Centrality dependence of dilepton production via γγ processes from Wigner distributions of photons in nuclei
aa r X i v : . [ h e p - ph ] D ec Centrality dependence of dilepton production via γγ processesfrom Wigner distributions of photons in nuclei Mariola K lusek-Gawenda, ∗ Wolfgang Sch¨afer, † and Antoni Szczurek
1, 2, ‡ Institute of Nuclear Physics Polish Academy of Sciences,ul. Radzikowskiego 152, PL-31-342 Krak´ow, Poland College of Natural Sciences, Institute of Physics,University of Rzesz´ow, ul. Pigonia 1, PL-35-310 Rzesz´ow, Poland
Abstract
We propose a new complete method, based on the Wigner distributions of photons, how tocalculate differential distributions of dileptons created via photon-photon fusion in semicentral( b < R A ) AA collisions. The formalism is used to calculate different distributions of invariantmass, dilepton transverse momentum and acoplanarity for different regions of centrality. Theresults of calculation are compared with recent STAR, ALICE and ATLAS experimental data.Very good agreement with the data is achieved without free parameters and without includingadditional mechanisms such as a possible rescattering of leptons in the quark-gluon plasma. ∗ [email protected] † [email protected] ‡ [email protected] . INTRODUCTION Ultrarelativistic Heavy Ions of large charge Z are accompanied by a large flux ofWeizs¨acker–Williams photons. This opens up the opportunity to study a variety of photoin-duced nuclear processes, as well as photon-photon processes. See for example the reviewswith focus on RHIC and LHC [1–5]. Until recently, most investigations have focused onultraperipheral collisions, where the coherent enhancement ∝ Z of Weizs¨acker-Williamsfluxes is evident. Here the impact parameter of the collision satisfies b > R A , with R A being the nuclear radius. A prominent role play the dileptons created via photon-photonfusion, for recent calculations at collider kinematics, see for example [6, 7].However, if one interprets Weizs¨acker-Williams photons as partons of the nucleus, itappears natural that the coherent photon cloud also contributes in semicentral or centralcollisions, where b < R A . In such collisions the colliding nuclei will interact stronglygenerating an ”underlying event” for the γγ process, which may include the production of aquark-gluon plasma (QGP). In fact, such contributions have long been suggested [8]. Firstexperimental evidence for the relevance of photoproduction processes in inelastic Heavy Ionreactions was reported by the ALICE collaboration [9]. Indeed, the large enhancement of J/ψ at low transverse momenta observed in [9] can be readily explained through the presenceof photoproduction mechanisms [10].It was realized only recently that also coherent photon-photon processes survive in semi-central collisions. Two years ago the STAR collaboration at RHIC [11] observed a largeenhancement at very low transverse momenta of the dielectron pair, P T <
150 MeV . Thisenhancement was interpreted soon as due to photon-photon fusion [12–15]. Dilepton pro-duction in heavy ion collisions is traditionally considered as a source of information on theproperties of the QCD matter produced in the collision [16, 17]. Besides the contributionsof medium-modified vector mesons and thermal radiation from the QGP, there are severalother mechanisms of dilepton production in ultrarelativistic heavy ion collisions. These areconventionally subsumed as the hadronic cocktail contribution which involves essentiallyall sources in nucleon-nucleon collisions (Dalitz decays, vector meson production, Drell-Yanmechanism, semileptonic decays of pairs of mesons).In [12] we performed a comprehensive study of the interplay of all these mechanisms,highlighting the dominance of γγ processes at very low P T . However, in Ref.[12], the P T dis-tribution of di-electrons was obtained using a k T -factorization method. In such an approachthe distribution in P T is independent of the impact parameter (and therefore centrality),and only the normalization contains information on the latter.In [14, 15] it has been proposed to use an approach that has been put forward longago in [18]. However the formalism presented in [18] applies only to the impact parameterdependence of invariant mass distributions of dileptons, and cannot be readily employed inan ”unintegrated” form to yield transverse momentum distributions.In [13] it was suggested that rescattering in QGP may lead to a broadening of the P T peak and acoplanarity distribution of dileptons.In this paper we present a more complete approach that allows to calculate the centralitydependence of the γγ mechanism of dilepton production. It is based on so-called Wignerdistributions . We present the formalism in the next section. Then we shall confront results Preliminary results of this work have been presented in [WS - 40th International Conference on HighEnergy Physics ICHEP2020, 30.07-5.08.2020 virtual meeting, Prague, MKG - Zim´anyi School WinterWorkshop 2020, 7-10.12.2020 virtual meeting Budapest] a similar approach based on Wigner functions has recently been obtained in [19].
