV}, 1\;\rm{ GeV}]$; (b) $ \cos4\phi $ asymmetry as a function of $ q_\perp $ for the $ \pi^+\pi^- $ process in electron-nucleus collisions at a center-of-mass energy of 100 GeV at EIC, where $ y_1, y_2 $ is integrated over $ [2, 3] $, and $ Q $ is integrated over $ [0.6 \rm{ GeV}, 1\rm{ GeV}] $. The blue solid line in the figure represents the total result, the black dashed line is from the contribution of final state radiation, and the red dotted line is from the contribution of the elliptic gluon Wigner distribution. The figures are taken from Ref. [58]

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图 14 RHIC和LHC能区UPC相干产生$ J/\psi $过程的非极化截面随t变化的曲线　(a) RHIC能区, J/$ \psi $的快度积分区间为[–1, 1]; (b) LHC能区; J/$ \psi $的快度积分区间为[–0.8, 0.8]; 图片取自文献[59]

Figure 14. Azimuthal averaged cross section of coherent $ J/\psi $ production as a function of $ t $ in unrestricted UPCs at RHIC and LHC energies: (a) For RHIC kinematics, the rapidity of the J/$ \psi $ is integrated over the range [–1, 1]; (b) for LHC kinematics, the rapidity is integrated over [–0.8, 0.8]. The figures are taken from Ref. [59]

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图 15 LHC能区UPC相干产生$ J/\psi $过程的非极化截面随快度变化的曲线, 其中J/$ \psi $的横动量在[0, 0.2] GeV区间积分.　(a) ALICE&CMS $ \sqrt{s}=2.76 $ TeV; (b) ALICE&LHCb $ \sqrt{s}=5.02 $ TeV. 图片取自文章[59]

Figure 15. Azimuthal averaged cross section of coherent $ J/\psi $ production in unrestricted UPCs at LHC energy. The transverse momentum of the J/$ \psi $ is integrated over the range [0, 0.2] GeV. (a) ALICE&CMS $ \sqrt{s}=2.76 $ TeV; (b) ALICE&LHCb $ \sqrt{s}=5.02 $ TeV. The figures are taken from Ref.[59].

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图 16 在RHIC, LHC和EIC能区$ J/\psi $相干产生的$ \cos 2\phi $方位角不对称性　(a) RHIC能区, 双轻子对的快度积分区间为[–1, 1]; (b) LHC能区, 双轻子对的快度积分区间为[–0.8, 0.8]; (c) EIC能区, 双轻子对的快度积分区间为[2, 3](实验室系). 在RHIC和EIC上, $ J/\psi $通过$ J/\psi\rightarrow e^+e^- $衰变模式重建, 在LHC上通过$ J/\psi\rightarrow \mu^+\mu^- $重建. 图片取自文献[59]

Figure 16. $ \cos 2\phi $ azimuthal asymmetry in coherent $ J/\psi $ production at RHIC, LHC and EIC energies: (a) At RHIC kinematics, the rapidity of the di-lepton pair is integrated over the range [–1, 1]; (b) at LHC kinematics, the rapidity of the di-lepton pair is integrated over the range [–0.8, 0.8]; (c) at EIC kinematica region, the rapidity of the di-lepton pair is integrated over the range [2, 3] in the Lab frame. The $ J/\psi $ is reconstructed via the decay mode $ J/\psi\rightarrow e^+e^- $ at RHIC and EIC, and $ J/\psi\rightarrow \mu^+\mu^- $ at LHC, respectively. The figures are taken from Ref. [59]

