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]

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

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]

Fig. 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]

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]

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

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]

Fig. 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].

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]

Fig. 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]

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]

Fig. 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]

图 7  UPC过程中$ \rho^0 $介子衍射产生示意图

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

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 $

Fig. 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 $

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

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

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]

Fig. 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]

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

Fig. 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

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

Fig. 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

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]

Fig. 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]

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]

Fig. 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]

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]

Fig. 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].

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]

Fig. 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]