Slicing Pomerons in ultraperipheral collisions using forward neutrons from nuclear breakup
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This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Slicing Pomerons in ultraperipheral collisions using forward neutrons from nuclear breakup © Authors 2024 Published version Alvioli, M.; Guzey, V.; Strikman, M. Alvioli, M., Guzey, V., & Strikman, M. (2024). Slicing Pomerons in ultraperipheral collisions using forward neutrons from nuclear breakup. Physical Review C, 110(2), Article 025205. https://doi.org/10.1103/physrevc.110.025205 2024
PHYSICAL REVIEW C 110, 025205 (2024) Slicing Pomerons in ultraperipheral collisions using forward neutrons from nuclear breakup M. Alvioli ,1,2V. Guzey ,3,4and M. Strikman 5 1Consiglio Nazionale delle Ricerche, Istituto di Ricerca per la Protezione Idrogeologica, via Madonna Alta 126, I-06128 Perugia, Italy 2Istituto Nazionale di Fisica Nucleare,Sezione di Perugia, via Pascoli 23c, I-06123 Perugia, Italy 3Department of Physics, University of Jyvaskyla, P.O. Box 35, FI-40014 University of Jyvaskyla, Finland 4Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland 5Pennsylvania State University, University Park, Pennsylvania 16802, USA (Received 28 March 2024; revised 20 May 2024; accepted 22 July 2024; published 14 August 2024) We argue that measurements of forward neutrons from nuclear breakup in inclusive high energy photonnucleus (γA) scattering provide a novel way to study small-xdynamics of QCD in heavy-ion ultraperipheral collisions (UPCs). Using models for hadronic fluctuations of the real photon and neutron emission in nuclear fragmentation, we calculate the distribution over the number of evaporation neutrons produced in γPb collisions at the Large Hadron Collider. We show that it is correlated with the number of wounded nucleons (inelastic collisions) and, hence, can constrain the mechanism of nuclear shadowing and its xdependence. DOI: 10.1103/PhysRevC.110.025205 I. INTRODUCTION AND MOTIVATION Understanding of the QCD dynamics of hard high energy interactions and the structure of nuclei and nucleons is one of the main directions of theoretical and experimental studies at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC). Of particular interest is the limit of very small momentum fractions x, when the linear DokshitzerGribov-Lipatov-Altarelli-Parisi (DGLAP) approximation is expected to break down [1,2] and a regime close to the black disk limit (BDL) [3] may set in. Its observation is one of the prime objectives of the planned Electron-Ion Collider (EIC) at Brookhaven National Laboratory [4,5], which will ultimately reach x∼10−3for momentum transfers of a few GeV. At the same time, it was pointed out some time ago that ultraperipheral collisions (UPCs) of two ions at the LHC, where a photon emitted by one of the nuclei interacts with the other nucleus, allow one to probe down to x∼10−5–10−4, depending on a particular reaction channel and the detector geometry [6,7]. Electron-nucleus collisions at the EIC and UPCs of heavy ions at the LHC present two options for studying small-x dynamics, which are largely complementary. At the LHC practically all data are collected for one heavy nucleus and one cannot directly access the dependence of cross sections on the virtuality of the probe. At the same time, one can reach very small x, which is provided by a wide rapidity coverage of the LHC detectors and the large invariant photon-nucleus Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. collision energies exceeding by a factor of 100 the design energies at the EIC. Over the last decade the data taken in the LHC and RHIC kinematics revealed a significant nuclear suppression of coherent J/ψ photoproduction in Pb-Pb and Au-Au UPCs compared to the impulse approximation prediction [8]. When interpreted in the leading twist approximation (LTA) [9], it amounts to strong gluon nuclear shadowing [10,11]: Rg A(x,Q2)=gA(x,Q2) AgN(x,Q2)<1,(1) where gA(x,Q2) and gN(x,Q2) are the nucleus and nucleon gluon densities, respectively. Typical numbers reported by the LHC experiments (see [8] for references) correspond to Rg Pbx=10−3,Q2 eff =3GeV 2≈0.6, Rg Pbx=10−4,Q2 eff =3GeV 2≈0.5,(2) with a similar suppression extending down to x∼10−5.Here Qeff is the effective resolution scale determined by the charm quark mass. These values of Rg Pb agree very well with the LTA predictions for nuclear shadowing made more than 10 years ago [9]. Note that this interpretation of the J/ψ UPC data is complicated at the next-to-leading order (NLO) of the perturbative expansion in powers of αslog Q2(perturbative QCD) due to large cancellations between the leading-order (LO) and NLO gluon terms and a numerically important quark contribution [12,13]. A way to stabilize the perturbation series and restore the gluon dominance in this process on the proton target was suggested in [14,15]. Other hard UPC processes considered in the literature are inclusive [6,16] and diffractive [17] dijet photoproduction, which are still to produce final results [18,19], timelike Compton scattering [20–22], and heavy quark photoproduction [23–25]. Overall these findings confirm the conclusion 2469-9985/2024/110(2)/025205(8) 025205-1 Published by the American Physical Society
