Photonuclear and Two-photon Interactions at High-Energy Nuclear Colliders
PPhotonuclear and
Two-photon Interactions atHigh-Energy Nuclear
Colliders
Spencer R. Klein and Peter Steinberg Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CAUSA 94720; email: [email protected] Brookhaven National Laboratory, Upton, NY 11973-5000; email:[email protected]
Keywords ultra-peripheral collisions, photonuclear interactions, two-photoninteractions, heavy-ion collisions, vector mesons, nuclear imaging
Abstract
Ultra-peripheral collisions of heavy ions and protons are the energyfrontier for electromagnetic interactions. Both photonuclear and two-photon collisions are studied, at collision energies that are far higherthan are available elsewhere. In this review, we will discuss physicstopics that can be addressed with UPCs, including nuclear shadowingand nuclear structure and searches for beyond-standard-model physics. a r X i v : . [ nu c l - e x ] M a y ontents
1. Introduction: ultraperipheral collisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. The photon flux from a relativistic ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1. Impact parameter dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2. Nuclear dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3. k T spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4. Uncertainties on the photon flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73. Photoproduction processes: γ + p and γ + A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.1. Low energy photonuclear interactions (including nuclear dissociation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2. Probing nuclear parton distributions with incoherent photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3. Coherent and incoherent photoproduction of vector mesons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4. The dipole model and nuclear imaging with coherent photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.5. Incoherent Photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.6. Photoproduction of exotic hadrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204. Two photon interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1. Two-photon luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2. Dilepton production: γ + γ → (cid:96) + (cid:96) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.3. Dilepton p T and impact parameter selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.4. Bound-free pair production, antihydrogen production and accelerator luminosity limits . . . . . . . . . . . . . . 244.5. Light-by-light scattering: γ + γ → γ + γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.6. Hadron production: γ + γ → X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265. Future prospects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1. Introduction: ultraperipheral collisions
Ultra-peripheral collisions (UPCs) involve collisions of relativistic nuclei (heavy ions or pro-tons) at impact parameters ( b ) that are large enough so that there are no hadronic interac-tions. Instead, the ions interact electromagnetically, either via photonuclear or two-photoninteractions. In UPCs, the photons are nearly real, with virtuality Q < (¯ h/R A ) , where R A is the nuclear radius. Typical photonuclear interactions are vector meson photoproduc-tion or production of dijets. Typical γγ interactions lead to final states such as dileptons,single mesons or meson pairs, or two photons (via light-by-light scattering). Figure 1 showssome of the reactions that will be discussed here. Ultra-peripheral collisions have previouslybeen reviewed elsewhere (1, 2, 3, 4, 5, 6); the focus here is on newer developments. Wewill also briefly discuss photoproduction and two-photon interactions in peripheral hadroniccollisions.This review will primarily focus on collisions involving nuclei and/or protons atBrookhaven’s Relativistic Heavy Ion Collider (RHIC) and at CERN’s Large Hadron Col-lider (LHC). The LHC collisions are the energy frontier for photonuclear and two-photonphysics, while RHIC typically provides higher integrated luminosities and photon energieswell suited for photonuclear interactions involving Reggeon exchange. We also briefly con-sider collisions at CERN’s proposed future circular collider (FCC), China’s proposed SPPC(7), and AFTER, a proposed fixed-target experiment utilizing a beam extracted from theLHC (8). AFTER has a lower maximum γp center of mass energy, W γp ≈ c de f gb h PbPb Pb c ¯ c Pb k k PbPb Pb µ + µ − Pb k k PbPb Pb µ + γµ − Pb PbPb Pb γγ PbPbPb Pb ! + X Pb PbPb Pb ! +Xjet/ ¯ Q jet/ Q Pb PbPb Pb c ¯ c Pb ! PbPb Pb ! γγ Pb ! Figure 1: Some of the UPC reactions that will be discussed in this review: (a) genericphotonuclear interaction with neutron breakup of the target, (b) incoherent photoproduc-tion, generic to heavy quarks and jets, (c) exclusive photoproduction of a vector meson(d) coherent photoproduction of a vector meson, accompanied by nuclear excitation, (e)dilepton production γγ → l + l − (f) dilepton production γγ → l + l − + γ , including higherorder final-state radiation (g) light-by-light scattering, with no nuclear breakup (h) centralexclusive diphoton production, with double breakup.studied at e + e − colliders. Table 1 gives the maximum energies for different ion species atthese machines. Nuclear beams provide several distinct advantages1. a large effective photon luminosity boost proportional to Z for each nucleus, com-pensating for the overall lower luminosity of nuclear beams2. reduced virtuality3. the possibility of multi-photon exchange between a single ion pair, allowing for taggingof different impact parameter distributions and photon spectra.Early UPC studies largely focused on e + e − pair production and low-energy nuclearphysics (1). In the late 1980’s, interest grew in using UPCs to probe fundamental physics,most notably two-photon production of the Higgs (9, 10). Although the resulting γγ lu-minosities were not encouraging for observing the Higgs, they did stimulate work on γγ production of other particles. The first calculations of coherent photoproduction with goldbeams at RHIC predicted high rates of vector meson photoproduction (11), which werequickly confirmed by the STAR Collaboration (12). The combination of large cross-sectionsand available experimental data stimulated further interest. With the advent of the LHC,the energy reach for UPCs extended dramatically, and the field has blossomed.A key to development of UPC as a precision laboratory for electromagnetic and stronginteraction processes is the development of event generators that simulate both the ini-tial photon flux and the relevant physics processes. The most widely-used generator codeis STARLight (13) which has been available since the early days of the RHIC program.It implements one and two photon processes, and includes a set of final states includingvector mesons, meson pairs, and dileptons, with more general photonuclear processes ac- ••
Ultra-peripheral collisions (UPCs) involve collisions of relativistic nuclei (heavy ions or pro-tons) at impact parameters ( b ) that are large enough so that there are no hadronic interac-tions. Instead, the ions interact electromagnetically, either via photonuclear or two-photoninteractions. In UPCs, the photons are nearly real, with virtuality Q < (¯ h/R A ) , where R A is the nuclear radius. Typical photonuclear interactions are vector meson photoproduc-tion or production of dijets. Typical γγ interactions lead to final states such as dileptons,single mesons or meson pairs, or two photons (via light-by-light scattering). Figure 1 showssome of the reactions that will be discussed here. Ultra-peripheral collisions have previouslybeen reviewed elsewhere (1, 2, 3, 4, 5, 6); the focus here is on newer developments. Wewill also briefly discuss photoproduction and two-photon interactions in peripheral hadroniccollisions.This review will primarily focus on collisions involving nuclei and/or protons atBrookhaven’s Relativistic Heavy Ion Collider (RHIC) and at CERN’s Large Hadron Col-lider (LHC). The LHC collisions are the energy frontier for photonuclear and two-photonphysics, while RHIC typically provides higher integrated luminosities and photon energieswell suited for photonuclear interactions involving Reggeon exchange. We also briefly con-sider collisions at CERN’s proposed future circular collider (FCC), China’s proposed SPPC(7), and AFTER, a proposed fixed-target experiment utilizing a beam extracted from theLHC (8). AFTER has a lower maximum γp center of mass energy, W γp ≈ c de f gb h PbPb Pb c ¯ c Pb k k PbPb Pb µ + µ − Pb k k PbPb Pb µ + γµ − Pb PbPb Pb γγ PbPbPb Pb ! + X Pb PbPb Pb ! +Xjet/ ¯ Q jet/ Q Pb PbPb Pb c ¯ c Pb ! PbPb Pb ! γγ Pb ! Figure 1: Some of the UPC reactions that will be discussed in this review: (a) genericphotonuclear interaction with neutron breakup of the target, (b) incoherent photoproduc-tion, generic to heavy quarks and jets, (c) exclusive photoproduction of a vector meson(d) coherent photoproduction of a vector meson, accompanied by nuclear excitation, (e)dilepton production γγ → l + l − (f) dilepton production γγ → l + l − + γ , including higherorder final-state radiation (g) light-by-light scattering, with no nuclear breakup (h) centralexclusive diphoton production, with double breakup.studied at e + e − colliders. Table 1 gives the maximum energies for different ion species atthese machines. Nuclear beams provide several distinct advantages1. a large effective photon luminosity boost proportional to Z for each nucleus, com-pensating for the overall lower luminosity of nuclear beams2. reduced virtuality3. the possibility of multi-photon exchange between a single ion pair, allowing for taggingof different impact parameter distributions and photon spectra.Early UPC studies largely focused on e + e − pair production and low-energy nuclearphysics (1). In the late 1980’s, interest grew in using UPCs to probe fundamental physics,most notably two-photon production of the Higgs (9, 10). Although the resulting γγ lu-minosities were not encouraging for observing the Higgs, they did stimulate work on γγ production of other particles. The first calculations of coherent photoproduction with goldbeams at RHIC predicted high rates of vector meson photoproduction (11), which werequickly confirmed by the STAR Collaboration (12). The combination of large cross-sectionsand available experimental data stimulated further interest. With the advent of the LHC,the energy reach for UPCs extended dramatically, and the field has blossomed.A key to development of UPC as a precision laboratory for electromagnetic and stronginteraction processes is the development of event generators that simulate both the ini-tial photon flux and the relevant physics processes. The most widely-used generator codeis STARLight (13) which has been available since the early days of the RHIC program.It implements one and two photon processes, and includes a set of final states includingvector mesons, meson pairs, and dileptons, with more general photonuclear processes ac- •• Two-photon and Photonuclear reactions 3
ABLE 1: This table compares the capabilities of different colliders, in terms of available energy for pho-tonuclear and photon-photon processes. The table shows the accelerator, ion species, √ s NN , the maximumphoton energy (in the target rest frame, relevant for cosmic-ray studies), W γp (the γp photonuclear center-of-mass energy), and the maximum γγ energy for two-photon interactions. For the photonuclear interactions,the maximum energies correspond to x = 1 in Eq. 1 with b = R + R , the sum of the nuclear radii. For γγ interactions, the maximum photon energy is given for x = 1 when b is the nuclear radius. For the proton,we use r = 0 . W γp is higher when the photons from proton strike the heavy ion than forthe reverse case. The table lists the opposite case, since the reaction rate for that direction is usually muchhigher. For pPb at the LHC, the proton and ion beams have different Lorentz boosts, so the per-nucleoncenter of mass is boosted with respect to the lab frame. For the electron-ion colliders, we used the energiesfrom the cited references (the designs are still evolving, so the beam energies may change), with the samemaximum photon energy criteria as for UPCs. Facility System √ s NN or √ s eN Max. E γ Max. W γp Max √ s γγ RHIC AuAu 200 GeV 320 GeV 25 GeV 6 GeVpAu 200 GeV 1.5 TeV 52 GeV 30 GeVpp 500 GeV 20 TeV 200 GeV 150 GeVLHC (17) PbPb 5.1 TeV 250 TeV 700 GeV 170 GeVpPb 8.16 TeV 1.1 PeV 1.5 TeV 840 GeVpp 14 TeV 16 PeV 5.4 TeV 4.2 TeVFCC-hh (18) PbPb 40 TeV 13 PeV 4.9 TeV 1.2 TeVSPPC (7) pPb 57 TeV 58 PeV 10 TeV 6.0 TeVpp 100 TeV 800 PeV 39 TeV 30 TeVeRHIC (19) eAu 89 GeV 4.0 TeV 89 GeV 15 GeVLHeC (20) ePb 820 GeV 360 TeV 820 GeV 146 GeV cessible using the DPMJET3 code. The SuperCHIC 3 Monte Carlo (14) also implementsnuclear photon fluxes, and computes many of the same processes. Finally, event generatorsmore commonly-used for proton-proton reactions, particularly
Pythia
2. The photon flux from a relativistic ion2.1. Impact parameter dependence
A relativistic ion carries Lorentz-contracted electric and magnetic fields; the electric fieldradiates outward from the ion, while the magnetic field circles the ion. Fermi (21), vonWeizs¨acker (22) and Williams (23) showed that these perpendicular fields may be treatedas a flux of linearly polarized virtual photons; the energy spectrum is given by the Fouriertransform of their spatial (along the ion direction) dependence. In the relativistic limit( β →
1) at a distance b from an ion (where b > R A ), the photon energy ( k ) spectrum from n ion with charge Z , velocity βc , Lorentz boost γ is N ( k, b ) = Z αk π γ ¯ h β (cid:18) K ( x ) + K ( x ) γ (cid:19) , K and K are Bessel functions and x = kb/βγ ¯ hc . For x < N ( k, b ) ∝ /x , while,for x >
1, the flux is exponentially suppressed. The larger the photon energy, the smallerthe range of b that can contribute to the flux. Impact parameter: b i is the genericdistance from one ofthe ions, while b and b are thedistances from eachof the two ions. b isthe ion-ion impactparameter. Momentum: k is aphoton momentum, k and k are thephoton momenta intwo-photoninteractions, q is forthe exchangegluon/Pomeron,capital P themomentum of thefinal state Momentum transfer: t is the squaredmomentum transfer,which is q in anelastic process. Pairs: M (cid:96)(cid:96) is thefinal state mass for adi-lepton state, and Y (cid:96)(cid:96) is the final statepair rapidity. The values of β and γ are frame-dependent. At colliders, the Lorentz boost of thephoton-emitting nucleus in the target rest frame is Γ = 2 γ −
1, so photon energies in thePeV range (1 PeV = 10 eV) are accessible in the target rest frame. The target frame isuseful for comparison with cosmic-ray air showers.The total photon flux is found by integrating Eq. 1 over b . The integration rangedepends on the application. For ultra-peripheral collisions, we exclude collisions where thenuclei interact hadronically, to allow for reconstruction of exclusive final states. This canbe done by taking the minimum impact parameter b min to be 2 R A . The total flux is N ( k ) = Z αk π γ ¯ h β (cid:18) K ( u ) + K ( u ) γ (cid:19) , α ≈ /
137 is the fine structure constant and u = γ ¯ hc/b min = γ ¯ hc/ R A .Equation 2 ignores the nuclear skin thickness (about 0.5 fm) and the range of the stronginteraction. The flux can be more accurately calculated with N ( k ) = (cid:90) d bN ( k, b ) P ( b ) , P ( b ) is the probability of not having a hadronic interaction. P ( b ) can be calcu-lated with a Glauber calculation (24) which accounts for the nuclear shape and interactionprobability. In these calculations, the nucleon distribution of heavy nuclei is well describedby a Woods-Saxon distribution, while a Gaussian form factor is appropriate for lighter nu-clei ( Z ≤
6) (13). For protons, a dipole form factor is found to work well (25, 16, 26). Thiscorresponds to an exponential charge distribution.