2f the new method with existing experimental data. Conclusions will close our paper.
II. CENTRALITY DEPENDENT CROSS SECTION OF DILEPTON PRODUC-TION Q − Q ω , q + Q2 ω , q − Q2 ω , q − Q2 ω , q + Q2 Pb A A i jk lM M † FIG. 1. The cut off-forward A A → A A amplitude. Its Fourier transform w.r.t. Q yields theimpact-parameter dependent cross section of dilepton production. For the ion moving at longitudinal boost γ , let us denote the electric field vector: E ( ω, q ) = Z r α em π q F ch ( q + q k ) q + q k , where q k = ωγ , (2.1)and F ch ( Q ) is the charge form factor of the nucleus.The impact parameter dependent cross section of interest is obtained from the Fouriertransform of the cut off-forward A A → A A amplitude shown in Fig.1.The relevant factorization formula can be written in terms of the Wigner function N ij ( ω, b , q ) = Z d Q (2 π ) exp[ − i bQ ] E i (cid:16) ω, q + Q (cid:17) E ∗ j (cid:16) ω, q − Q (cid:17) (2.2)= Z d s exp[ i qs ] E i (cid:16) ω, b + s (cid:17) E ∗ j (cid:16) ω, b − s (cid:17) . (2.3)It has the property of being a density matrix in photon polarizations (here we use thebasis of cartesian linear polarizations), and depends on impact parameter and transversemomentum.Being a Wigner function, the standard photon fluxes in momentum space and impactparameter space, are obtained after integration over impact parameter or momentum space,respectively, a summation over photon polarizations is implied: N ( ω, q ) = δ ij Z d b N ij ( ω, b , q ) = δ ij E i ( ω, q ) E ∗ j ( ω, q ) = (cid:12)(cid:12)(cid:12) E ( ω, q ) (cid:12)(cid:12)(cid:12) ,N ( ω, b ) = δ ij Z d q (2 π ) N ij ( ω, b , q ) = δ ij E i ( ω, b ) E ∗ j ( ω, b ) = (cid:12)(cid:12)(cid:12) E ( ω, b ) (cid:12)(cid:12)(cid:12) . (2.4)3hen the cross section for lepton pair production can be written as a convolution over impactparameters and transverse momenta dσd b d P = Z d b d b δ (2) ( b − b + b ) Z d q π d q π δ (2) ( P − q − q ) × Z dω ω dω ω N ij ( ω , b , q ) N kl ( ω , b , q ) 12ˆ s X λ ¯ λ M λ ¯ λik M λ ¯ λ † jl d Φ( l + l − ) . (2.5)Here again we sum over cartesian photon polarizations i, j, k, l , and the invariant phase spaceof the leptons is: d Φ l + l − = (2 π ) δ (4) ( P − p − p ) d p (2 π ) δ ( p − m l ) d p (2 π ) δ ( p − m l ) . (2.6)We now parametrize b = R + B , b = R − B ⇒ d b d b = d R d B . (2.7)Below, we also use the notation P T ≡ | P | for the transverse momentum of the dileptonpair. Inserting the representation of the generalized Wigner function given in Eq. (2.2) ,and integrating out R (the delta function puts b = B ), we obtain dσd b d P = Z d Q (2 π ) exp[ − i bQ ] Z d q π d q π δ (2) ( P − q − q ) Z dω ω dω ω × E i (cid:16) ω , q + Q (cid:17) E ∗ j (cid:16) ω , q − Q (cid:17) E k (cid:16) ω , q − Q (cid:17) E ∗ l (cid:16) ω , q + Q (cid:17) × s X λ ¯ λ M λ ¯ λik M λ ¯ λ † jl d Φ( l + l − ) . (2.8)Notice, that our approach predicts “flow-like” correlations between the dilepton transversemomentum and the impact parameter b . We defer the discussion of these correlations to afuture publication, and in this work we will average over directions of b . The cross section ina certain centrality class is obtained by integrating over the corresponding range of impactparameters: dσ [ C ] = Z b max b min db dσdb . (2.9)If we are interested in the cross section in a certain centrality class C , we can get rid of theintegration over d b . We start from integrating over all possible orientations of b . Z d b exp[ − i bQ ]( . . . ) → π Z dbbJ ( bQ )( . . . ) . (2.10)Integrating over a range [ b min , b max ] of impact parameters, we obtain Z b max b min db bJ ( bQ ) = 1 Q (cid:16) Qb max J ( Qb max ) − Qb min J ( Qb min ) (cid:17) ≡ w ( Q ; b max , b min ) . (2.11)4hus the cross section for a certain centrality class C is: dσ [ C ] d P = Z d Q π w ( Q ; b max , b min ) Z d q π d q π δ (2) ( P − q − q ) Z dω ω dω ω × E i (cid:16) ω , q + Q (cid:17) E ∗ j (cid:16) ω , q − Q (cid:17) E k (cid:16) ω , q − Q (cid:17) E ∗ l (cid:16) ω , q + Q (cid:17) × s X λ ¯ λ M λ ¯ λik M λ ¯ λ † jl d Φ( l + l − ) . (2.12)The impact parameter intervals [ b min , b max ] corresponding to a given centrality class areobtained from a simple optical Glauber approach, as described in more detail in [12]. Now,we come to the helicity structure of the γγ → l + l − amplitude. Here, indices i, j correspondto linear polarizations of photons, while λ, ¯ λ are the helicities of leptons. The amplitudetakes the form (below M ( λ λ , λ ¯ λ )is the helicity amplitude for the γ ( λ ) γ ( λ ) → l − ( λ ) l + (¯ λ )process): M λ ¯ λik = − (cid:16) ˆ x i ˆ x k + ˆ y i ˆ y k (cid:17)(cid:16) M (++ , λ ¯ λ ) + M ( −− , λ ¯ λ ) (cid:17) − i (cid:16) ˆ x i ˆ y k − ˆ y i ˆ x k (cid:17)(cid:16) M (++ , λ ¯ λ ) − M ( −− , λ ¯ λ ) (cid:17) + 12 (cid:16) ˆ x i ˆ x k − ˆ y i ˆ y k (cid:17)(cid:16) M ( − + , λ ¯ λ ) + M (+ − , λ ¯ λ ) (cid:17) + i (cid:16) ˆ x i ˆ y k + ˆ y i ˆ x k (cid:17)(cid:16) M ( − + , λ ¯ λ ) − M (+ − , λ ¯ λ ) (cid:17) . (2.13)Let us introduce the shorthand notation M λ ¯ λik = δ ik M (0 , +) λ ¯ λ − iǫ ik M (0 , − ) λ ¯ λ + P k ik M (2 , +) λ ¯ λ + iP ⊥ ik M (2 , − ) λ ¯ λ . (2.14)Here δ ik = ˆ x i ˆ x k + ˆ y i ˆ y k , ǫ ik = ˆ x i ˆ y k − ˆ y i ˆ x k , P k ik = ˆ x i ˆ x k − ˆ y i ˆ y k , P ⊥ ik = ˆ x i ˆ y k + ˆ y i ˆ x k . (2.15)Then, in the cross-section of interest, we need X λ ¯ λ M λ ¯ λik M λ ¯ λ † jl = δ ik δ jl X λ ¯ λ (cid:12)(cid:12)(cid:12) M (0 , +) λ ¯ λ (cid:12)(cid:12)(cid:12) + ǫ ik ǫ jl X λ ¯ λ (cid:12)(cid:12)(cid:12) M (0 , − ) λ ¯ λ (cid:12)(cid:12)(cid:12) + P k ik P k jl X λ ¯ λ (cid:12)(cid:12)(cid:12) M (2 , +) λ ¯ λ (cid:12)(cid:12)(cid:12) + P ⊥ ik P ⊥ jl X λ ¯ λ (cid:12)(cid:12)(cid:12) M (2 , − ) λ ¯ λ (cid:12)(cid:12)(cid:12) . (2.16)Here we decomposed the γγ → l + l − amplitude