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[1]	Skokov V, Illarionov A Y, Toneev V 2009 Int. J. Mod. Phys. A 24 5925 Google Scholar
[2]	Bzdak A, Skokov V 2012 Phys. Lett. B 710 171 Google Scholar
[3]	Deng W T, Huang X G 2012 Phys. Rev. C 85 044907 Google Scholar
[4]	Roy V, Pu S 2015 Phys. Rev. C 92 064902 Google Scholar
[5]	Pu S, Roy V, Rezzolla L, Rischke D H 2016 Phys. Rev. D 93 074022 Google Scholar
[6]	ATLAS Collaboration 2017 Nature Phys. 13 852 Google Scholar
[7]	STAR Collaboration 2021 Phys. Rev. Lett. 127 052302 Google Scholar
[8]	Zha W M, Brandenburg J D, Tang Z B, Xu Z B 2020 Phys. Lett. B 800 135089 Google Scholar
[9]	Breit G, Wheeler J A 1934 Phys. Rev. 46 1087 Google Scholar
[10]	Hattori K, Itakura K 2013 Annals Phys. 330 23 Google Scholar
[11]	Hattori K, Itakura K 2013 Annals Phys. 334 58 Google Scholar
[12]	Hattori K, Taya H, Yoshida S 2021 JHEP 01 093
[13]	Hattori K, Itakura K 2022 Annals Phys. 446 169114 Google Scholar
[14]	Adler S L 1971 Annals Phys. 67 599 Google Scholar
[15]	Jackiw R, Kabat D N, Ortiz M 1992 Phys. Lett. B 277 148 Google Scholar
[16]	Bethe H A, Maximon L C 1954 Phys. Rev. 93 768 Google Scholar
[17]	Ivanov D, Melnikov K 1998 Phys. Rev. D 57 4025 Google Scholar
[18]	Tuchin K 2009 Phys. Rev. D 80 093006 Google Scholar
[19]	Baltz A J, McLerran L D 1998 Phys. Rev. C 58 1679 Google Scholar
[20]	Baltz A J 2003 Phys. Rev. C 68 034906 Google Scholar
[21]	Lee R N, Milstein A I 2000 Phys. Rev. A 61 032103 Google Scholar
[22]	Baltz A J 2008 Phys. Rev. Lett. 100 062302 Google Scholar
[23]	Zha W M, Tang Z B 2021 JHEP 08 083
[24]	Knapen S, Lin T Y and Lou H K, Melia T 2017 Phys. Rev. Lett. 118 171801 Google Scholar
[25]	Xu I, Lewis N, Wang X F, Brandenburg J D, Ruan L J 2022 arXiv: 2211.02132[hep-ex]
[26]	The DELPHI Collaboration 2004 Eur. Phys. J. C 35 159 Google Scholar
[27]	ATLAS Collaboration 2022 arXiv: 2204.13478[hep-ex]
[28]	The CMS Collaboration 2019 Phys. Lett. B 797 134826 Google Scholar
[29]	Ellis J, Mavromatos N E, You T 2017 Phys. Rev. Lett. 118 261802 Google Scholar
[30]	STAR Collaboration 2018 Phys. Rev. Lett. 121 132301 Google Scholar
[31]	ATLAS Collaboration 2018 Phys. Rev. Lett. 121 212301 Google Scholar
[32]	CMS Collaboration 2021 Phys. Rev. Lett. 127 122001 Google Scholar
[33]	Klein S R, Nystrand J, Seger J, Gorbunov Y, Butterworth J 2017 Comput. Phys. Commun. 212 258 Google Scholar
[34]	Vidovic M, Greiner M, Best C, Soff G 1993 Phys. Rev. C 47 2308