For heavy nuclei, Zα ≈ .
6, so the probability of exchanging more than one photon betweenthe two ions in an individual collision must be considered. These photons are essentiallyindependent of each other, even if they are emitted by the same nucleus (27). The additionalphotons may dissociate one or both nuclei, or, less often, introduce additional particles intothe detector. Because of the radial dependence of the photon flux, the presence of theseadditional photons can preferentially select certain impact parameter ranges, and so caninfluence the photon spectrum of the other photons.Some triggers or analyses may require either the presence or absence of neutrons inforward zero-degree calorimeters (ZDCs). Additional photons may break up one or bothnuclei, producing neutrons. Mutual Coulomb Excitation (MCE), via two additional ex-changed photons generally leads to neutrons in both ZDCs.If a harder photon spectrum is desired, one can require neutrons in one or both ZDCsto select events with additional Coulomb excitation, i. e. with smaller impact parameters. ••
6, so the probability of exchanging more than one photon betweenthe two ions in an individual collision must be considered. These photons are essentiallyindependent of each other, even if they are emitted by the same nucleus (27). The additionalphotons may dissociate one or both nuclei, or, less often, introduce additional particles intothe detector. Because of the radial dependence of the photon flux, the presence of theseadditional photons can preferentially select certain impact parameter ranges, and so caninfluence the photon spectrum of the other photons.Some triggers or analyses may require either the presence or absence of neutrons inforward zero-degree calorimeters (ZDCs). Additional photons may break up one or bothnuclei, producing neutrons. Mutual Coulomb Excitation (MCE), via two additional ex-changed photons generally leads to neutrons in both ZDCs.If a harder photon spectrum is desired, one can require neutrons in one or both ZDCsto select events with additional Coulomb excitation, i. e. with smaller impact parameters. •• Two-photon and Photonuclear reactions 5 − − − - d y ) ( G e V / c ) T N / ( dp ( - % ) d < 0.76 GeV/c ee > 0.2 GeV/c eT p | < 1 ee | < 1, |y e η | ( m b ) T ( X n X n ) / dp σ ( U P C ) d (GeV/c) P T UPC Au+Au 200 GeV60-80% Au+Au 200 GeV (UPC) - e + e →γγ (60-80%) - e + e →γγ − α α d s N d s N ATLAS = 5.02 TeV NN s -1 Pb+Pb, 0.49 nb a b V OLUME
89, N
UMBER
ULY
TABLE I. Cross sections and median impact parameters b m , for production of vector mesons.Meson Overall XnXn n n s (mb) b m (fm) s (mb) b m (fm) s (mb) b m (fm)Gold beams at RHIC ( g cm ! ) r
590 46 39 18 3.5 19 v
59 46 3.9 18 0.34 19 f
39 38 3.1 18 0.27 19 J ! c g cm ! ) r v
490 290 19 19 1.1 22 f
460 220 20 19 1.1 22 J ! c
32 68 2.5 19 0.14 21
Table I gives the production cross sections and medianimpact parameters b m for the different tags, as calculatedfrom Eq. (5). The XnXn and n n cross sections areabout ! and ! of the untagged cross sections,respectively.Figure 2 compares the probability of r production asa function of impact parameter for XnXn and n n ex-citation and also without requiring nuclear excitation for(a) gold-gold collisions at a center of mass energy p s NN ! GeV per nucleon, as are found at the RelativisticHeavy Ion Collider (RHIC) at Brookhaven National Labo-ratory, and for (b) lead-lead collisions at p s NN ! TeVper nucleon as are planned at the Large Hadron Collider p ( b ) a) b [ fm ] p ( b ) b) FIG. 2. The probability of r production with (a) gold beamsat RHIC and (b) lead beams at the LHC as a function of b ,with XnXn (dashed curve) and n n (dotted curve) and withoutnuclear excitation (solid curve). The n n curve is multipliedby 10 to fi t on the plot. (LHC) at CERN. These curves were obtained by evalu-ating the integrand of Eq. (5) at different b . The b dis-tributions are very different for tagged and untagged r production; this is re fl ected in the vastly different b m inTable I. The n n and XnXn spectra are closer, exceptthat
XnXn is more strongly peaked for b , fm, likelyre fl ecting the increased phase space for high-energy exci-tations there. With nuclear breakup, b m is almost indepen-dent of the fi nal state vector meson.Figure 3 shows the rapidity distribution d s ! dy for r and J ! c production at RHIC and the LHC. Spectra for XnXn and n n breakup are shown, along with the un-tagged d s ! dy . The d s ! dy are symmetric around y ! because either nucleus can emit the photon. Since thephoton spectrum falls as ! k and y ! ! ln " k ! M V , the y d σ / d y [ m b ] a) b)y d σ / d y [ µ b ] y d σ / d y [ m b ] c) d)y d σ / d y [ m b ] FIG. 3. Rapidity spectrum d s ! dy for (a) r production atRHIC, (b) J ! c production at RHIC, (c) r production at LHC,and (d) J ! c production at the LHC. The solid line is the totalproduction, the dashed line is for XnXn , multiplied by 10, andthe dotted line is n n , multiplied by 100.
10b (fm)00.51 ( b ) f n P STARLIGHT 3.13LHC beam energyXnXn0n0nXn0n a b
Figure 2: (a.) Impact parameter dependence of the probabilities, from
STARLight n n , or no neutron emission in eitherdirection, which selects impact parameters b >
40 fm 2) X n n , with neutron emission in onlyone direction, which selects impact parameters of b ∼
20 fm, and 3) X n X n , with neutronemission in both directions, selecting impact parameters b <
15 fm. (b.)
STARLight calculation of the impact parameter dependence of coherent ρ production, assuming differentZDC fragmentation scenarios, from Ref. (28). The difference between MCE and no breakupis quite stark at larger impact parameters.Adding breakup conditions leads to N ( k ) = (cid:90) d bN ( k, b ) P ( b ) P ( b ) P ( b ) , P and P are the excitation probability for the two nuclei. Generally, P i ( b ) ∝ /b , so requiring nuclear excitation leads to smaller impact parameters. Thisis demonstrated using STARLight for the three possible cases in Fig 2 (a), which showsthe functional forms of P fn ( b ), the impact-parameter-dependent probability of a particularforward neutron configuration: X n X n ( P ( b ) P ( b )), X n n ((1 − P ) P + (1 − P ) P ), and0 n n ((1 − P )(1 − P )). Calculations from Ref. (28), shown in Fig 2 (b), demonstrate thestark differences in the impact parameter dependence of ρ photoproduction for differentZDC topologies (X n X n , 1 n n , and 0 n n here) for collisions at RHIC.Eq. 4 can also be applied to meson photoproduction. At the LHC, when b = 2 R A ,the probability of producing a ρ is about 3%; assuming that the electromagnetic fields arenot depleted, the probability of ρ photoproduction should be Poisson distributed, so theprobability of producing two ρ is about 5 × − . This is roughly 1 million pairs in a 1-month LHC heavy ion run (11). More exotic pairs, like ρJ/ψ , should also be visible. Thesepairs are of interest because the two vector mesons should share a common polarization(27). Since they are bosons, there should be an enhanced probability to produce the twomesons in the same final state, and, potentially, observe stimulated decays.For some applications, the photon flux within the nucleus ( b < R A ) is of interest. Twoexamples are γγ production of lepton pairs, which may occur within one of the nuclei(without dissociating it), even when b > R A , and for studying electromagnetic processesin peripheral collisions, where there are also hadronic interactions. At transverse distance b i < R A from the nuclear center, only nucleons in a cylinder with radius b i contributecoherently to the interaction (29). This can be handled by adding a form factor to the hoton emission flux (30, 31, 32). It is also possible that the hadronic interaction mightdisrupt the coherent photon emission. However, since the photons are nearly real, theyshould be mostly emitted at a time before the hadronic interaction occurs. k T spectrum The photon k T spectrum can be derived from the equivalent photon approximation (EPA).If one integrates the photon flux over all b , then the photon k T may be determined exactly(30) d Nd k T = αZ F ( k T + k z /γ ) k T π ( k T + k z ) , F ( k ) is the nuclear form factor. When integrated over k T , this gives Eq. 3.If the range of b is restricted, such as by requiring b > R A or by weighting the b -distribution by the requirement that there be an additional photon or photons exchanged,the problem becomes much more complicated, because k T and b are conjugate variables.This is seen in more complete QED calculations, e.g. Ref. (30) and (32). As the range of b is restricted, the mean k T should increase. Unfortunately, we do not yet have a method tocalculate the k T spectrum for these cases. Calculations for two-photon interactions are morecomplicated because the γγ interaction point is distinct from the radial positions relativeto each of the two nuclei. In principle, restrictions on the ion-ion impact parameter do notaffect the photon p T spectrum at this third point. However, final states clearly identifiedwith γγ → l + l − show significant k T broadening as the impact parameter range is restrictedto smaller values in hadronic heavy ion collisions (33, 34, 35), as we discuss below. The photon flux calculations are subject to a number of theoretical uncertainties:1.
Overlap condition
The implementation of P is straightforward, but imple-mented using optical Glauber calculations, which are known to be limited in ap-plicability.2. Restriction on production points
It is typically assumed that UPC processes cannot originate within a nucleus, i.e. b i > R i , but this is not clearly established usingdata. It is possible that some range within a nucleus could be accessible to theseprocesses, contributing to the observed enhancement of J/ψ in peripheral collisions.3.