into channels of total angular momentumprojection J z = 0 , ± θ read: X λ ¯ λ (cid:12)(cid:12)(cid:12) M (0 , +) λ ¯ λ (cid:12)(cid:12)(cid:12) = g − β ) β (1 − β cos θ ) , X λ ¯ λ (cid:12)(cid:12)(cid:12) M (0 , − ) λ ¯ λ (cid:12)(cid:12)(cid:12) = g − β )(1 − β cos θ ) , X λ ¯ λ (cid:12)(cid:12)(cid:12) M (2 , +) λ ¯ λ (cid:12)(cid:12)(cid:12) = g β sin θ (1 − β cos θ ) (cid:16) − β sin θ (cid:17) , X λ ¯ λ (cid:12)(cid:12)(cid:12) M (2 , − ) λ ¯ λ (cid:12)(cid:12)(cid:12) = g β sin θ (1 − β cos θ ) , (2.17)where g = 4 πα em , and β = r − m l M (2.18)is the lepton velocity in the dilepton cms-frame. Notice that in the ultrarelativistic limit β →
1, the | J z | = 2 terms dominate, while for β ≪
1, relevant for heavy fermions, the J z = 0 components are the leading ones. A brief comment on the approach used in Ref.[19]is in order: the helicity structure used for the hard γγ → l + l − process in [19] correspondsto the sum of our | J z | = 2 terms for β → y , and transversemomenta p , p of leptons. Then the cross section fully differential in lepton variables isobtained as dσ [ C ] dy dy d p d p = Z d Q π w ( Q ; b max , b min ) Z d q π d q π δ (2) ( p + p − q − q ) × E i (cid:16) ω , q + Q (cid:17) E ∗ j (cid:16) ω , q − Q (cid:17) E k (cid:16) ω , q − Q (cid:17) E ∗ l (cid:16) ω , q + Q (cid:17) × π ˆ s X λ ¯ λ M λ ¯ λik M λ ¯ λ † jl . (2.19)The delta-functions in the phase space element determine the photon energies as: ω = 12 (cid:16) m t exp(+ y ) + m t exp(+ y ) (cid:17) , ω = 12 (cid:16) m t exp( − y ) + m t exp( − y ) (cid:17) . (2.20)where m it = p p i + m l . We perform the multidimensional integration using the VEGASMonte Carlo method [20]. III. RESULTS OF THE NEW APPROACH VERSUS EXPERIMENTAL DATA
In this section we present predictions for the centrality dependence of l + l − productionAu-Au collisions at RHIC energy ( √ s NN =200 GeV) and Pb-Pb collisions at LHC energy( √ s NN =5.02 TeV). The results of our approach will be compared to STAR, ALICE andATLAS experimental data. 6 a) (GeV) - e + e M − − − − − − − − − − −
10 110 ( / G e V ) - e + e / d M - e + e d N STAR 200GeV Au: 60 80% ×
40 60% ×
10 40% e + e →γγ + QGP ρ in medium cocktail (b) (GeV) T P − − − − − − − − − − −
10 110 ( / G e V ) T / d P - e + e d N STAR 200GeV Au: 0.40 0.76 GeV × × Wigner function e + e →γγ factorization t k e + e →γγ FIG. 2. Theoretical predictions vs. STAR experimental data at RHIC energy ( √ s = 200 GeV)[11]. (a) Dielectron invariant mass spectra for three ranges of centrality: 60 - 80 % (upper curve),40 - 60 % (middle curve) and 10 - 40 % (lower curve) [11]. Thermal radiation (dotted lines) andhadronic cocktail (dashed lines) contributions are compared with γγ → e + e − process [12]. (b)Distribution of transverse momentum of dielectron pair for three invariant mass limits [11]. k T -factorization result (dashed lines) [12] is shown for comparison