[35]	Hencken K, Trautmann D, Baur G 1995 Phys. Rev. A 51 1874 Google Scholar
[36]	Hencken K, Baur G, Trautmann D 2004 Phys. Rev. C 69 054902 Google Scholar
[37]	Zha W, Ruan L, Tang Z, Xu Z, Yang S 2018 Phys. Lett. B 781 182 Google Scholar
[38]	Brandenburg J D, Li W, Ruan L J, Tang Z B, Xu Z B, Yang S, Zha W M 2020 arXiv: 2006.07365 [hep-ph]
[39]	Brandenburg J D, Zha W M, Xu Z B 2021 Eur. Phys. J. A 57 299 Google Scholar
[40]	Li C, Zhou J, Zhou, Y J 2020 Phys. Rev. D 101 034015 Google Scholar
[41]	Wang X F, Brandenburg J D, Ruan L J, Shao F L, Xu Z B, Yang C, Zha W M 2022 arXiv: 2207.05595 [nucl-th]
[42]	Wang R J, Pu S, Wang Q 2021 Phys. Rev. D 104 056011 Google Scholar
[43]	Wang R J, Lin S, Pu S, Zhang Y F, Wang Q 2022 Phys. Rev. D 106 034025 Google Scholar
[44]	Lin S, Wang R J, Wang J F, Xu H J, Pu S, Wang Q 2023 Phys. Rev. D 107 054004
[45]	Klein S, Mueller A H, Xiao B W, Yuan F 2019 Phys. Rev. Lett. 122 132301 Google Scholar
[46]	Klein S, Mueller A H, Xiao B W, Yuan F 2020 Phys. Rev. D 102 094013 Google Scholar
[47]	Li C, Zhou J, Zhou Y J 2019 Phys. Lett. B 795 576 Google Scholar
[48]	Xiao B W, Yuan F, Zhou J 2020 Phys. Rev. Lett. 125 232301 Google Scholar
[49]	Hatta Y, Xiao B W, Yuan F, Zhou J 2021 Phys. Rev. Lett. 126 142001 Google Scholar
[50]	Hatta Y, Xiao B W, Yuan F, Zhou J 2021 Phys. Rev. D 104 054037 Google Scholar
[51]	Brandenburg J D, Seger J, Xu Z B, Zha W M 2022 arXiv: 2208.14943 [hep-ph]
[52]	Heisenberg W, Euler H 1936 Z. Phys. 98 714 Google Scholar
[53]	Zhou J 2022 EPJ Web Conf. 259 13014 Google Scholar
[54]	STAR Collaboration 2022 Phys. Rev. C 105 014901 Google Scholar
[55]	STAR Collaboration 2023 Sci. Adv. 9 3903 Google Scholar
[56]	Xing H X, Zhang C, Zhou J, Zhou Y J 2020 JHEP 10 064
[57]	Hagiwara Y, Zhang C, Zhou J, Zhou Y J 2021 Phys. Rev. D 103 074013 Google Scholar
[58]	Hagiwara Y, Zhang C, Zhou J, Zhou Y J 2021 Phys. Rev. D 104 094021 Google Scholar
[59]	Brandenburg J D, Xu Z B, Zha W M, Zhang C, Zhou J, Zhou Y J 2022 Phys. Rev. D 106 074008 Google Scholar
[60]	Zha W M, Brandenburg J D, Ruan L J, Tang Z B, Xu Z B 2021 Phys. Rev. D 103 033007 Google Scholar
[61]	Wu X, Li X B, Tang Z B, Wang P F, Zha W M 2022 Phys. Rev. Res. 4 L042048 Google Scholar
[62]	Brodsky S J, Frankfurt L, Gunion J F, Mueller A H, Strikman M 1994 Phys. Rev. D 50 3134
[63]	Weizsäcker von C F 1934 Z. Phys. 88 612 Google Scholar
[64]	Williams E J 1934 Phys. Rev. 45 729 Google Scholar
[65]	Jackson J D 1998 Classical Electrodynamics (State of New Jersey: Wiley)