Assumption of a uniform flux
Normally, the photon flux is taken to be constantacross the entire target nucleus, well represented by a plane wave. This assumptionignores the fact that the maximum photon energy (and flux) are higher on the nearside of the nucleus, and lower on the far side.For two-photon interactions, the effect of changing impact parameter cutoffs has beenstudied. The uncertainty rises with increasing W γγ / √ s nn , reaching about 5% at half ofthe maximum W γγ in Table 1 (36). For the others, precise experimental measurements arerequired to assess their relative importance. ••
Normally, the photon flux is taken to be constantacross the entire target nucleus, well represented by a plane wave. This assumptionignores the fact that the maximum photon energy (and flux) are higher on the nearside of the nucleus, and lower on the far side.For two-photon interactions, the effect of changing impact parameter cutoffs has beenstudied. The uncertainty rises with increasing W γγ / √ s nn , reaching about 5% at half ofthe maximum W γγ in Table 1 (36). For the others, precise experimental measurements arerequired to assess their relative importance. •• Two-photon and Photonuclear reactions 7 . Photoproduction processes: γ + p and γ + A Since the photon spectrum scales roughly as 1 /k , the most common photonuclear inter-actions involve low-energy nuclear excitations. The Coulomb excitation with the largestcross-section is the Giant Dipole Resonance (GDR). In it, protons and neutrons oscillatecollectively, against each other (37). The GDR has the same quantum numbers as the pho-ton J PC = 1 −− , so it is readily excited by them. GDRs decay primarily by single neutronemission, while most higher excitations involve the emission of multiple neutrons. For thisreason, it is a useful calibration signal. The total excitation cross-section is determined bycombining the photon spectrum with the photonuclear excitation cross-section: σ (Excitation) = (cid:90) dk dNdk σ ( γA → A (cid:63) ) . σ ( γA → A (cid:63) ) is determined from a compilation of photoexcitation data (38), or, in somecases, from first principles (39). Because these cross-sections can be very large, correctionsmay be needed to account for unitarity, because without them, P i ( b ) can be large for b ≈ R A (38). Multiple photon absorption leads to higher excitations. The Coulombexcitation cross-section is about 95 barns with gold-gold collisions at RHIC, and 220 barnswith lead-lead collisions at the LHC .Interactions with different requirements on nuclear breakup (or non-breakup, wherewe require no observed neutrons) can be calculated in an impact parameter dependentformalism. For example, MCE primarily occurs via two-photon exchange, with each photonexciting one nucleus. The cross-section for MCE is σ (X n X n ) = (cid:90) d bP ( b ) P ( b ) P had ( b ) , P ( b ) when b ≈ R A . This uncertainty can be avoided by instead calculating andmeasuring the summed cross-section for MCE plus hadronic interactions (40). Alternately,events with one neutron in each ZDC generally correspond to mutual GDR excitation whichhas lower backgrounds from hadronic interaction than MCE in general(41), although thecross-sections are lower, so the statistics are limited.The neutron multiplicity distribution in Coulomb exchange processes has been stud-ied by several groups (42), most recently by the ALICE experiment (43), whose ZDCscould separate events containing from one to four neutrons. Their measurements werein generally good agreement with the predictions of the RELDIS model (39), which usesthe Weizsacker-Williams photon flux, measured photonuclear cross-sections and neutronemission via cascade and evaporation codes. The n n afterburner (44) performs similarcalculations, but in a Monte Carlo format which can be used with existing simulations tosimulate vector meson photoproduction with nuclear breakup. As Fig. 1(b) shows, the photon-gluon fusion process directly probes the gluons in the on-coming nucleus, so it can be used to directly study nuclear shadowing (45). Triggering on x − − −
10 1 b / G e V ] µ [ A x d T H d σ ∼ d − − − − − − < 50 GeV T H
42 < ) -1 × < 59 GeV ( T H
50 < ) -2 × < 70 GeV ( T H
59 < ) -3 × < 84 GeV ( T H
70 < ) -4 × < 100 GeV ( T H
84 < ) -5 × < 119 GeV ( T H
100 < ) -6 × < 141 GeV ( T H
119 < ) -7 × < 168 GeV ( T H
141 < ) -8 × < 200 GeV ( T H
168 <
Preliminary
ATLAS -1 NN s =0.4 jets R t k anti- > 20 GeV leadT p > 35 GeV jets m Not unfolded for detector response
DataPythia+STARlightscaled to data a b
Figure 3: (a.) Event display of an event with a large gap in one direction, with two jets inthe other direction. (b.) Uncorrected triple differential cross sections, from Ref. (46).such processes is aided by the fact that the photon emitter typically does not break up.However the recoiling partons will in general excite the nucleus, leading to nuclear dissoci-ation, and an accompanying partonic connection (‘string’) between the reaction productsand the nuclear remnants.This leads to a distinct event signature, with limited transverse energy, neutrons in onlyone direction, and one or more reconstructed jets, easily implemented in an experimentaltrigger. Fig. 3 (a) shows an example event, triggered using an exclusive one-arm ZDCtrigger and containing two forward reconstructed jets.Jets are straightforward to reconstruct, particularly in low-multiplicity photonuclearevents, but the condition that they are well-reconstructed imposes a minimum p T , which re-stricts the kinematic coverage in Bjorken- x (the fraction of the nucleon momentum) and Q ,the hardness scale of the interaction. ATLAS has presented preliminary triple-differentialquasi-cross sections corrected for trigger efficiency, but not yet unfolded for experimentalresolution (46). The experimental variables are H T , the scalar sum of the observed jettransverse momenta, z γ , which reflects the energy fraction of the incoming nucleon energycarried by the photon, and x A , the per-nucleon momentum fraction in the struck nucleus.The data are compared to a Pythia µ + N interactions, medi-ated by a nearly-real photon, with the photon spectrum reweighted to match STARLight and finally with the normalization adjusted to match to the data. The particular resultshown in Fig. 3 (b) shows cross sections vs. x A for selections in H T . Although the data hasnot yet been compared in detail with Pythia , the general agreement is very promising.Photoproduction of open charm also proceeds via photon-gluon fusion. Open charm canbe detected relatively near threshold ( M cc ≈ few m c ), so it can probe lower x and Q gluonsthan dijets (47). Charmed quarks, with charge +2 / e have a particularly large cross-section(48, 49). The disadvantage is that charm quarks can hadronize to several different hadrons,each with many possible final states. Many of the final states are difficult to reconstruct, so ••
Figure 3: (a.) Event display of an event with a large gap in one direction, with two jets inthe other direction. (b.) Uncorrected triple differential cross sections, from Ref. (46).such processes is aided by the fact that the photon emitter typically does not break up.However the recoiling partons will in general excite the nucleus, leading to nuclear dissoci-ation, and an accompanying partonic connection (‘string’) between the reaction productsand the nuclear remnants.This leads to a distinct event signature, with limited transverse energy, neutrons in onlyone direction, and one or more reconstructed jets, easily implemented in an experimentaltrigger. Fig. 3 (a) shows an example event, triggered using an exclusive one-arm ZDCtrigger and containing two forward reconstructed jets.Jets are straightforward to reconstruct, particularly in low-multiplicity photonuclearevents, but the condition that they are well-reconstructed imposes a minimum p T , which re-stricts the kinematic coverage in Bjorken- x (the fraction of the nucleon momentum) and Q ,the hardness scale of the interaction. ATLAS has presented preliminary triple-differentialquasi-cross sections corrected for trigger efficiency, but not yet unfolded for experimentalresolution (46). The experimental variables are H T , the scalar sum of the observed jettransverse momenta, z γ , which reflects the energy fraction of the incoming nucleon energycarried by the photon, and x A , the per-nucleon momentum fraction in the struck nucleus.The data are compared to a Pythia µ + N interactions, medi-ated by a nearly-real photon, with the photon spectrum reweighted to match STARLight and finally with the normalization adjusted to match to the data. The particular resultshown in Fig. 3 (b) shows cross sections vs. x A for selections in H T . Although the data hasnot yet been compared in detail with Pythia , the general agreement is very promising.Photoproduction of open charm also proceeds via photon-gluon fusion. Open charm canbe detected relatively near threshold ( M cc ≈ few m c ), so it can probe lower x and Q gluonsthan dijets (47). Charmed quarks, with charge +2 / e have a particularly large cross-section(48, 49). The disadvantage is that charm quarks can hadronize to several different hadrons,each with many possible final states. Many of the final states are difficult to reconstruct, so •• Two-photon and Photonuclear reactions 9 he overall reconstruction efficiency is small. Open bottom should also be visible at rateshigh enough for parton distribution studies (50), and top quark pair production may beaccessible in pA collisions at the LHC (51, 52).Inelastic photoproduction is also a topic of interest in its own right. Proceeding bythe fluctuation of the photon to a hadronic state, typically a ρ meson, it provides anotherexample of collective behavior in small systems. Early results from ATLAS (53) indicatethat these collisions show a ”ridge” structure in the two-particle azimuthal correlationfunction, similar to that seen in pp , but with a smaller magnitude, possibly reflecting a morecompact quark-antiquark configuration compared to the proton with its three constituentquarks. Coherent photoproduction refers to reactions where theincident nuclei primarily remain intact, so the final state consists of the two incident nu-clei plus a vector meson. This reaction does not transfer color, so it must proceed viathe exchange of at least two gluons. At high energies, this two gluon exchange is oftenreferred to as ‘Pomeron exchange.’ The Pomeron has the same quantum numbers as thevacuum, J PC = 0 ++ , so it can also be described as representing the absorptive part of thecross-section (54). At lower photon energies, meson photoproduction can also proceed via‘Reggeon exchange,’ where the Reggeons represent collective meson trajectories. Reggeonscarry a much wider range of quantum numbers than the Pomeron, and can be either neutralor charged. So, the range of final state spin and parity is much wider, and charged finalstates and exotica are possible. In UPCs, lower photon energies corresponds to productionat forward rapidities, so this physics can best be studied with forward spectrometers.The vector-meson rapidity distribution dσ/dy can be converted to the incoming lab-frame photon and Pomeron energy via the relationships k , = M V e ± y , q , = M V e ∓ y , M V is the vector meson mass; we neglect the k T and q T . The ± and ∓ signs arisefrom the two-fold ambiguity over which nucleus emitted the photon. Away from y = 0, thetwo possibilities have different photon and Pomeron energies. This degeneracy complicatesextraction of energy-dependent photoproduction cross-sections. It can be largely avoided in pA or other asymmetric collisions, where the photon comes predominantly from the heavyion, with the proton as a target (55, 56, 57). Unfortunately, this does not allow us to probeion targets. For pp collisions, HERA data can be used to fix the cross-section for one of thephoton directions, allowing the cross-section for the other direction to be found (58). Forion-ion collisions, another strategy is required: selecting sets of events with different photonspectra, leading to different ratios for production in the two directions. This can be done byselecting set of events with different impact parameter distributions. For example, eventsaccompanied by MCE have a harder photon energy spectrum (28, 27). Or, one can comparephotoproduction in peripheral and ultra-peripheral collisions (59). By using multiple datasets with different impact-parameter distributions, it is possible to unambiguously find theenergy dependence of the cross-section σ ( k ), albeit with increased errors due to the coupledequations.