to the new results (solid lines). Thecentrality is in the limit: (60-80)% We start the presentation of our results from the invariant mass distribution of low- P T dielectrons. In Fig.2(a) we show our γγ -fusion results (solid lines) together with the STARexperimental data [11] for three different ranges of centrality as defined in the STAR exper-iment. The calculation of the invariant mass distribution reproduces very well the results ofour earlier work [13]. The photon-photon process dominates for peripheral collisions. For themost central collisions, (10 - 40 )%, the γγ process starts to underestimate the experimentaldata. The detailed discussion of thermal radiation and hadronic cocktail is found in [12] andmust not be repeated here. We stress that the theoretical results are calculated includingSTAR experimental cuts i.e. p t,e > . | η e | < | y e + e − | < P T < .
15 GeV.In Fig.2(b) we show the distribution in transverse momentum of the dielectron pairs forthree centrality intervals. We get very good description of the low- P T enhancement, withinthe newly presented approach.In our previous work [12] we calculated the P T -distribution in what we dub a k T -factorization approach, where the transverse momentum of dileptons involves a convolutionof the q -dependent photon fluxes, schematically: N l + l − ( P ) ∝ Z dω ω dω ω Z d q π d q π δ (2) ( P − q − q ) N ( ω , q ) N ( ω , q ) σ γγ → l + l − (4 ω ω ) . (3.1)While our previous calculations in [12] convincingly demonstrated the dominance of the γγ process at low P T , the peak of the distribution obtained from Eq. (3.1) is systematicallyat too low values of P T , and neglects the correlation of P T with centrality.Our new theoretical results give an excellent description of both the shape and normal-ization of the low- P T enhancement. In our approach here we use a charge form factor of7he nucleus obtained from a realistic charge distribution described in [6]. The form factoralmost coincides with the one used in STARlight simulation code [21]. b (fm) ) / db ( nb /f m ) - e + A u A ue → ( A u A u σ d =200 GeV, NN s |<1 e η >0.2 GeV, | t,e p <1 GeV - e + e M <2 GeV - e + e - e + e - e + e FIG. 3. Impact parameter dependence for √ s NN = 200 GeV and different windows of dielectroninvariant mass. For completeness, in Fig.3 we show cross section for the
AuAu → e + e − AuAu processas a function of impact parameter. Here we have taken kinematical cuts adequate for theSTAR experiment. We note that the shape in impact parameter depends on the windowof dielectron mass. The impact parameter cannot be directly measured. As previouslydone in [12], we use an optical Glauber model [22] to estimate geometric quantities. Fornormalization we need the total hadronic inelastic cross section. We use the following valuesof cross sections: σ AuAu ( √ s NN = 200 GeV) = 6 936 mb and σ P bP b ( √ s NN = 5 .
