Collectivity in ultra-peripheral heavy-ion collisions

We present full (3+1)D dynamical simulations to study collective behavior in ultra-peripheral nucleus-nucleus collisions (UPC) at the Large Hadron Collider (LHC) with the 3DGlauber+MUSIC+UrQMD framework. By extrapolating from asymmetric p+Pb collisions, we simulate a quasi-real photon $\gamma^*$ interacting with the Pb nucleus in an ultra-peripheral collision at the LHC, assuming strong final-state effects. We study the elliptic flow hierarchy between p+Pb and $\gamma^*$+Pb collisions, which is dominated by the difference in longitudinal flow decorrelations. Our theoretical framework provides a quantitative tool to study collectivity in small asymmetric collision systems at current and future collider experiments.


Introduction
Collective features of strongly-coupled systems have been observed in relativistic nuclear collisions with light and heavy nuclei, such as p+Au, d+Au, 3 He+Au at the Relativistic Heavy-Ion Collider (RHIC) [3,4], and p+p and p+Pb collisions at the Large Hadron Collider (LHC) [5][6][7].The theoretical interpretation of these flow-like signals has been a hot topic, driving our field to unravel how the collective behavior emerges depending on the collision system size [8,9].Recently, the ATLAS Collaboration measured the two-particle azimuthal correlations in ultra-peripheral Pb+Pb collisions (UPCs) at the LHC [10].The high multiplicity UPC events created from the photo-nuclear interactions showed the persistence of collective phenomena with correlations comparable to those observed in p+p and p+Pb collisions at similar multiplicity [10].
Quantitative understanding of the many-body dynamics in these small collision systems requires the development and application of full (3+1)D simulations beyond Bjorken's boostinvariance paradigm in the high energy limit [11][12][13][14][15][16][17][18].In photon-nucleus collisions, the quasireal photon γ * 's energy fluctuates event-by-event, and is much smaller than the energy of the incoming Pb nucleus.Such unbalanced and fluctuating kinematics leads to a highly asymmetric collision system, strongly violating the longitudinal boost invariance.In these asymmetric systems, the rapidity decorrelation of the collision geometry plays a crucial role when computing and measuring the anisotropic flow coefficients.
In this proceeding, we study the flow rapidity decorrelation in detail for γ * +Pb and p+Pb collisions, providing complementary information to Ref. [1].

Fluctuations in collision kinematics of γ * +A collisions in UPCs
The fast-moving Pb spectators in the UPC events generate strong fluxes of quasi-real photons.The emitted photons have the following energy spectrum [19,20], where α = 1/137 and w AA R = 2k γ R A /γ L , with the longitudinal Lorentz contraction factor γ L = √ s NN /(2m N ).The functions K 0 (x) and K 1 (x) are the modified Bessel functions of the second kind.For the Pb nucleus, R A = 6.62 fm and Z = 82.The kinematics for incoming photon projectile and nucleon target in the Pb nucleus are P µ γ ≃ (k γ , 0, 0, k γ ) and , where we neglect the photon's virtuality and nucleon's rest mass.The center of mass collision energy for the γ * +A system is From Eqs. ( 1) and ( 2), we can compute the probability distribution for the center of mass energy in γ * +A collisions, with the photon momentum k γ = s γ * N /(2 √ s NN ).Because of the unequal incoming longitudinal momentum between the quasi-real photons and the target nucleon, the center of mass rapidity of the γ * +Pb system differs from the lab frame rapidity by where the beam rapidity for a given center-of-mass collision energy can be computed as . The left panel of Figure 1 shows the probability distributions of the center-of-mass collision energies in Au+Au and Pb+Pb UPC events at RHIC and LHC.The center-of-mass collision energies in γ * +A collisions are much smaller than in their corresponding heavy-ion collisions.The values of √ s γ * N fluctuate over wide ranges, which results in broad intervals for rapidity shifts between the center-of-mass frame and lab frame, as shown in the right panel of Figure 1.For UPC events in Pb+Pb collisions at 5020 GeV, the rapidity shifts fluctuate from −2 to −8.5.Therefore, it is important to include these kinematics fluctuations in γ * +A collisions, which result in non-trivial effects in the rapidity direction.We note that small collision energy and large global rapidity shift result in little particle production at mid-rapidity in the lab frame.Therefore, triggering high multiplicity events at mid-rapidity effectively selects the γ * +A collisions with large √ s γ * N .

Flow rapidity decorrelation in γ * +Pb and p+Pb collisions
In the work [1], we found the different amounts of longitudinal flow decorrelations in γ * +Pb and p+Pb collisions led to the elliptic flow hierarchy observed by the ATLAS Collaboration [10].The different flow rapidity decorrelations in γ * +Pb and p+Pb collisions come from the difference in center-of-mass collision energy and the global rapidity shift in γ * +Pb collisions [1].To investigate the flow rapidity correlations at a charged hadron multiplicity of 40 − 50, we focus on the following analysis with γ * +Pb collisions at their highest energy, 894 GeV.The left panel of Figure 2 shows that the values of initial-state ellipticity are almost the same between γ * +Pb and p+Pb collisions as a function of the particle multiplicity, which means that the shape fluctuations in the transverse plane are at the same level for the two collision systems.The right panel of Figure 2 shows the evolution of event-plane correlations in steps from p+Pb collisions at 5020 GeV to γ * +Pb at 894 GeV collisions.The ATLAS Collaboration measured the two-particle correlation with a rapidity gap of |∆η| > 2. This analysis method computes the flow angular correlation between the two pseudorapidity intervals, namely η 1 ∈ [−2.5, −1] and η 2 ∈ [1, 2.5].The right panel of Figure 2 shows that the angular correlations of the elliptic flow vectors are strong in p+Pb collisions at 5020 GeV, very close to unity between these two η intervals.Reducing the collision energy to 894 GeV shortens the length of the produced strings in the rapidity space, weakening the event-plane correlation to ∼ 0.9.The extra global rapidity shift in γ * +Pb collisions further reduces the correlation strength to ∼ 0.7.
We applied a newly developed (3+1)D dynamical framework to study the collectivity in highly asymmetric relativistic nuclear collisions, such as p+A collisions and γ * +A in the ultra-peripheral A+A collisions at RHIC and LHC energies [1,2].In this proceeding, we present a detailed analysis of the flow rapidity decorrelation in γ * +Pb and p+Pb collisions.We discuss how to include fluctuating collision energies in simulating the 3D dynamics of γ * +A collisions in the UPC events.At LHC energies, the elliptic flow hierarchy between the γ * +Pb and p+Pb collisions can be explained by the different amounts of flow rapidity decorrelations in these systems, demonstrating the necessity of full (3+1)D simulations for these asymmetric collision systems.

Figure 1 .
Figure 1.Left Panel: The probability distributions of the center-of-mass collision energies for photonnucleus collisions in Au+Au and Pb+Pb UPC events at three collision energies.Right Panel: The probability distributions of the global rapidity shifts in γ * +A collisions from the center-of-mass frame to the lab frame.Negative ∆y represents the shift towards the nucleus-going direction.