[66]	McLerran L D, Venugopalan R 1994 Phys. Rev. D 49 3352
[67]	Kovchegov Y V 1996 Phys. Rev. D 54 5463 Google Scholar
[68]	Aichelburg P C, Sexl R U 1971 Gen. Rel. Grav. 2 303 Google Scholar
[69]	Jackson J D 2008 Am. J. Phys 76 704 Google Scholar
[70]	Fermi E 1924 Z. Phys. 29 315 Google Scholar
[71]	Belitsky A V, Ji X D, Yuan F 2004 Phys. Rev. D 69 074014 Google Scholar
[72]	Mulders P J, Rodrigues J 2001 Phys. Rev. D 63 094021 Google Scholar
[73]	Metz A, Zhou J 2011 Phys. Rev. D 84 051503 Google Scholar
[74]	Dominguez F, Qiu J W, Xiao B W, Yuan F 2012 Phys. Rev. D 85 045003 Google Scholar
[75]	Boer D, Hagiwara Y, Zhou J, Zhou Y J 2022 Phys. Rev. D 105 096017 Google Scholar
[76]	Boer D, Mulders P J, Pisano C, Zhou J 2016 JHEP 08 001
[77]	Pisano C, Boer D, Brodsky S J, Buffing M G A, Mulders P J 2013 JHEP 10 024
[78]	Hencken Kai, Trautmann D, Baur G 1994 Phys. Rev. A 49 1584 Google Scholar
[79]	Catani S, Grazzini M, Torre A 2014 Nucl. Phys. B 890 518
[80]	Catani S, Grazzini M, Sargsyan H 2017 JHEP 06 017
[81]	Baur G, Hencken K, Trautmann D 1998 J. Phys. G 24 1657 Google Scholar
[82]	Mignani R P, Testa V, Caniulef D G, Taverna R, Turolla R, Zane S, Wu K 2017 Mon. Not. Roy. Astron. Soc. 465 492 Google Scholar
[83]	Sun Z H, Zheng D X, Zhou J, Zhou Y J 2020 Phys. Lett. B 808 135679 Google Scholar
[84]	Dilks C 2016 PoS DIS2016 212
[85]	PHENIX Collaboration 2019 Phys. Rev. Lett. 123 122001 Google Scholar
[86]	Lansberg J P, Massacrier L, Szymanowski L, Wagner J 2019 Phys. Lett. B 793 33 Google Scholar
[87]	Hatta Y, Rajan A, Yang D L 2019 Phys. Rev. D 100 014032 Google Scholar
[88]	ALICE, ATLAS, CMS, LHCb and STAR Collaborations 2021 Nucl. Phys. A 1005 122007
[89]	Ryskin M G 1993 Z. Phys. C 57 89 Google Scholar
[90]	Kopeliovich B Z, Nemchik J, Schafer A, Tarasov A V 2002 Phys. Rev. C 65 035201 Google Scholar
[91]	Lappi T, Mantysaari H 2011 Phys. Rev. C 83 065202 Google Scholar
[92]	Kowalski H, Teaney D 2003 Phys. Rev. D 68 114005 Google Scholar
[93]	Kowalski H, Motyka L, Watt G 2006 Phys. Rev. D 74 074016 Google Scholar
[94]	Bartels J, Golec-Biernat K J, Peters K 2003 Acta Phys. Polon. B 34 3051
[95]	Hatta Y, Xiao B W, Yuan F 2017 Phys. Rev. D 95 114026 Google Scholar
[96]	Ma Y G 2023 Nucl. Sci. Technol. 34 16 Google Scholar
[97]	STAR Collaboration 2017 Phys. Rev. C 96 054904 Google Scholar
[98]	Golec-Biernat K J, Wusthoff M 1998 Phys. Rev. D 59 014017 Google Scholar
[99]	Golec-Biernat K J, Wusthoff M 1999 Phys. Rev. D 60 114023 Google Scholar
[100]	STAR Collaboration 2022 Phys. Rev. Lett. 128 122303 Google Scholar