10 Klein et al. .3.2. Cross-section for γp interactions. The bidirectional ambiguity problem goes beyondsumming the cross-sections for the two photon directions. For coherent photoproduction,the reactions with different photon directions are indistinguishable, so they interfere witheach other (60). The sign of the interference depend on the how the two possibilities arerelated. A reaction where ion 1 emits a photon can be transformed into a reaction where ion2 emits a photon by a parity exchange. Vector mesons are negative parity, so the interferenceis destructive. For pp collision at the Fermilab Tevatron, the relevant symmetry is CP , sothe interference is constructive. There is also a propagator exp ( i(cid:126)p T · (cid:126)b ) present. For aninteraction at a given impact parameter d σdbdy = (cid:12)(cid:12) A ( b, k ) − e i(cid:126)p T · (cid:126)b A ( b, k ) (cid:12)(cid:12) , A ( b, k ) and A ( b, k ) are the amplitudes for the two directions. When y ≈
0, inthe limit p T →
0, interference is complete, and σ →
0. Away from y = 0, the photonenergies corresponding to the two directions are different, so A ( b, k ) and A ( b, k ) aredifferent, reducing the degree of interference. When p T (cid:29) ¯ h/R A , the propagator oscillatesrapidly with small changes in b , and so averages out. Because of the oscillatory behavior,this interference does not significantly affect the total cross-section. As the inset in Fig. 4(b) shows, suppression is visible for p T <
30 MeV (41), at the expected level (61).One interesting aspect of this interference is that the production amplitudes at thetwo nuclei are physically separated and share no common history. Moreover, the two vectormeson amplitudes decay almost immediately. The ρ has lifetime of order 10 − s, producingtwo pions which travel in opposite directions. These pions become physically separated longbefore the wave functions for production at the two ions can overlap. With the interference-imposed requirement that the pair p T not be zero, the pion pair can only be described witha non-local wave function. This is an example of the Einstein-Podolsky-Rosen paradox (62). γp interactions have been extensively studied at fixed-target experiments (63) and theHERA ep collider (64). A wide range of final states have been observed. At high ener-gies, Pomeron exchange dominates, and the most common final states are vector mesons,including the ρ , ω , φ , J/ψ , ψ (cid:48) and Υ states. Direct π + π − pairs are also produced. Theirproduction may be modelled as photon fluctuations directly to a pair of charged pions.The cross-section to produce a vector meson V depends on the probability for the photonto fluctuate to a qq pair and on the cross-section for that pair to scatter elastically fromthe target, emerging as a real vector meson. The fluctuation probability depends on thequark charge and vector meson wave function; it is quantified with the coupling f v , whichis determined from Γ ll , the leptonic partial width for for V → e + e − . The elastic scatteringcross-sections are then determined using σ ( γp → V p ) and f v .In lowest order perturbative QCD, the reaction proceeds via two gluon exchange. Twogluons are required to preserve color neutrality. The forward scattering cross-section toproduce a vector meson with mass M V is often given as (65) dσdt (cid:12)(cid:12)(cid:12)(cid:12) t =0 = Γ ll M v π α (cid:20) α S ( Q ) Q xg ( x, Q (cid:1) (cid:0) Q M V (cid:1)(cid:21) , α S is the strong coupling constant, x is the Bjorken − x of the gluon and Q =( Q + M V ) /
4, where Q is the photon virtuality, which is generally small. The division byfour is because there are two gluons, each assumed to carry half the virtuality; as we will ••
4, where Q is the photon virtuality, which is generally small. The division byfour is because there are two gluons, each assumed to carry half the virtuality; as we will •• Two-photon and Photonuclear reactions 11 ee later, this assumption is problematic. The vector meson mass provides a hard scale,allowing the use of perturbative QCD, even when the photon virtuality is small. pQCD isusually assumed to be applicable for photoproduction of the
J/ψ and heavier mesons. Twogluons form the simplest color neutral object that can be exchanged. More sophisticatedmodels treat Pomeron exchange as a gluon ladder (66).The two-gluon approach has some important caveats (67), many of which also applyto incoherent photoproduction. The gluon density, g ( x, Q ) is squared, to account for thetwo gluons, but there is no reason the two gluons should have the same x and Q values.In fact, the largest contribution occurs when the two gluons have very different x values, x (cid:29) x , so the softer gluon is relatively unimportant. One way to account for the softgluon is to treat the interaction using a generalized parton distribution (GPD). Anotherapproach is to account for the second gluon using a Shuvaev transformation (68); this leadsto a multiplicative factor in Eq. 10. As long as x (cid:29) x , the Bjorken − x of the dominantgluon can be related to the Pomeron energy from Eq. 8 via x = q/m p = M V /m p exp ( ∓ y ),where m p is the proton mass.There are also small corrections to account for higher order photon fluctuations (‘re-solved photons’), such as to qqg . Finally, there is some uncertainty due to the choice of massscale, µ = Q , used to evaluate the gluon distribution (65). All of these considerations arethe subject of intense theoretical discussion (69). One important next step is to extend thecalculation to next-to-leading order (NLO). There is not yet a complete NLO calculation,but most of the elements exist, and there are several partial-NLO results.The NLO calculation includes contributions from many Feynman diagrams, includingseveral where the quark distributions in the target are important. A problem arises withthe NLO calculation, at least at LHC energies: the NLO amplitude is larger than the LOamplitude. This is because of the parton distributions used as input. There is no gluondata in this x, Q range, so the parton distributions extrapolate downward in x , findinga very small gluon contribution. This leads to a very small LO cross-section, so it isunsurprising that the NLO diagrams give a larger contribution. By starting with a largergluon contribution, such as can be inferred from the J/ψ coherent photoproduction data,this problem disappears.The cross-section is sensitive to the choice of factorization and renormalization scalesand the choice of the minimum virtuality to consider. These can be reduced with a carefulchoice of minimum virtuality, Q (70). With an optimal choice, the scale uncertainty isreduced to the ±
15% to ±
25% range for the Υ, somewhat larger for the
J/ψ . This range isnot small, but it is small enough to allow for photoproduction to meaningfully contributeto parton distribution fits in this x, Q range, even with the systematic uncertainties (71).The longitudinal momentum transfer q z in photoproduction is determined by the kine-matics: q z = 4 k/M V . The maximum momentum transfer is set by the coherence conditionapplied to the proton size R p , q < ¯ h/R p . More precisely, the p T is regulated by the protonform factor, and the cross-section can be written σ ( γp → V p ) = dσdt (cid:12)(cid:12)(cid:12)(cid:12) t =0 (cid:90) ∞ t min | F ( t ) | dt, t ≈ p T and F ( t ) is the proton form factor and t min is the minimum momentumtransfer, M V / k (with k in the target frame). dσ/dt | t =0 encodes all of the hadronic physicsof the reaction. Because Eq. 10 is decoupled from the nuclear form factor in Eq. 11, in thisapproach, changes in the gluon distribution do not alter the nuclear shape.
12 Klein et al. everal groups have used UPCs to study
J/ψ photoproduction on proton targets, ex-tending the data collected at HERA. Above the threshold region, HERA and fixed-targetexperiments found that the
J/ψ photoproduction cross-section is well described by a powerlaw σ ∝ W αγp , with α = 0 . ± .
03 (58). This linear relationship is expected in LO pQCD,Eq. 10 as long as the low − x gluon distribution itself follows a power-law, g ( x, Q ) ∝ x − α/ .A deviation from this power law would signal that higher order diagrams are becoming im-portant, a possible precursor to saturation. The ALICE collaboration used pPb collisionsto extend the measurement up to roughly W γp =800 GeV, probing gluons with x ≈ × − and finding no deviation from the power-law behavior (72). In the overlap region, the datawere in good agreement with the HERA data. It should be noted that, at these energiesNLO calculations predict J/ψ cross-sections similar to LO.The LHCb collaboration made a similar study in pp collisions at √ s =7 TeV and √ s =13TeV (58). They used HERA data to fix the cross-section in the direction correspondingto the low-energy photon solution, and then solved for the cross-section in the high-energyphoton direction. At √ s =13 TeV, their highest rapidity point, (cid:104) y (cid:105) = 4 .
37 corresponded to W γp ≈ . x ≈ × − . Unfortunately, the results from the different energiesshow some tension. The √ s =7 TeV data follows the HERA power law, while the √ s =13TeV is lower, consistent with a NLO prediction. The found similar power law behavior forthe ψ (cid:48) , albeit with larger statistical uncertainty (73).The Υ states are of interest because the LO and NLO calculations differ more especiallywith increasing collision energy, making them more sensitive to the presence of higher ordercontributions (65). LHCb has also observed photoproduction of the three Υ states (73).For the Υ(1 S ), where the statistics are best, they observe good agreement with their NLOcalculations, above the LO predictions.The CMS collaboration studied ρ photoproduction on protons in pPb collisions, focusingon the p T spectrum. They showed a pion pair p T spectrum out to 1 GeV/c (56) andfound that it was well described by a mixture of exclusive interactions, plus ‘incoherent’interactions, where the proton dissociated, and ρ (770) feeddown from ρ (1700) decays.From this, they extracted the ρ (770) component of the dipion spectrum, and found thatthe cross-section was in agreement with HERA predictions, but that dσ/dt dropped fasterthan an exponential. Their data was well fit by the form exp( − bt + ct ), with c ≈ σ fromzero. This indicates that the proton size depends on the Q at which it is observed.CMS used a similar technique to study the Υ in pPb collisions (55). They resolved theΥ(1 S ) andΥ(2 S ) peaks, and concentrated on the Υ(1 S ), where the statistics were better.Because of the scaling with Z , the continuum background from γγ → µµ was substantiallylarger in these pPb collisions than in pp collisions. The cross-section was consistent with apower law in W γp , at a level between the NLO and LO predictions shown by CMS. γA interactions. One driver for studies of vector meson photopro-duction in γA is to study how the parton distributions in nucleons change when they areembedded in nuclei - the phenomenon of ”nuclear shadowing”. Ignoring shadowing, thecross-section may be found via a Glauber calculation (74): dσ γA → V A dt = dσ γp → V p dt (cid:12)(cid:12) t =0 (cid:12)(cid:12)(cid:12)(cid:12) (cid:90) d b (cid:90) dze i ( (cid:126)q t · (cid:126)b + q l z ) ρ ( b, z ) e − σ tot ( V p ) T A ( b,z ) (cid:12)(cid:12)(cid:12)(cid:12) , ••
37 corresponded to W γp ≈ . x ≈ × − . Unfortunately, the results from the different energiesshow some tension. The √ s =7 TeV data follows the HERA power law, while the √ s =13TeV is lower, consistent with a NLO prediction. The found similar power law behavior forthe ψ (cid:48) , albeit with larger statistical uncertainty (73).The Υ states are of interest because the LO and NLO calculations differ more especiallywith increasing collision energy, making them more sensitive to the presence of higher ordercontributions (65). LHCb has also observed photoproduction of the three Υ states (73).For the Υ(1 S ), where the statistics are best, they observe good agreement with their NLOcalculations, above the LO predictions.The CMS collaboration studied ρ photoproduction on protons in pPb collisions, focusingon the p T spectrum. They showed a pion pair p T spectrum out to 1 GeV/c (56) andfound that it was well described by a mixture of exclusive interactions, plus ‘incoherent’interactions, where the proton dissociated, and ρ (770) feeddown from ρ (1700) decays.From this, they extracted the ρ (770) component of the dipion spectrum, and found thatthe cross-section was in agreement with HERA predictions, but that dσ/dt dropped fasterthan an exponential. Their data was well fit by the form exp( − bt + ct ), with c ≈ σ fromzero. This indicates that the proton size depends on the Q at which it is observed.CMS used a similar technique to study the Υ in pPb collisions (55). They resolved theΥ(1 S ) andΥ(2 S ) peaks, and concentrated on the Υ(1 S ), where the statistics were better.Because of the scaling with Z , the continuum background from γγ → µµ was substantiallylarger in these pPb collisions than in pp collisions. The cross-section was consistent with apower law in W γp , at a level between the NLO and LO predictions shown by CMS. γA interactions. One driver for studies of vector meson photopro-duction in γA is to study how the parton distributions in nucleons change when they areembedded in nuclei - the phenomenon of ”nuclear shadowing”. Ignoring shadowing, thecross-section may be found via a Glauber calculation (74): dσ γA → V A dt = dσ γp → V p dt (cid:12)(cid:12) t =0 (cid:12)(cid:12)(cid:12)(cid:12) (cid:90) d b (cid:90) dze i ( (cid:126)q t · (cid:126)b + q l z ) ρ ( b, z ) e − σ tot ( V p ) T A ( b,z ) (cid:12)(cid:12)(cid:12)(cid:12) , •• Two-photon and Photonuclear reactions 13 here T A ( z ) = (cid:90) ∞ z ρ ( b, z (cid:48) ) dz (cid:48) ρ ( b, z ) is the nuclear density. σ tot ( V p ) is the total vector meson-nucleon cross-section,determined using the optical theorem: σ ( V p ) = 16 π dσ ( V p → V p ) dt (cid:12)(cid:12) t =0 . dσ ( V p → V p ) /dt is determined from the measuredphotoproduction cross-section, after factoring out the γ → V fluctuation probability. Theexponential exp ( i ( (cid:126)q t · (cid:126)b + q l z )) accounts for coherence across the nucleus.The Glauber calculation accounts for multiple interactions - a single dipole encounter-ing a nucleus may interact more than once, but can only produce a single vector meson.For small σ tot ( V p ) (i.e., heavy mesons like the
J/ψ ), multiple interactions are unlikely,the amplitudes add linearly and the forward cross-section dσ/dt | t = 0 scales as A . Lightmesons, with large σ tot ( V p ) will interact on the front surface of the target nucleus, so theamplitude depends on the frontal surface area of the target, A / and dσ/dt | t =0 ∝ A / .The Glauber calculation accurately interpolates between these limits, under the assump-tion that the γp cross-section is the same for isolated protons, and for those in nuclei. Therange of t for which coherent photoproduction is possible decreases as A − / , moderatingthe increase in total coherent cross-section. If significant shadowing is present, then thecross-section is reduced below the Glauber expectation. For heavy nuclei at RHIC/LHCenergies, the resulting cross-section is only slightly dependent on the photon energy, evenif the γp cross-section shows a significant photon energy dependence.With these caveats in mind, it is useful to compare the heavy-ion data with pQCDcalculations. Fig. 4 (a) shows CMS central and ALICE forward muon spectrometer dataon dσ/dy for J/ψ photoproduction on a lead target. Both are about a factor of two belowthe impulse approximation, which treats the lead nucleus as a collection of free nucleons. Itis, however, consistent with a ‘leading twist’ pQCD calculation (76, 77). This is essentiallyan extension of the Glauber calculation discussed above which accounts for the possibilityof the incident quark and antiquark to interact multiple times while traversing the nucleus,including excited intermediate states. It treats shadowing as due to multiple scattering,without requiring changes in the actual parton densities. It will be very interesting to seedata on shadowing in Υ photoproduction, where the Q is larger. Unfortunately, the largerbackground from γγ → l + l − will be a bigger problem than in pPb or pp collisions.For lighter mesons, like the ρ and ω , the Q is low enough so that perturbative QCD isnot expected to be applicable. One can use γp data to predict the γA cross-sections with aGlauber calculation (74), as described above. Experiments observe a dipion mass spectrumwith three components: ρ → π + π − , ω → π + π − and direct π + π − production. These threechannels are indistinguishable, so they all interfere with each other. The direct π + π − is flat,independent of mass, but, through interference, enhances the π + π − spectrum below the ρ mass and depletes the spectrum above it. The branching ratio for ω → π + π − is only 2.2%,but, through its interference with the ρ , the ω produces a kink in the mass spectrum, nearthe ω mass (41, 56). The relative amplitudes of the three channels seem consistent withHERA data. Surprisingly, data on ρ photoproduction, from both STAR (78) and ALICE(79), shows a ρ cross-section that is larger than that predicted by Glauber calculations, Eq.12. One possibility is that nuclear inelastic scattering (by intermediate higher mass photonfluctuations) increases in the cross-section (80).
