PHYSICAL REVIEW D 102, 094013 (2020) Lepton pair production through two photon process in heavy ion collisions Spencer Klein ,1 A. H. Mueller,2 Bo-Wen Xiao,3,4 and Feng Yuan1 1Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 2Department of Physics, Columbia University, New York, New York 10027, USA 3Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China 4School of Science and Engineering, The Chinese University of Hong Kong, 518172, Shenzhen, China (Received 29 June 2020; accepted 28 October 2020; published 13 November 2020) This paper investigates the electromagnetic production of lepton pairs with low total transverse momentum in relativistic heavy-ion collisions. We estimate the initial photons’ transverse momentum contributions by employing models where the average transverse momentum squared of the incoming photon can be calculated in the equivalent photon approximation. We further derive an all order QED resummation for the soft photon radiation, which gives an excellent description of the ATLASdata in ultraperipheral collisions at the LHC. For peripheral and central collisions, additional pT -broadening effects from multiple interactions with the medium and the magnetic field contributions from the quark-gluon plasma are also discussed. DOI: 10.1103/PhysRevD.102.094013 I. INTRODUCTION momentum squared that a parton acquires in the medium of length L. The experimental study of the medium related There have been strong interests in the electromagnetic p -broadening effects of the jet is an important step forward process of dilepton production in two-photon scattering T in heavy-ion collisions in the last few years [1–5]. These to clarify and understand the underlying mechanism for the experiments have made great efforts to select the dilepton jet energy loss in heavy-ion collisions. In the last few years, events through the kinematic constraints where they are there have been a lot of progresses in the understanding of the produced by the purely electromagnetic two-photon reac- pT-broadening effects in dijet, photon-jet, and hadron-jet – tion: γγ → lþl−. These experimental results have attracted productions in heavy-ion collisions [9 14]. It was found quite a lot of attention in the community because they may the vacuum Sudakov effects dominates [9] the transverse provide a potential probe for the electromagnetic property momentum broadening of dijets for the typical dijet kinemat- of the quark-gluon plasma created in heavy-ion collisions. ics measured at the LHC [15,16]. On the other hand, in The medium effects being considered include the medium the RHIC energy regime, the quark-gluon-plasma medium effect is comparable to the Sudakov effects, and the medium induced transverse momentum (pT) broadening from multiple interaction effects and/or the magnetic field effects pT-broadening has been observed in the measurements of from the medium. The confirmation of either effect would hadron-jet correlation [11,17] by the STAR collaboration. We be an important pathway in future explorations of the expect future measurements at both the LHC and RHIC will electromagnetic properties of the quark-gluon plasma. allow us to gain further important and quantitative informa- Furthermore, the physics related to the acoplanarity of the tion on the medium transverse momentum broadening effect. dilepton pair is very similar to that in dijet productions To be able to probe in-medium or magnetic effects in described in QCD. One popular description of the jet medium peripheral collisions, it is important to have a baseline interactions in QCD is the Baier-Dokshitzer-Mueller-Peigne- measurement. Ultraperipheral collisions (UPCs), where the Schiff (BDMPS) approach [6–8]. In addition to jet energy nuclei do not interact hadronically (roughly, with impact parameter b>2R where R is the nuclear radius), can loss, the BDMPS formalism also predicts the pT broadening A A effects, since these two effects are physically related. In the provide this baseline data. UPCs encompass both photo- BDMPS formalism, qLˆ characterizes the typical transverse production and two-photon interactions [18–22] and have a long history. Using the so-called equivalent photon approximation [23], which is also known as the Weizsäcker Williams method [24,25], the photon distribu- Published by the American Physical Society under the terms of tion from a relativistically moving charge particle can be the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to computed from its boosted electromagnetic fields. Photons the author(s) and the published article’s title, journal citation, can strike the oppositely moving nucleus, or they can and DOI. Funded by SCOAP3. interact with the electromagnetic field of the other nucleus, 2470-0010=2020=102(9)=094013(22) 094013-1 Published by the American Physical Society KLEIN, MUELLER, XIAO, and YUAN PHYS. REV. D 102, 094013 (2020) creating a pair of leptons in the two-photon process azimuthal correlations in heavy-ion collisions to di-lepton γγ → μþμ−. In