[101]	Schmidke W 2021 talk presented in DIS 2021, NY, US
[102]	ALICE Collaboration 2021 Phys. Lett. B 817 136280 Google Scholar
[103]	Anderle P D, Bertone V, Cao X, Chang L, Chang N B, Chen G, Chen X R, Chen Z J, Cui Z F, Dai L Y, Deng W T, Ding M H, Feng X, Gong C, Gui L C, Guo F K, Han C D, He J, Hou T J, Huang H X, Huang Y, KumeričKi K, Kaptari L P, Li D M, Li H N, Li M X, Li X Q, Liang Y T, Liang Z T, Liu C, Liu C, Liu G M, Liu J, Liu L M, Liu X, Liu T B, Luo X F, Lyu Z, Ma B Q, Ma F, Ma J P, Ma Y G, Mao L J, Mezrag C, Moutarde H, Ping J L, Qin S X, Ren H, Roberts C D, Rojo J, Shen G D, Shi C, Song Q T, Sun H, Sznajder P, Wang E K, Wang F, Wang Q, Wang R, Wang R R, Wang T F, Wang W, Wang X Y, Wang X Y, Wu J J, Wu X G, Xia L, Xiao B W, Xiao G Q, Xie J J, Xie Y P, Xing H X, Xu H S, Xu N, Xu S H, Yan M S, Yan W B, Yan W C, Yan X H, Yang J C, Yang Y B, Yang Z, Yao D L, Ye Z H, Yin P L, Yuan C P, Zhan W L, Zhang J H, Zhang J L, Zhang P M, Zhang Y F, Chang C H, Zhang Z Y, Zhao H W, Chao K T, Zhao Q, Zhao Y X, Zhao Z G, Zheng L, Zhou J, Zhou X, Zhou X R, Zou B S, Zou L P 2021 Front. Phys. 16 64701 Google Scholar
[104]	曹须, 常雷, 畅宁波, 陈旭荣, 陈卓俊, 崔著钫, 戴凌云, 邓维天, 丁明慧, 龚畅, 桂龙成, 郭奉坤, 韩成栋, 何军, 黄虹霞, 黄银, Kaptari L P, 李德民, 李衡讷, 李民祥, 李学潜, 梁羽铁, 梁作堂, 刘国明, 刘杰, 刘柳明, 刘翔, 罗晓峰, 吕准, 马伯强, 马伏, 马建平, 马余刚, 冒立军, Mezrag C, 平加伦, 秦思学, 任航, Roberts C D, 申国栋, 史潮, 宋勤涛, 孙昊, 王恩科, 王凡, 王倩, 王荣, 王睿儒, 王涛峰, 王伟, 王晓玉, 王晓云, 吴佳俊, 吴兴刚, 肖博文, 肖国青, 谢聚军, 谢亚平, 邢宏喜, 徐瑚珊, 许怒, 徐书生, 鄢文标, 闫文成, 闫新虎, 杨建成, 杨一玻, 杨智, 姚德良, 尹佩林, 詹文龙, 张建辉, 张金龙, 张鹏鸣, 张肇西, 张振宇, 赵红卫, 赵光达, 赵强, 赵宇翔, 赵政国, 郑亮, 周剑, 周详, 周小蓉, 邹冰松, 邹丽平 2020 核技术 43 20001 Google Scholar Cao X, Chang L, Chang N B, Chen X R, Chen Z J, Cui Z F, Dai L Y, Deng W T, Ding M H, Gong C, Gui L C, Guo F K, Han C D, He J, Huang H X, Huang Y, Kaptari L P, Li D M, Li H N, Li M X, Li X Q, Liang Y T, Liang Z T, Liu G M, Liu J, Liu L M, Liu X, Luo X F, Lv Z, Ma B Q, Ma F, Ma J P, Ma Y G, Mao L J, Mezrag C, Ping J L, Qin S X, Ren H, Roberts C D, Shen G D, Shi C, Song Q T, Sun H, Wang E K, Wang F, Wang Q, Wang R, Wang R R, Wang T F, Wang W, Wang X Y, Wang X Y, Wu J J, Wu X G, Xiao B W, Xiao G Q, Xie J J, Xie Y P, Xing H X, Xu H S, Xu N, Xu S S, Yan W B, Yan W C, Yan X H, Yang J C, Yang Y B, Yang Z, Yao D L, Yin P L, Zhan W L, Zhang J H, Zhang J L, Zhang P M, Zhang Z X, Zhang Z Y, Zhao H W, Zhao G D, Zhao Q, Zhao Y X, Zhao Z G, Zheng L, Zhou J, Zhou X, Zhou X R, Zhou B S, Zhou L P 2020 Nucl. Sci. Tech. 43 20001 Google Scholar

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