14 Klein et al. - / d y [ m b ] c oh s d CMS dataALICE dataImpulse approximationLeading twist approximation (2.76 TeV) -1 b µ y Pb+Pb+J/ ® Pb+Pb
CMS ] -t [(GeV/c) ] / d t [ m b / ( G e V / c ) s d - -
10 110 fit XnXn -bt e fit 1n1n -bt eXnXn 1n1n ] -t [(GeV/c)0 0.001 0.002 0.003 ] / d t [ m b / ( G e V / c ) s d Figure 4: (a) CMS and ALICE measurements of the
J/ψ dσ/dy as a function of rapidity,for LHC Run 1 data. (75). (b) dσ/dt for ρ photoproduction in gold-gold collisions at acenter of mass energy of 200 GeV/nucleon as measured by the STAR Collaboration (41).These data are for ρ photoproduction accompanied by mutual Coulomb excitation; the twocurves are for different selections of numbers of neutrons in each ZDC. The inset shows dσ/dt at very low t , where interference between the two directions is visible.Photoproduction can also be used for vector meson spectroscopy. Although mesonphotoproduction has long been studied in fixed target experiments (63) and at HERA,current UPC analyses have collected large data samples (up to ≈
1M events) with high-quality detectors, comparable in size and with larger maximum mass reach, and are startingto produce interesting results. STAR has observed a π + π − resonance with a mass around1.65 GeV and a width around 165 MeV (81) The rate appears roughly consistent withphotoproduction of the ρ (1690); this would be an interesting observation of a spin-3 mesonat a W γp where production via Pomeron exchange dominates. STAR (82) and ALICE (83)have also studied photoproduction of π + π − π + π − final states, observing a broad resonancewhich seems consistent with a mixture of the ρ (1450) and ρ (1700) states. Data alreadycollected, but not-yet analyzed, could be used to significantly improve our knowledge ofheavier vector meson states. An alternate approach to vector meson photoproduction treats the interacting photon as aquark-antiquark dipole with separation r T . This dipole may scatter in the target, emergingas a vector meson. This approach treats protons and ions in a similar manner, via a targetconfiguration Ω that describes positions of the gluons in the target. It meshes smoothlywith the Good-Walker approach to diffraction (84), allowing calculations of incoherentphotoproduction. The cross-section to produce a vector meson is (85, 86, 45) dσdt = 116 π (cid:12)(cid:12) A γA → V A (cid:12)(cid:12) (1 + β ) , ••
1M events) with high-quality detectors, comparable in size and with larger maximum mass reach, and are startingto produce interesting results. STAR has observed a π + π − resonance with a mass around1.65 GeV and a width around 165 MeV (81) The rate appears roughly consistent withphotoproduction of the ρ (1690); this would be an interesting observation of a spin-3 mesonat a W γp where production via Pomeron exchange dominates. STAR (82) and ALICE (83)have also studied photoproduction of π + π − π + π − final states, observing a broad resonancewhich seems consistent with a mixture of the ρ (1450) and ρ (1700) states. Data alreadycollected, but not-yet analyzed, could be used to significantly improve our knowledge ofheavier vector meson states. An alternate approach to vector meson photoproduction treats the interacting photon as aquark-antiquark dipole with separation r T . This dipole may scatter in the target, emergingas a vector meson. This approach treats protons and ions in a similar manner, via a targetconfiguration Ω that describes positions of the gluons in the target. It meshes smoothlywith the Good-Walker approach to diffraction (84), allowing calculations of incoherentphotoproduction. The cross-section to produce a vector meson is (85, 86, 45) dσdt = 116 π (cid:12)(cid:12) A γA → V A (cid:12)(cid:12) (1 + β ) , •• Two-photon and Photonuclear reactions 15 here A γA → V A = i (cid:90) d (cid:126)r T (cid:90) dz π (cid:90) d (cid:126)b T ψ ∗ γ ( (cid:126)r T , z, Q ) N Ω ( (cid:126)r T ,(cid:126)b T ) ψ V ( (cid:126)r T , z, Q ) e − i(cid:126)b T · (cid:126)k T / ¯ h , (cid:126)b T is the transverse position within the nucleus, (cid:126)r T is the transverse size of the dipole, z the fraction of the photon momentum carried by the quark (the antiquark has momentumfraction 1 − z ) and Q the photon virtuality. The wave function of the incident photon, ψ ∗ γ ( (cid:126)r T , z, Q ) includes the probability of the photon fluctuating to a dipole. This is relatedto Γ ll . The wave function includes the probability distribution for the quark to carry amomentum fraction z . This probability is symmetric around z = 0 .
5, and weighted towardlow mass dipoles, where z ≈ . ψ V ( (cid:126)r T , z, Q ) (87). Quark models indicate that it should be Gaussian in (cid:126)r T . The Gaussian-light-cone form is ψ V ( (cid:126)r T , z, Q ) = N [ z (1 − z )] e − R T /σ , N and width σ come from are based on fits to data. The “BoostedGaussian” is slightly more complex, based on the Fourier transform of the (momentum-space) light cone wave function.Here, N Ω ( (cid:126)r T ,(cid:126)b T ) is the imaginary part of the forward dipole-target scattering amplitudefor a dipole with transverse size (cid:126)r T , impacting the target at transverse position (cid:126)b T . Thesmall real part of the amplitude is accounted for by the (1 + β ) term in Eq. 15. Thesubscript Ω denotes the target configuration (nucleon positions, etc.). This formulationassumes that the dipole size is smaller than the nuclear target; if the dipole is larger theexponential becomes slightly more complicated.The optical theorem provides a simple relationship with the dipole scattering cross-section: N Ω ( (cid:126)r T ,(cid:126)b T ) = d σ qq /d b . In a pQCD context, the cross-section depends on thegluon density g ( x, µ ) (88) d σ qq d b = 2 (cid:18) − exp [ − π N c r α s ( µ ) xg ( x, µ T ( b ))] (cid:19) . T ( b ) is the thickness function - the integrated material encountered by a photonarriving at impact parameter b . The exponential accounts for the probability of the dipoleundergoing multiple interactions. For small dipoles, d σ qq /d b ∝ r T .This dipole formulation has some limitations. It assumes that the dipole does notchange as it traverses the target. The lifetime of the fluctuation, ¯ h/M qq must be longerthan the time spent in the nucleus, i. e. E > ¯ hc/R A , the same condition as in the pQCDformulation, but it is only implicit here. It is usually satisfied at RHIC and the LHC, butcan fail for high-mass final states, particularly at large rapidity for the lower photon-energychoice in Eq. 8.Since the quark and antiquark momentum fractions are z and 1 − z respectively, thereis no room for soft gluons; this is necessarily a lowest order formulation for the photon.However, there is much more freedom in characterizing the target. It is easy to do cal-culations with colored glass condensates or other saturation models by altering Eq. 18.The presence of significant shadowing leads to a narrowing of the k T distribution in theinteraction, shifting the meson p T to smaller values (89).
16 Klein et al. he dipole approach can also accommodate impact-parameter dependent variations inthe cross-section. It has been used for a large number of different vector meson photopro-duction calculations, using different wave functions and dipole-target cross-sections. Thecross-sections often use different models of gluon shadowing and/or saturation, including adifferent impact parameter dependence. One expects more gluon shadowing in the core ofthe nucleus (small (cid:126)b T ) than in its periphery (90).Figure 5 (b) compares ALICE J/ψ dσ/dy lead-target data with predictions from afew representative calculations. (91). The impulse approximation treats the nucleus as acollection of independent nucleons, while
STARLight uses a Glauber calculation basedon parametrized HERA data. BKG-I is a Glauber-Gribov calculation, which uses a gluondensity extracted from HERA data (92). Also shown is a leading-twist calculation (‘LTA’),while the green line and shaded band show a pQCD calculation where gluons shadowingfollowing the EPS09 nuclear shadowing parameterization, which is based on non-UPC data.The figure displays three other dipole calculations with different models of the nucleus. The’IIM-BG’ curve is based on a colored-glass condensate (CGC) model. CGCs are a form ofsaturation model, whereby the nuclei are represented by a disordered classical gluon field. Inthe ’IPSat’ (impact-parameter dependent saturation) model the dipole-proton cross-sectiondepends on the dipole-proton impact parameter; the proton is represented with a Gaussiantransverse matter distribution. Finally, the GG-HS model includes gluon ‘hot spots,’ as willbe discussed below. Aside from the impulse approximation, which, not surprisingly is farabove the data, and the IIM BG calculation, which is considerably below it, all of the modelsare in at least marginal agreement with the data. The hot-spot and EPS09 calculationsare are in broad agreement with the data at large rapidity (corresponding mostly to lowerphoton energies), but diverge for more central rapidities. Fig. 4(a) shows this data, butthe only theory comparison is with the LTA, where the agreement is good. This is slightlysurprising, since Fig. 5(b) shows that the LTA curve tends to diverge from the data as | y | is reduced. There are many of other calculations of this process, with different treatmentsof gluon density in leadOverall, most of these models do a reasonable job of matching the data. Looking ahead,it will be very desirable to have a more complete set of comparison data, including the J/ψ , ψ (cid:48) and Υ, all covering a wide range of rapidities, to more broadly test these models. Equation 16, F ( b ) is the two-dimensional distribution of interac-tion sites in the target. The same equation provides a way to fairly directly probe forchanges in the nuclear profile, F ( b ) due to shadowing. . For protons, this offers a way toprobe the generalized parton distributions (93). For UPCs, we focus on heavier ions. Thetransformation is straightforward (94): F ( b ) ∝ (cid:90) ∞ p T dp T J ( bp T ) (cid:114) dσdt , J is a modified Bessel function.There are significant difficulties when this is put into practice, particularly for ions.The relationship is exact if the integral is unbounded, and bp T must cover several cycles ofthe Bessel function for an accurate transform. However, the coherent cross-section dropsfaster with increasing t than both incoherent production and the background, so the datahas a limited maximum useful p T . A cutoff at finite p T introduces windowing artifacts inthe transform; the data is effectively convolved with a box function (41), so the calculated ••
STARLight uses a Glauber calculation basedon parametrized HERA data. BKG-I is a Glauber-Gribov calculation, which uses a gluondensity extracted from HERA data (92). Also shown is a leading-twist calculation (‘LTA’),while the green line and shaded band show a pQCD calculation where gluons shadowingfollowing the EPS09 nuclear shadowing parameterization, which is based on non-UPC data.The figure displays three other dipole calculations with different models of the nucleus. The’IIM-BG’ curve is based on a colored-glass condensate (CGC) model. CGCs are a form ofsaturation model, whereby the nuclei are represented by a disordered classical gluon field. Inthe ’IPSat’ (impact-parameter dependent saturation) model the dipole-proton cross-sectiondepends on the dipole-proton impact parameter; the proton is represented with a Gaussiantransverse matter distribution. Finally, the GG-HS model includes gluon ‘hot spots,’ as willbe discussed below. Aside from the impulse approximation, which, not surprisingly is farabove the data, and the IIM BG calculation, which is considerably below it, all of the modelsare in at least marginal agreement with the data. The hot-spot and EPS09 calculationsare are in broad agreement with the data at large rapidity (corresponding mostly to lowerphoton energies), but diverge for more central rapidities. Fig. 4(a) shows this data, butthe only theory comparison is with the LTA, where the agreement is good. This is slightlysurprising, since Fig. 5(b) shows that the LTA curve tends to diverge from the data as | y | is reduced. There are many of other calculations of this process, with different treatmentsof gluon density in leadOverall, most of these models do a reasonable job of matching the data. Looking ahead,it will be very desirable to have a more complete set of comparison data, including the J/ψ , ψ (cid:48) and Υ, all covering a wide range of rapidities, to more broadly test these models. Equation 16, F ( b ) is the two-dimensional distribution of interac-tion sites in the target. The same equation provides a way to fairly directly probe forchanges in the nuclear profile, F ( b ) due to shadowing. . For protons, this offers a way toprobe the generalized parton distributions (93). For UPCs, we focus on heavier ions. Thetransformation is straightforward (94): F ( b ) ∝ (cid:90) ∞ p T dp T J ( bp T ) (cid:114) dσdt , J is a modified Bessel function.There are significant difficulties when this is put into practice, particularly for ions.The relationship is exact if the integral is unbounded, and bp T must cover several cycles ofthe Bessel function for an accurate transform. However, the coherent cross-section dropsfaster with increasing t than both incoherent production and the background, so the datahas a limited maximum useful p T . A cutoff at finite p T introduces windowing artifacts inthe transform; the data is effectively convolved with a box function (41), so the calculated •• Two-photon and Photonuclear reactions 17 igure 5: (a) Dimuon p T distribution for dielectron pairs in the J/ψ mass window, (b)Differential cross section dσ/dy for UPC events in 5.02 TeV Pb+Pb data. From Ref. (91). F ( b ) includes the box function as well. The equation also assumes that p T is the Pomerontransverse momentum, but the measured p T also includes the photon p T . For ion targets, dσ/dt shows diffractive minima, e.g. as shown by STAR data (41) in Fig. 4 (b), whichsignals a sign change in the photoproduction amplitude. In Eq. 19, (cid:112) dσ/dt is this am-plitude, so it is necessary to flip its sign when crossing each minimum. In UPCs, theseminima are smeared out because of the photon p T , so determining the dip positions is notstraightforward. Studies of the dipion mass (a proxy for Q ) dependence of F ( b ) in dipionphotoproduction show an intriguing trend, but the systematic uncertainties are large (26).Other approaches for measuring the change in shape of dσ/dt may be more promising. While coherent photoproduction probes the average nuclear configuration, incoherent pho-toproduction is sensitive to fluctuations, both spatial nuclear fluctuations and local fluc-tuations in the gluon density. This relationship comes from the optical theorem, and isusually embodied in the Good-Walker formalism for diffraction (84). In the Good-Walkerapproach, the total cross-section is (45) dσ tot dt = 116 π (cid:104)| A Ω | (cid:105) , A from Eq. 16 explicitly shows that it depends on thetarget nuclear configuration Ω. In coherent scattering, the initial and final nuclear statesare the same, so the amplitudes for the different states are summed and then squared, and dσ coherent dt = 116 π |(cid:104) A Ω (cid:105)| . dσ incoherent dt = 116 π (cid:0) (cid:104)| A Ω | (cid:105) − |(cid:104) A Ω (cid:105)| (cid:1) .