02 TeV) =7 642 mb.We now proceed to LHC energies. In Fig. 4 we show our results compared to the pre-liminary experimental results obtained by the ALICE collaboration [23]. We get a similarlygood description of the preliminary ALICE data as for the case of the STAR data. Forillustration we show also result of the k T -factorization (dashed line) proposed in [12], whichclearly fails to describe the position of the peak. Indeed, the peak of the P T distributionpredicted by the k T -factorization formula Eq. (3.1) runs away towards smaller and smaller P T with increasing energy. This is related to the fact, that in the photon distribution N ( ω, q ) ∝ | E ( ω, q ) | ∝ q [ q + ( ω/γ ) ] F ( q + ( ω/γ ) ) , (3.2)the “cutoff” ω/γ decreases with increasing cm-energy (or boost γ of the ion).Consequently, for the much lower STAR energies the k T -factorization approach is onlyslightly worse than that in the new approach (see Fig. 2(b)).8 T P − − − − − ) - ( G e V T d N / d P e v / N ALICE prelim.Wignerfrom UPC =5.02 TeV, c = (70-90)% NN s |<0.8 e η >0.2 GeV, | t,e <2.7 GeV, p ee FIG. 4. Distribution in transverse momentum of the dielectron pair for √ s = 5.02 TeV. The resultsof the present approach is shown by the solid line. The preliminary ALICE data [23] are shownfor comparison. Finally in Fig.5 we show the acoplanarity distribution for dimuon production as measuredby the ATLAS collaboration [24, 25]. The acoplanarity is defined as: α = 1 − | ∆ φ l + l − | π , (3.3)where ∆ φ l + l − is the difference of the azimuthal angles of two leptons. The measurementof the dimuon production via γγ scattering process was done at rather large transversemomenta ( p t,µ > . γγ -fusion alone for the high invariant mass even for low centrality. Our result isalso in surprisingly good agreement for the case of very central collisions ( c = (0 − α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (0-10)% ATLAS prelim.ATLAS (2018)theory
FIG. 5. Acoplanarity distribution for µ + µ − production for the kinematics of the ATLAS experi-ment. For comparison we show preliminary results [24] as well as previously published ones [25]. α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (0-5)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (5-10)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (10-20)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (20-30)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (30-40)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (40-50)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (50-60)% ATLAS prelim.theory α α / d - µ + µ c = ( - ) % d N b = a ll / N | < 2.4 η = (4-45) GeV, | - µ + µ > 4 GeV, M µ t, p c = (60-70)% ATLAS prelim.theory
FIG. 6. Acoplanarity distribution for µ + µ − production for the kinematics of the ATLAS experi-ment [24, 25]. The solid line represents result of the approach presented in this paper. Each panelcorresponds to a different centrality class. V. CONCLUSION
In this paper we have presented a formalism how to calculate differential distributions ofleptons produced in semi-central ( b < R A ) nucleus-nucleus collisions for a given centrality.In this approach the differential cross section is calculated using the complete polarizationdensity matrix of photons resulting from the Wigner distribution formalism.We have presented results of calculation of several differential distributions such as invari-ant mass of dileptons, dilepton transverse momentum and acoplanarity for different regionsof centrality. The results of the calculations have been compared to experimental data ofthe STAR, ALICE and ATLAS collaboration. A good agreement has been achieved in allcases. Our approach gives much better agreement with experimental data than the previousapproaches used in the literature. Recently the CMS collaboration measured modificationsof α distributions [26] correlated with neutron multiplicity. A very new ATLAS study alsopresents the dimuon cross sections in the presence of forward and/or backward neutronproduction [27]. This goes beyond present studies, and we plan such studies it in the fu-ture. Our formalism can be readily extended to such processes, using the impact parameterdistributions obtained in [28].We have obtained a good description of the data without introducing additional finalstate rescattering of leptons in the quark-gluon plasma. More work is necessary to identifyobservables that can probe electromagnetic properties of the QGP. ACKNOWLEDGEMENTS
This work was partially supported by the Polish National Science Center under grant No.2018/31/B/ST2/03537 and by the Center for Innovation and Transfer of Natural Sciencesand Engineering Knowledge in Rzesz´ow (Poland). [1] Gerhard Baur, Kai Hencken, Dirk Trautmann, Serguei Sadovsky, and Yuri Kharlov.Coherent gamma gamma and gamma-A interactions in very peripheral collisions atrelativistic ion colliders.