two-photon fusion processes, the final state angular correlations. Because the experimentally measured has a small total pT, so the leptons are nearly back-to-back. lepton pairs [1] have very small pair pT, the associated The first dedicated study of γγ → eþe− was by the STAR physics is a bit different than for dijet correlation. We focus Collaboration in 2004 [26]. STAR studied final states on three important aspects here. The first one is the consisting of the lepton pair, accompanied by neutrons transverse momentum distribution of the incoming photons in each zero degree calorimeter. The neutrons are assumed in the two-photon processes. In particular, these distribu- to come from the mutual Coulomb excitations of the two tions should depend on the impact parameter of the nuclei by two additional photons, not directly associated collisions. However, as far as we know, there is no first- with the pair production [27]. The additional photons principle calculation on the joint transverse momentum and biased the production toward smaller impact parameters impact parameter dependent photon distribution within the (but still with b>2RA) [28]. original EPA framework. On one hand, we first make some Two-photon fusion production of lepton pairs has been approximation and estimate the average transverse momen- calculated with both the equivalent-photon approximation tum for the photons, which turns out a mild dependence (EPA), where the photons are treated as massless [27], and on the impact parameter. On the other hand, we try to via full lowest-order QED calculations, which included generalize the EPA framework by introducing the photon non-zero virtual photon masses [29]. The two calculations Wigner distribution which contains both the transverse agreed well, except that the EPA calculation predicted more momentum and impact parameter information of the pairs with pair pT < 20 MeV=c. The data was in good incoming photon, and find that this generalization indicates agreement with the calculations, favoring the QED calcu- the impact parameter dependence of the transverse momen- lation at a small pair pT. The STAR paper attributed this to tum broadening could be stronger in the central collisions. a breakdown of the EPA approach, but the issue may have We would like to emphasize that further theoretical devel- been that the EPA calculation did not account for the opments are needed to address this issue. change in single-photon transverse momentum (kT) dis- The second one is the QED Sudakov effects in the lepton tribution due to the biasing toward small impact parameters pair production. Much of this study will be similar to the [30]. This can be seen as broadening the pair pT spectrum. previous studies for dijet azimuthal correlations. However, Newer UPC studies of dileptons have mostly focused even beyond the much smaller QED coupling constant, the on J=ψ or heavier vector mesons, with the two-photon QED Sudakov has its own unique features. The formalism is production treated as a background. However, the ATLAS much simpler, and more importantly, the Sudakov contri- collaboration has recently made a high-statistics study of bution has distinguishable behavior compared to the pri- two-photon production of muon pairs in UPCs, finding mordial kT distribution from the two incoming photon mostly good agreement with an EPA calculation, but fluxes. The theory predictions for the UPC events agree accompanied by a tail containing about 1% of the events, very well with the recent measurement from ATLAS [31], of pairs with relatively high acoplanarity [31]. Acoplanarity which, for the first time, clearly demonstrates the importance is closely related to the pair pT. ATLAS focused on of the Sudakov effects in the moderately larger acoplanarity acoplanarity to reduce their sensitivity to resolution effects. region. Third, we discuss the QED medium effects on the At the same time, several experiments have reported on pair pT-broadening due to the leptons. This part is similar to the two-photon production of lepton pairs in peripheral the BDMPS formalism. With this physics included, we collisions, with b<2RA. The ATLAS collaboration stud- compare our calculation to the experimental data and com- ied pair production in lead-lead collisions and observed ment on the implications of the ATLAS measurements. a significant increase in acoplanarity with decreasing It is quite interesting to compare the pT-broadening centrality, consistent with an increase in pair pT [1]. The effects in QED and in QCD, which helps to provide a STAR Collaboration studied pair production at low pT, new perspective of studying the property of quark-gluon pT < 200 MeV/c in gold-gold and uranium-uranium col- plasma created in heavy-ion collisions. The medium lisions [2], also found evidence for momentum broadening, pT-broadening effect of lepton pairs is the probe to the with pT spectra different from calculations without in- electromagnetic constituents of the quark-gluon plasma, – medium effects [32 35].