18 Klein et al. hrough the first term, the incoherent cross-section is sensitive to event-by-event fluctua-tions in the target configuration (95). It requires that the target have an internal structure;without internal structure, there are no inelastic interactions.One consequence of the Good-Walker approach is that, at very high energies, incoher-ent photoproduction should disappear. The photonuclear cross-section rises with photonenergy, as photoproduction occurs on gluons with smaller and smaller x values. When thephotonuclear cross-section is large enough, the nucleus looks like a black disk. At thatpoint, the internal structure disappears, and the incoherent cross-section vanishes (96).Theorists have used incoherent HERA data on J/ψ photoproduction to study protonshape fluctuations (88). Their analysis found that the cross-section for incoherent photo-production was above the expectations for a smooth proton, but was consistent a modelwhere the proton contained regions of high gluon density (‘hot spots’). The number ofhot spots should increase with photon energy, as the target gradually becomes opaque. Inone calculation, the incoherent
J/ψ photoproduction cross-section increases with energy,reaching a maximum at W γp = 500 GeV, and then decreases with further increases in W γp (97), within the reach of LHC data. The same calculation found that the energy at whichthe incoherent maximum appears increases with vector meson mass, so it is only about W γp = 20 GeV for the ρ .Similar approaches can be applied to nuclei (98). The hot spots are the same as inprotons and the number of hot spots in a nucleus is A times larger than in a proton.Although the differences in inelastic cross-sections between the two models are smaller thanfor proton targets, the hot spot model predicts a larger inelastic J/ψ production, with thedifference rising with increasing t . Because saturation sets in at much lower W γp for the ρ , the incoherent ρ photoproduction cross-section is predicted to be a small fraction (lessthan 5%) of the coherent ρ cross-section. That prediction is in some tension with STARdata, where the ratios inferred from integrating dσ/dt = A exp( − bt ) from Refs. (78) andRef. (99) seem to be considerably higher.Experimentally, the distinction between coherent and incoherent is not completelystraightforward for nuclei. The STAR data in Fig. 4(b) is actually from the reaction AA → A ∗ A ∗ ρ ; the STAR trigger required neutron emission from each nucleus. In princi-ple, the Good-Walker requirement for coherent photoproduction, that the initial and finalstates are the same, is not satisfied. However, the data shows a clear coherence peak for p T < ¯ h/R A , and at least one diffractive minimum. This may be explained using Eq. 16,where coherence depends only on the transverse position of the nucleons. Nuclear excita-tion is a relatively soft process, and the time scales for it to affect the target nucleus aremuch longer than the time scales required to produce the vector meson. If the excitationis caused by an additional photon, then it does not destroy the coherence of the vectormeson photoproduction. The process essentially factorizes (27, 28). The STAR and AL-ICE ρ cross-section measurements show that this factorization seems to hold quite well(12, 78, 91), except possibly at large p T .If the presence or absence of neutrons does not completely determine whether a reactionis coherent or incoherent, the coherent cross-section may be found by fitting the incoherentcomponent at large p T , extrapolating down to small p T and subtracting. The accuracy ofthis method depends on the functional form that is used. Although an exponential functionhas frequently been used to model the incoherent dσ/dt , a high-statistics analysis showedthat an exponential is not a good fit to the data. A dipole form factor provides a bettermatch (26). Alternately, the form can be derived from Monte Carlo simulations (91) which ••
J/ψ photoproduction cross-section increases with energy,reaching a maximum at W γp = 500 GeV, and then decreases with further increases in W γp (97), within the reach of LHC data. The same calculation found that the energy at whichthe incoherent maximum appears increases with vector meson mass, so it is only about W γp = 20 GeV for the ρ .Similar approaches can be applied to nuclei (98). The hot spots are the same as inprotons and the number of hot spots in a nucleus is A times larger than in a proton.Although the differences in inelastic cross-sections between the two models are smaller thanfor proton targets, the hot spot model predicts a larger inelastic J/ψ production, with thedifference rising with increasing t . Because saturation sets in at much lower W γp for the ρ , the incoherent ρ photoproduction cross-section is predicted to be a small fraction (lessthan 5%) of the coherent ρ cross-section. That prediction is in some tension with STARdata, where the ratios inferred from integrating dσ/dt = A exp( − bt ) from Refs. (78) andRef. (99) seem to be considerably higher.Experimentally, the distinction between coherent and incoherent is not completelystraightforward for nuclei. The STAR data in Fig. 4(b) is actually from the reaction AA → A ∗ A ∗ ρ ; the STAR trigger required neutron emission from each nucleus. In princi-ple, the Good-Walker requirement for coherent photoproduction, that the initial and finalstates are the same, is not satisfied. However, the data shows a clear coherence peak for p T < ¯ h/R A , and at least one diffractive minimum. This may be explained using Eq. 16,where coherence depends only on the transverse position of the nucleons. Nuclear excita-tion is a relatively soft process, and the time scales for it to affect the target nucleus aremuch longer than the time scales required to produce the vector meson. If the excitationis caused by an additional photon, then it does not destroy the coherence of the vectormeson photoproduction. The process essentially factorizes (27, 28). The STAR and AL-ICE ρ cross-section measurements show that this factorization seems to hold quite well(12, 78, 91), except possibly at large p T .If the presence or absence of neutrons does not completely determine whether a reactionis coherent or incoherent, the coherent cross-section may be found by fitting the incoherentcomponent at large p T , extrapolating down to small p T and subtracting. The accuracy ofthis method depends on the functional form that is used. Although an exponential functionhas frequently been used to model the incoherent dσ/dt , a high-statistics analysis showedthat an exponential is not a good fit to the data. A dipole form factor provides a bettermatch (26). Alternately, the form can be derived from Monte Carlo simulations (91) which •• Two-photon and Photonuclear reactions 19 nclude the photon p T .A recent ALICE study (91) went further, and divided the incoherent interactions intotwo classes. In the first, the nucleus dissociated, but the individual nucleons remainedintact. In the second, the individual nucleons were excited into higher states. For the firstclass, they used a p T template from the STARLight
Monte Carlo (13). For the second,they used a parametrization obtained by HERA studies of the same type of reaction. As Fig.5(a) shows, this combination provides a very good fit to the measured
J/ψ p T spectrum.Even without a trigger that requires neutrons, separating coherent and incoherent in-teractions is not simple, especially for heavy ions. Since Zα ≈ .
6, additional photonsmay be exchanged, exciting one of the nuclei. It is impossible to tell whether one photonincoherently produced a vector meson, or one photon coherently produced that meson, anda second photon dissociated the nucleus.
Becauseit can accelerate polarized protons, RHIC can uniquely study polarized generalized partondistributions (GPDs), which describe where the partons are within a nucleon (i. e. as afunction of b , similar to Eq. 19, but for protons). Polarized GPDs are sensitive to partonpolarization (100). The primary experimental observable is the single spin asymmetry (101),which is proportional to the GPD E g , which quantifies the gluon orbital momentum. TheSTAR Collaboration performed an initial measurement of this observable, albeit with alarge statistical uncertainty (102). They used pA collisions, where photons from the goldnucleus illuminated the polarized proton target. The proposed AFTER experiment plansto study this process with unpolarized lead ions striking a polarized proton target (101). Reggeon exchange allows a wide range of final states, since spin and charge can be exchangedBecause the spin or charge exchange alters the target, coherence is unlikely to be maintained,so most studies of Reggeon exchange have considered proton targets. Reggeon exchangerates are high. The predicted photoproduction rate for the a +2 (1320), a ‘standard candle’ qq meson is about a billion mesons/year, at both RHIC and the LHC (103). So, stateswith small couplings to photons can be observed. The cross-sections peak at low (a fewtimes threshold) photon energies. These low photon energies correspond to large-rapidityfinal states. A given final state will be nearer mid-rapidity at RHIC than at the LHC.Measurements at RHIC will provide good opportunities (103), especially with future forwardupgrades such as the STAR Forward Tracking and Calorimeter Systems (104).UPC photoproduction is a way to study the exotic XY Z states (105). These states areheavy, containing a cc pair, so are mostly beyond the reach of fixed-target photoproduction.Photoproduction data would help elucidate the nature of these states (106, 107, 108). Pen-taquarks may also be produced, via γp → P (109). Jefferson Lab’s GlueX experiment hasrecently put strong limits on photoproduction of cc containing pentaquarks (110). UPCsshould be useful to study heavier pentaquarks, such as those containing bb pairs. Although the criterion b > R A impacts its visibility (and provides the largest rate, via Z ), photoproduction still occurswhen b < R A . Both STAR (111) and ALICE(112) have observed an excess, over hadronicexpectations, of J/ψ with p T <
150 MeV/c in peripheral collisions. The cross-section for
20 Klein et al. hese
J/ψ generally agrees with photoproduction calculations (113, 29, 114). These calcu-lations raise an interesting question: Do nucleons that interact hadronically also contributeto the photoproduction amplitude? If they lose energy, the photoproduction cross-sectionwill be drastically reduced. This affects both the p T distribution of the J/ψ as well as theirabundance. The
J/ψ survival probability also merits study. A
J/ψ produced inside thehadronic fireball may be dissociated before it can decay. Even if it is produced outside thefireball, with its low transverse velocity and long lifetime (compared to the fireball), it maybe engulfed before it decays. High-statistics studies of how the cross-section depends on b could shed light on these questions.Photoproduced J/ψ can also aid our understanding of the hadronic collision, by pro-viding an independent (from the hadronic interaction) measurement of the reaction plane.Two variables have some sensitivity to the reaction plane. First, Eq. 9, which relates the
J/ψ p T spectrum to the angle between the J/ψ p T and to (cid:126)b . The J/ψ polarization providesadditional information, since the
J/ψ linear polarization follows the photon polarization,which follows its (cid:126)E field, which is correlated with (cid:126)b . This polarization may be observed byazimuthal angle of the decay lepton p T . Their transverse momenta tend to follow the J/ψ polarization (27). These handles depend on the direction of (cid:126)b , and, from that, the reactionplane.