Phys. Rept. , 364:359–450, 2002. arXiv:hep-ph/0112211 , doi:10.1016/S0370-1573(01)00101-6 .[2] Carlos A. Bertulani, Spencer R. Klein, and Joakim Nystrand. Physics of ultra-peripheralnuclear collisions. Ann. Rev. Nucl. Part. Sci. , 55:271–310, 2005. arXiv:nucl-ex/0502005 , doi:10.1146/annurev.nucl.55.090704.151526 .[3] J.G. Contreras and J.D. Tapia Takaki. Ultra-peripheral heavy-ion collisions at the LHC. Int.J. Mod. Phys. A , 30:1542012, 2015. doi:10.1142/S0217751X15420129 .[4] Spencer Klein and Peter Steinberg. Photonuclear and Two-photon Interactions at High-Energy Nuclear Colliders.
Ann.Rev.Nucl.Part.Sci. , 70:232, 2020. arXiv:2005.01872 , doi:10.1146/annurev-nucl-030320-033923 .[5] Wolfgang Sch¨afer. Photon induced processes: from ultraperipheral to semicentral heavy ioncollisions. Eur. Phys. J. A , 56(9):231, 2020. doi:10.1140/epja/s10050-020-00231-8 .[6] M. Klusek-Gawenda and A. Szczurek. Exclusive muon-pair productions in ultrarelativisticheavy-ion collisions – realistic nucleus charge form factor and differential distributions.
Phys.Rev. C , 82:014904, 2010. arXiv:1004.5521 , doi:10.1103/PhysRevC.82.014904 .
7] C. Azevedo, V.P. Gon¸calves, and B.D. Moreira. Exclusive dilepton production in ultrape-ripheral
P bP b collisions at the LHC.
Eur. Phys. J. C , 79(5):432, 2019. arXiv:1902.00268 , doi:10.1140/epjc/s10052-019-6952-8 .[8] N. Baron and G. Baur. Unraveling gamma gamma dileptons in central relativistic heavy ioncollisions. Z. Phys. C , 60:95–100, 1993. doi:10.1007/BF01650434 .[9] Jaroslav Adam et al. Measurement of an excess in the yield of
J/ψ at very low p T in Pb-Pbcollisions at √ s NN = 2.76 TeV. Phys. Rev. Lett. , 116(22):222301, 2016. arXiv:1509.08802 , doi:10.1103/PhysRevLett.116.222301 .[10] Mariola K lusek-Gawenda and Antoni Szczurek. Photoproduction of J/ψ mesons in peripheraland semicentral heavy ion collisions.
Phys. Rev. C , 93(4):044912, 2016. arXiv:1509.03173 , doi:10.1103/PhysRevC.93.044912 .[11] Jaroslav Adam et al. Low- p T e + e − pair production in Au+Au collisions at √ s NN = 200 GeVand U+U collisions at √ s NN = 193 GeV at STAR. Phys. Rev. Lett. , 121(13):132301, 2018. arXiv:1806.02295 , doi:10.1103/PhysRevLett.121.132301 .[12] Mariola K lusek-Gawenda, Ralf Rapp, Wolfgang Sch¨afer, and Antoni Szczurek. Dilepton Ra-diation in Heavy-Ion Collisions at Small Transverse Momentum. Phys. Lett. B , 790:339–344,2019. arXiv:1809.07049 , doi:10.1016/j.physletb.2019.01.035 .[13] Spencer Klein, A.H. Mueller, Bo-Wen Xiao, and Feng Yuan. Acoplanarity of a Lepton Pairto Probe the Electromagnetic Property of Quark Matter. Phys. Rev. Lett. , 122(13):132301,2019. arXiv:1811.05519 , doi:10.1103/PhysRevLett.122.132301 .[14] Wangmei Zha, James Daniel Brandenburg, Zebo Tang, and Zhangbu Xu. Initial transverse-momentum broadening of Breit-Wheeler process in relativistic heavy-ion collisions. Phys. Lett.B , 800:135089, 2020. arXiv:1812.02820 , doi:10.1016/j.physletb.2019.135089 .