4. Two photon interactions
The large photon fluxes from each nucleus, which each scale as Z , provide a high rateof photon-photon collisions, spanning a wide kinematic range, particularly at the LHCwhere the Lorentz factor is quite large. Photon interactions lead to a wide variety of finalstates. They couple to all charged particles, including leptons, quarks, and charged gaugebosons (2, 115). They also couple to neutral final states through loop diagrams, and sooffer the possibility of observing direct production of Higgs bosons as well as two-photonfinal states (now also known as ‘light by light’ scattering (116)). The production rates for exclusive particle production from two photon collisions can befactorized into a two photon ”luminosity” (or flux) and the cross section ( σ ( γ + γ → X ) (117, 118). The ultraperipheral two photon flux (often referred to as the “two pho-ton luminosity”) is typically calculated by integrating over the two separate fluxes, withthe requirements that 1) the nuclei do not overlap, using P , 2) that the productiondoes not take place inside either nucleus, 3) requiring a specific forward neutron topologyselection (or ignoring this for an inclusive selection) (119, 13): d Ndk dk = (cid:90) b >R A d (cid:126)b (cid:90) b >R A d (cid:126)b N ( k , b ) N ( k , b ) P ( | (cid:126)b − (cid:126)b | ) P fn ( | (cid:126)b − (cid:126)b | ) . b and b and the angle between them (10, 120). This approach is used in most calculations.The second assumption, that there is no production inside either nucleus, is perhaps toostrong, although the contributions to the flux should be limited due to the rapid fall off ofthe field strengths inside a nucleus. ••
The large photon fluxes from each nucleus, which each scale as Z , provide a high rateof photon-photon collisions, spanning a wide kinematic range, particularly at the LHCwhere the Lorentz factor is quite large. Photon interactions lead to a wide variety of finalstates. They couple to all charged particles, including leptons, quarks, and charged gaugebosons (2, 115). They also couple to neutral final states through loop diagrams, and sooffer the possibility of observing direct production of Higgs bosons as well as two-photonfinal states (now also known as ‘light by light’ scattering (116)). The production rates for exclusive particle production from two photon collisions can befactorized into a two photon ”luminosity” (or flux) and the cross section ( σ ( γ + γ → X ) (117, 118). The ultraperipheral two photon flux (often referred to as the “two pho-ton luminosity”) is typically calculated by integrating over the two separate fluxes, withthe requirements that 1) the nuclei do not overlap, using P , 2) that the productiondoes not take place inside either nucleus, 3) requiring a specific forward neutron topologyselection (or ignoring this for an inclusive selection) (119, 13): d Ndk dk = (cid:90) b >R A d (cid:126)b (cid:90) b >R A d (cid:126)b N ( k , b ) N ( k , b ) P ( | (cid:126)b − (cid:126)b | ) P fn ( | (cid:126)b − (cid:126)b | ) . b and b and the angle between them (10, 120). This approach is used in most calculations.The second assumption, that there is no production inside either nucleus, is perhaps toostrong, although the contributions to the flux should be limited due to the rapid fall off ofthe field strengths inside a nucleus. •• Two-photon and Photonuclear reactions 21 B [GeV] µµ M
10 20 30 40 50 60 b / G e V ] µ [ µµ M / d σ d − − − − Preliminary
ATLAS - µ + + µ + (*) +Pb (*) Pb → Pb+Pb = 5.02 TeV NN s -1 b µ = 515 int L |<2.4 µ η > 4 GeV, | µ T, p |<2.4 µµ Data |Y |<2.4 µµ STARLIGHT |Y|<2.4 µµ Data 1.6<|Y |<2.4 µµ STARLIGHT 1.6<|Y µµ Y − b ] µ [ µµ Y / d σ d − − Preliminary
ATLAS -1 b µ = 515 int = 5.02 TeV L NN sPb+Pb <20 GeV µµ Data 10 10 1 )) ( m b / ( G e V / c d M ) - e + e → γγ ( σ d Au+Au UPC (QED) - e + e →γγ (gEPA) - e + e →γγ (STARLight) - e + e →γγ | < 1.0 e η > 0.2 GeV/c & | e P < 0.1 GeV/c| < 1.0 & P ee |y 13% ± Scale Uncertainty : STAR A Figure 6: (a.) Distribution of dielectron invariant mass from STAR (125). (b.) Distributionof dimuon rapidity, in invariant mass selections, from ATLAS (124). γ + γ → (cid:96) + (cid:96) Most existing measurements of γ + γ processes in heavy ion collisions involve leptonic finalstates γ + γ → (cid:96) + (cid:96) − . At lower pair masses, M < 10 GeV, they are typically performedin tandem with the vector meson measurements described previously (121, 122). The ex-clusive final state is particularly simple, consisting primarily of two back-to-back chargedparticles with opposite sign, and many high-energy and nuclear physics experiments havebeen designed with capabilities including excellent lepton identification and precise momen-tum measurements. STAR has performed a series of electron pair measurements using theirlarge acceptance time projection chamber (TPC), initially triggered by a mutual Coulombexchange (neutrons in both ZDCs, see Section 2.2), and confirmed by signals from the TPCand time-of-flight counters, to select events with electron pair candidates (33, 123). AT-LAS utilizes a sophisticated multi-level trigger system to select events with a single muon,vetoing on large transverse energies in the rest of the event, but with no selection on theforward neutron topology (124).Dilepton cross sections are shown in Fig. 6 from STAR (125) (as a function of invariantmass) and ATLAS (124) (as a function of pair rapidity, for three mass ranges), and comparedto calculations including STARLight (13). ATLAS restricts the measurements to relativelylarge muon transverse momenta ( p Tµ > | η | < . M µµ > 10 GeV), but has no restriction on the forward neutron topology,and thus measures the full fiducial cross section. STAR measures much softer electrons( p Te > . η < 1) and thus much lower masses, but its UPC pairs are required tohave forward neutrons in both ZDCs, which limits the cross section to only a small fractionof the total. STARLight describes the overall magnitude of the dilepton cross section overa wide range in pair mass and rapidity, although ATLAS sees an underprediction from itin the forward region, and STAR sees perhaps some overall underprediction of the data.Although generalized EPA and full QED calculations (32) describe the magnitude of thecross-section better than STARLight , STAR reports that all calculations have been foundto be consistent with the data within the stated overall scale uncertainties of 13%. TheSTAR data is for e + e − ; here the Weizsacker-Williams approach may be more questionablethan for heavier leptons, because, uniquely, m e < ¯ h/R A . Other groups (126, 127, 128, 129)have performed calculations of the exclusive dilepton cross sections, albeit with somewhat 22 Klein et al. ifferent assumptions on the impact parameter dependence of the absorptive corrections,or by explicit inclusion of the nuclear form factors. The details of these features can haveobservable consequences on the magnitudes of the cross section. In particular, the detailedshape of the pair spectrum at large values of either the pair invariant mass and pair rapiditydistributions are both sensitive to the higher energy photons in the initial state. Allowingpair production within the two nuclei improves agreement with the STAR data (130), andcould improve the agreement with the ATLAS data.STAR has also observed angular modulations of the pair momentum relative to thesingle electron momenta, reflecting the linear polarization of the initial photons (131, 125).Tau ( τ ) leptons can be pair-produced only for incoming diphoton invariant masses above3 . τ and photon is sensitive to acombination of modifications of a τ = ( g τ − / 2, e.g. due to lepton compositeness (133) orcoupling to supersymmetric particles (134), as well as an electric dipole moment (EDM) ofthe τ itself. This is predicted to have an observable effect on the p T of the decay leptonsand hadrons, with a systematic hardening of the spectrum correlating with changes in a τ or the τ electric dipole moment d τ (135). p T and impact parameter selections As has been emphasized throughout this review, and in particular Sec. 2.3, one key featurewhich distinguishes production processes in purely electromagnetic processes from heavyion collisions is the very low p T of the initial state photons. In dilepton processes, this leadsto final states pair p T ∼ − 30 MeV. The pair p T can be measured accurately for low p T leptons (e.g. in STAR) but only estimated through the dilepton opening angle for high p T leptons (e.g. the acoplanarity, α = 1 −| ∆ φ | /π ), as measured in ATLAS. The detailed shapesof these distributions are sensitive to several different aspects of the underlying physics.Large values of pair p T or α are generally inaccessible in most calculations, which typi-cally provide the intrinsic p T via the nuclear form factor. This part of the dilepton angularspectrum is generally sensitive to final-state higher-order photon emissions, as shown dia-grammatically in Fig. 1 (f). These have generally not been included in existing event gener-ators, although Refs. (136, 137) have demonstrated analytically, using a Sudakov formalism,that they are already consistent with the preliminary ATLAS data. Similar success mod-eling the experimental data should be possible using the final-state QED parton-showeringalready available in Pythia Pythia also incorporates nuclear photon fluxes (15),albeit without overlap removal.By contrast, pairs with small pair p T or α have been found to be particularly sensitiveto quantum interference effects related to constraints on the impact parameter betweenthe two colliding nuclei. Up to this point, all processes have been assumed to exclude thefraction of the cross section where the nuclei overlap as well as when the production vertexis inside either nucleus (119). This choice is made both out of convenience and to alleviatepotential conceptual issues. Distinguishing signal processes from backgrounds is generallymore difficult in events where hadronic processes also occur. There are also open questionsas to where a coherent process can take place, in proximity to more violent hadronic colli-sions. A subtler issue arises from the limits of the equivalent photon approximation. When •• Pythia also incorporates nuclear photon fluxes (15),albeit without overlap removal.By contrast, pairs with small pair p T or α have been found to be particularly sensitiveto quantum interference effects related to constraints on the impact parameter betweenthe two colliding nuclei. Up to this point, all processes have been assumed to exclude thefraction of the cross section where the nuclei overlap as well as when the production vertexis inside either nucleus (119). This choice is made both out of convenience and to alleviatepotential conceptual issues. Distinguishing signal processes from backgrounds is generallymore difficult in events where hadronic processes also occur. There are also open questionsas to where a coherent process can take place, in proximity to more violent hadronic colli-sions. A subtler issue arises from the limits of the equivalent photon approximation. When •• Two-photon and Photonuclear reactions 23 − − − - d y ) ( G e V / c ) T N / ( dp ( - % ) d < 0.76 GeV/c ee > 0.2 GeV/c eT p | < 1 ee | < 1, |y e η | ( m b ) T ( X n X n ) / dp σ ( U P C ) d (GeV/c) P T UPC Au+Au 200 GeV60-80% Au+Au 200 GeV (UPC) - e + e →γγ (60-80%) - e + e →γγ − α α d s N d s N ATLAS = 5.02 TeV NN s -1 Pb+Pb, 0.49 nb A B Figure 7: (a.) STAR data on dielectron p T distributions in UPC and peripheral Au+Aucollisions (125). (b.) ATLAS comparisons of dimuon acoplanarity ( α ) between UPC andcentral collisions (34).comparing typical EPA calculations with those using a more complete QED formalism, re-placing the photon probability densities with QED amplitudes based on point charge nucleiconvolved with measured form factors, These integrals involve a phase i(cid:126)b · (cid:126)q , where (cid:126)q is thevector pair transverse momentum (30, 31, 32). Restricting the impact parameter close tozero can lead to large oscillations that tend to deplete the cross sections for low pair p T andlead to increased broadening in the final p T or α distributions. This effect was first observedin dielectron data from STAR (123), by comparison to QED calculations from Hencken etal. (139) which evinced a clear suppression at low pair p T relative to EPA calculations.More recently, STAR studied data from Au+Au and U+U collisions measured witha UPC selection, and for very peripheral (60-80%) hadronic interactions (33, 125). Theyobserve a distinct broadening of the p T distributions, illustrated in Fig. 7 (a), an effectthat had been postulated to be evidence for trapped magnetic fields but which was revisedbased on the existence of updated calculations in Ref. (32). Similarly, ATLAS observednearly-back to back muon pairs in hadronic Pb+Pb collisions at the LHC, but over the full(0-100%) centrality range. They observed a clear centrality-dependent broadening of the α relative to a UPC-like selection (34), as shown in Fig. 7 (b). This was interpreted by ATLASand other authors as a possible probe of the charged constituents of the hot, dense quarkgluon plasma. However, a preliminary update of this measurement with more than threetimes the integrated luminosity (35) observed that the acoplanarity distributions were notjust broadened in more central collisions, but peaked at non-zero values. Intriguingly, theQED calculations in Ref. (32) seems to have predicted the dip at zero, and quantitativelydescribed a large fraction of the full distribution, suggesting that no exotic QCD physicsis needed, but rather a more careful treatment of QED interference effects, related toconstraints on the impact parameter range. Pair production does not always result in a free electron; the electron may be producedbound to one of the incident ions (1). This is known as bound-free pair production (BFPP). 24 Klein et al. he cross-section for BFPP with the electron captured into the K shell is (140) σ = 33 λ c Z T Z p α e παZ − , (cid:0) ln δγ − (cid:1) Z p and Z T are the charge of the photon emitting nucleus and target nucleus respec-tively, λ c is the Compton wavelength and δ ≈ . Z p is standardfor photon emission, while Z T enters at the 5th power because the depth and width ofthe electric potential well increase rapidly with Z . The total BFPP cross-section is about20% larger, because of the possibility for capture into higher orbitals. The cross-section ismaximal for relatively low-energy photons (2.5 MeV in the target rest frame), so the ionmomentum is largely unchanged, despite the charge change.The cross-section for BFPP is large, about 276 barns for each target beam for lead-leadcollisions at the LHC (38). Because the produced single-electron ions have a larger magneticrigidity, they are lost from the beam. Along with Coulomb excitation of ions, these singleelectron ions are a major source of beam and luminosity loss over time.BFPP at the LHC produces a fairly well collimated beam of single-electron lead ionswhich diverge from the circulating fully-stripped lead ions (141, 142). The trajectory ofthis beam depends on the the LHC magnet optics, but it will strike the beampipe morethan 100 m downstream of each interaction point. This beam carries significant powerwhich produces local heating that may cause the superconducting magnets to quench. Ina controlled test, a magnet quench occurred at a luminosity of 2 . × cm − s − , 2.3times the design luminosity (142). Although the local heating problem can be alleviatedby spreading out the single-ion beam via orbit bumps and/or providing increased cooling,BFPP is an important constraint on high-energy accelerator design for heavy ions.BFPP can also produce antihydrogen: positrons bound to antiprotons. This processwas used to produce the first antihydrogen atoms at the CERN’s Low Energy AntiprotonAccumulator (LEAR) ring (143) and then at the Fermilab Antiproton Accumulator (144).Detection is easier with low energy collisions, where the antihydrogen velocity is relativelymodest.Similar reactions occur with muons (145), taus and even charged mesons. The cross-section for muonic BFPP is has been calculated to be 0.16 mb (146); the cross-section forheavier particles is smaller, less than 100 µ b. Since these single-lepton atoms have largerapidities, they can only be detected with a far-forward spectrometer.It is also possible to produce the bound state µ + µ − (147). They are produced near mid-rapidity. In lead-lead collisions at the LHC, the cross-section is ≈ µ b, so the productionrate is large; the difficulty is in detecting the two soft photons in the para-muonium finalstate. γ + γ → γ + γ Classically, QED obeys the principle of superposition, such that electromagnetic fields arepurely additive, so photons do not interact with each other. However, the standard modelpredicts (116, 148) that photons can interact via loop diagrams, with internal lines contain-ing quarks, leptons, and charged W gauge bosons, as shown in Fig. 1. The cross-sectionis sensitive to beyond standard model processes such as magnetic monopoles (149), vectorfermions (150), and axion-like particles (ALPs) (151, 152). Related processes have beenobserved by Delbr¨uck scattering off the coulomb field of a nucleus (153), as well as photonsplitting (154), but the direct process was only recently observed, with greater than 5 σ •• 24 Klein et al. he cross-section for BFPP with the electron captured into the K shell is (140) σ = 33 λ c Z T Z p α e παZ − , (cid:0) ln δγ − (cid:1) Z p and Z T are the charge of the photon emitting nucleus and target nucleus respec-tively, λ c is the Compton wavelength and δ ≈ . Z p is standardfor photon emission, while Z T enters at the 5th power because the depth and width ofthe electric potential well increase rapidly with Z . The total BFPP cross-section is about20% larger, because of the possibility for capture into higher orbitals. The cross-section ismaximal for relatively low-energy photons (2.5 MeV in the target rest frame), so the ionmomentum is largely unchanged, despite the charge change.The cross-section for BFPP is large, about 276 barns for each target beam for lead-leadcollisions at the LHC (38). Because the produced single-electron ions have a larger magneticrigidity, they are lost from the beam. Along with Coulomb excitation of ions, these singleelectron ions are a major source of beam and luminosity loss over time.BFPP at the LHC produces a fairly well collimated beam of single-electron lead ionswhich diverge from the circulating fully-stripped lead ions (141, 142). The trajectory ofthis beam depends on the the LHC magnet optics, but it will strike the beampipe morethan 100 m downstream of each interaction point. This beam carries significant powerwhich produces local heating that may cause the superconducting magnets to quench. Ina controlled test, a magnet quench occurred at a luminosity of 2 . × cm − s − , 2.3times the design luminosity (142). Although the local heating problem can be alleviatedby spreading out the single-ion beam via orbit bumps and/or providing increased cooling,BFPP is an important constraint on high-energy accelerator design for heavy ions.BFPP can also produce antihydrogen: positrons bound to antiprotons. This processwas used to produce the first antihydrogen atoms at the CERN’s Low Energy AntiprotonAccumulator (LEAR) ring (143) and then at the Fermilab Antiproton Accumulator (144).Detection is easier with low energy collisions, where the antihydrogen velocity is relativelymodest.Similar reactions occur with muons (145), taus and even charged mesons. The cross-section for muonic BFPP is has been calculated to be 0.16 mb (146); the cross-section forheavier particles is smaller, less than 100 µ b. Since these single-lepton atoms have largerapidities, they can only be detected with a far-forward spectrometer.It is also possible to produce the bound state µ + µ − (147). They are produced near mid-rapidity. In lead-lead collisions at the LHC, the cross-section is ≈ µ b, so the productionrate is large; the difficulty is in detecting the two soft photons in the para-muonium finalstate. γ + γ → γ + γ Classically, QED obeys the principle of superposition, such that electromagnetic fields arepurely additive, so photons do not interact with each other. However, the standard modelpredicts (116, 148) that photons can interact via loop diagrams, with internal lines contain-ing quarks, leptons, and charged W gauge bosons, as shown in Fig. 1. The cross-sectionis sensitive to beyond standard model processes such as magnetic monopoles (149), vectorfermions (150), and axion-like particles (ALPs) (151, 152). Related processes have beenobserved by Delbr¨uck scattering off the coulomb field of a nucleus (153), as well as photonsplitting (154), but the direct process was only recently observed, with greater than 5 σ •• Two-photon and Photonuclear reactions 25 igure 8: (a.) Acoplanarity ( A φ ) distributions from ATLAS exclusive diphoton events (155),compared with expectations from the two primary backgrounds ( e + e − and CEP) (b.) Upperlimits set on axion-like particle production, assuming only coupling to photons (157).significance, by the ATLAS experiment (155) using 1.7 nb − of Pb+Pb data at 5.02 TeV,after earlier evidence published by ATLAS (156) and CMS (157) with only 0.4-0.5 nb − .ATLAS (155) utilized photons measured in their electromagnetic calorimeters, rejectingbackgrounds by requiring no tracks in the tracking detectors matched to the photon. Theprimary fiducial selection is to have each photon with E T > | η | < . ± A φ < . ± σ .The CMS result (157) utilized similar techniques and addressed the same backgroundcontributions, but with a slightly larger fiducial space ( E T > Mγγ > ± γγ → a → γγ , over a range 5 < m a < 90 GeV and translated these to limits onthe photon-axion coupling g aγ . These are performed using calculations (151) based on twoassumptions, the first being photon-only coupling (shown in Fig. 8 (b)), where new limitsare provided over 5 < m a < 50 GeV, and the other including hypercharge coupling (notshown) where new limits are set only in a more limited range 5 < m a < 10 GeV, justbeyond the region explored by an earlier ATLAS 3 γ analysis (158). γ + γ → X Many early papers discussed two-photon production of mesons and meson pairs. Unfortu-nately, however, the cross-sections and production rates are rather small (3), and even thebenchmark γγ → f (1270) process has not yet been observed. In many cases, the calculated 26 Klein et al. roduction rates due to feed-down from photoproduction are larger than the two-photonproduction rates. For example, the rate for coherent photoproduction of the J/ψ followedby J/ψ → η c γ is considerably larger than for γγ → η c (159). The photon is too soft to beseen in collider detectors, and the η c kinematics from the two processes are very similar. 5. Future prospects The current heavy-ion datasets (A+A and p+A) have not been fully utilized to explore allpossible aspects of the physics discussed in here. One can expect further improvements forprocesses involving higher photon energies based on the full integrated luminosity in theLHC Run 2 dataset (up to about 2 nb − ). However, LHC Runs 3 and 4, while keepingthe same beam energies (or perhaps increasing by 7.6%) will collect nearly an order ofmagnitude more integrated luminosity for both ion-ion and proton-ion collisions (17). Arun with intermediate mass ions is also possible; this allows higher UPC luminosity due tothe substantially-reduced BFPP and Coulomb excitation cross sections.CERN’s planned Future Circular Collider or the proposed Chinese SPPC (7) wouldallow for a greatly expanded scope of measurements. They will have a higher beam energyby nearly an order of magnitude, which should allow for studies of photoproduction of top,along with photoproduction and two-photon physics studies of vector bosons, and improvedopportunities to search for beyond-standard-model physics.The next generation of RHIC experiments, with an updated STAR detector andsPHENIX, a newly-built collider experiment focusing on extremely high data rates, willhave access to enhanced statistics on exclusive dilepton, vector meson, and possibly evenUPC jet physics. With the new generation of high-precision vertex detectors, studies ofphotoproduction of open charm should also be possible.UPC photoproduction studies will be complemented by photoproduction ( Q ≈ 0) andelectroproduction ( Q > 0) studied at a future electron-ion collider (EIC), such as theplanned U. S. electron-ion collider at Brookhaven National Laboratory (100) and CERN’sLHeC (20). Although, per Table 1, most of the EIC designs reach lower W γp than the LHC,they offer considerably higher luminosity. More importantly, electrons can radiate photonsover a wide range of Q , and this Q can be determined from observing the scatteredelectron, no matter what reaction occurred. The wide Q range corresponds to a broaddipole size distribution of dipoles, no matter what the reaction. This will allow us to betterprobe the gluon distribution in nuclei on different length scales. An EIC will also allow usto study two-photon physics where one of the photons is highly virtual. SUMMARY POINTS 1. Ultra-peripheral collisions are the energy frontier for photonuclear and two-photonphysics, with the LHC reaching higher center of mass energies than any existingalternative.2. High-precision J/ψ photoproduction data is consistent with moderate shadowingscenarios.3. Two-photon processes involving dilepton and two-photon final states are providingnew insights from QED and potential access to physics beyond the standard model •• J/ψ photoproduction data is consistent with moderate shadowingscenarios.3. Two-photon processes involving dilepton and two-photon final states are providingnew insights from QED and potential access to physics beyond the standard model •• Two-photon and Photonuclear reactions 27 UTURE ISSUES 1. Existing and future RHIC and LHC data can be probed to study a wide range ofphotoproduction and two-photon reactions, particularly including studies of a widerrange of final state mesons, all species of dileptons and heavy quarks2. Precision studies of benchmark photoproduction of multiple heavy mesons, withand without forward neutron topological selections, will be needed to improve ourknowledge of nuclear structure, to test different saturation and colored-glass con-densate models and measure nuclear shadowing.3. A future high-energy FCC-hh collider will extend photoproduction and two-photonphysics studies by a factor of 7 in energy, opening the door to study top quarkphysics, probe parton distributions down to x ≈ − , observe γ + γ → H andprovide complementary probes to physics beyond the standard model.4. A future electron-ion collider will be able to make high-precision complementarystudies of many photoproduction channels over a wide range of Q . DISCLOSURE STATEMENT The authors are not aware of any affiliations, memberships, funding, or financial holdingsthat might be perceived as affecting the objectivity of this review. ACKNOWLEDGMENTS The authors thank their STAR, ALICE and ATLAS colleagues. 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