[15] Cong Li, Jian Zhou, and Ya-Jin Zhou. Impact parameter dependence of the azimuthal asym-metry in lepton pair production in heavy ion collisions. Phys. Rev. D , 101(3):034015, 2020. arXiv:1911.00237 , doi:10.1103/PhysRevD.101.034015 .[16] Itzhak Tserruya. Electromagnetic Probes. Landolt-Bornstein , 23:176, 2010. arXiv:0903.0415 , doi:10.1007/978-3-642-01539-7_7 .[17] Ralf Rapp. Dilepton Spectroscopy of QCD Matter at Collider Energies. Adv. High EnergyPhys. , 2013:148253, 2013. arXiv:1304.2309 , doi:10.1155/2013/148253 .[18] M. Vidovic, M. Greiner, C. Best, and G. Soff. Impact parameter dependence of the electromag-netic particle production in ultrarelativistic heavy ion collisions. Phys. Rev. C , 47:2308–2319,1993. doi:10.1103/PhysRevC.47.2308 .[19] Spencer Klein, A.H. Mueller, Bo-Wen Xiao, and Feng Yuan. Lepton Pair Production ThroughTwo Photon Process in Heavy Ion Collisions. 3 2020. arXiv:2003.02947 .[20] G.Peter Lepage. A New Algorithm for Adaptive Multidimensional Integration.
J. Comput.Phys. , 27:192, 1978. doi:10.1016/0021-9991(78)90004-9 .[21] Spencer R. Klein, Joakim Nystrand, Janet Seger, Yuri Gorbunov, and Joey Butter-worth. STARlight: A Monte Carlo simulation program for ultra-peripheral collisionsof relativistic ions.
Comput. Phys. Commun. , 212:258–268, 2017. arXiv:1607.03838 , doi:10.1016/j.cpc.2016.10.016 .[22] Michael L. Miller, Klaus Reygers, Stephen J. Sanders, and Peter Steinberg. Glauber mod-eling in high energy nuclear collisions. Ann. Rev. Nucl. Part. Sci. , 57:205–243, 2007. arXiv:nucl-ex/0701025 , doi:10.1146/annurev.nucl.57.090506.123020 .[23] Sebastian Lehner. Dielectron production at low transverse momentum in Pb-Pb colli-sions at √ s NN = 5 .
02 TeV with ALICE.
PoS , LHCP2019:164, 2019. arXiv:1909.02508 , oi:10.22323/1.350.0164 .[24] Measurement of non-exclusive dimuon pairs produced via γγ scattering in Pb+Pb collisionsat √ s NN = 5 .
02 TeV with the ATLAS detector.
ATLAS-CONF-2019-051 .[25] Morad Aaboud et al. Observation of centrality-dependent acoplanarity for muon pairsproduced via two-photon scattering in Pb+Pb collisions at √ s NN = 5 .
02 TeV withthe ATLAS detector.
Phys. Rev. Lett. , 121(21):212301, 2018. arXiv:1806.08708 , doi:10.1103/PhysRevLett.121.212301 .[26] Albert M Sirunyan et al. Observation of forward neutron multiplicity dependence ofdimuon acoplanarity in ultraperipheral PbPb collisions at √ s NN = 5.02 TeV. 11 2020. arXiv:2011.05239 .[27] Georges Aad et al. Exclusive dimuon production in ultraperipheral Pb+Pb collisions at √ s NN = 5 .
02 TeV with ATLAS. 11 2020. arXiv:2011.12211 .[28] Mariola K lusek-Gawenda, Micha l Ciema la, Wolfgang Sch¨afer, and Antoni Szczurek. Elec-tromagnetic excitation of nuclei and neutron evaporation in ultrarelativistic ultrape-ripheral heavy ion collisions.
Phys. Rev. C , 89(5):054907, 2014. arXiv:1311.1938 , doi:10.1103/PhysRevC.89.054907 ..