M. ALVIOLI, V. GUZEY, AND M. STRIKMAN PHYSICAL REVIEW C 110, 025205 (2024) of [7] that UPCs provide a very effective tool to access the small-xdynamics of the strong interactions and the nuclear structure in hard, semihard, and soft regimes of QCD. So far the experimental studies of UPCs have mainly been focusing on coherent and incoherent production of light and heavy vector mesons. In this paper, we would like to outline several possible directions of future UPC studies, which were not discussed in the review [7] due to the lack of experimental confirmations of large nuclear shadowing. We explore for the first time possibilities of testing the small-xnuclear shadowing dynamics by measuring the rates of forward neutron production from nuclear breakup in the zero degree calorimeters (ZDCs) at the LHC. Our numerical studies demonstrate that the number of produced neutrons is correlated with the number of wounded nucleons (inelastic photon-nucleon interactions), which presents a complementary way to study the mechanism of nuclear shadowing. In particular, as follows from the title of this paper, it allows one to control the number of unitarity cuts of diffractive exchanges (Pomerons), which build up the effect of nuclear shadowing. This paper is organized as follows. In Sec. II we briefly summarize expectations based on applications of the Abramovski-Gribov-Kancheli (AGK) theorem to photonnucleus scattering, model the distribution over the number of wounded nucleons, and estimate its average value in the current UPC kinematics. Section III presents our predictions for the distributions over the number of emitted forward neutrons from nuclear breakup in inelastic photon-nucleus scattering. Our conclusions and outlook are given Sec. IV. II. ABRAMOVSKI-GRIBOV-KANCHELI (AGK) CUTTING RULES, NUCLEAR SHADOWING, AND THE NUMBER OF WOUNDED NUCLEONS IN γASCATTERING Part of the results discussed in this section have been presented in [26]; we summarize them below for completeness since they are needed for new results in Sec. III. It was demonstrated by Abramovski, Gribov, and Kancheli in 1973 [27] that different unitary cuts of the diagrams corresponding to multi-Pomeron (color singlet) exchanges result in different multiplicities of produced particles in the central rapidity region and that the absorptive part of the amplitude can be expressed in terms of a small number of cut diagrams. They are related by combinatorial factors, which are known as the Abramovski-Gribov-Kancheli (AGK) cutting rules or the AGK cancellation. For the interpretation of the AGK rules in QCD and other effective field theories, see Refs. [28–32]. The application of the AGK cutting rules to photon-nucleus scattering allows one to express the nuclear shadowing correction to the total nuclear cross section σγA tot in terms of the diffractive cross section on individual nucleons [9,33]. Another important application of the AGK cutting rules involves the total hadron-nucleus inelastic cross section defined as the difference between the total and total elastic (coherent plus incoherent) cross sections, which is obtained using the unitary form of the Glauber theory [34]. Generalizing this result to photon-nucleus scattering by taking into account that the photon takes part in the strong interactions by means of its hadronic fluctuations, the photon-nucleus total inelastic cross section can be presented in the following form [26]: σγA inel = A ν=1 σν,(3) where σν=A! (A−ν)!ν!d2 bdσPγ(σ)[σinelTA( b)]ν ×[1 −σinelTA( b)]A−ν.(4) In Eq. (4), bis the impact parameter (transverse coordinate) of the interacting nucleon, TA( b)=dzρA( b,z), where ρA( b,z) is the nuclear density normalized to unity, and σinel =0.85σ is the inelastic cross section for the interaction of a hadronic fluctuation of the photon with a target nucleon, which is based on the estimate that the ρmeson-nucleon elastic cross section constitutes approximately 15% of the total one. The cross sections σνin Eqs. (3) and (4) represent the physical process where νnucleons undergo inelastic scattering, while the remaining A−νnucleons provide absorption. In the literature, one uses the term “wounded nucleons” [35] and the notation ν=Ncoll. The distribution Pγ(σ) gives the probability density for hadronic fluctuations of the real photon to interact with nucleons with the cross section σ[26,36]. While the shape of Pγ(σ) cannot be calculated from the first principles, one can reliably model it using constraints on its first moments and the smallσand large-σlimits. Indeed, the total photon-proton cross section σγp(W) and the cross section of photon diffractive dissociation on the proton dσγp→Xp(W,t=0)/dt constrain the first two moments of Pγ(σ) as follows: σγp(W)=dσPγ(σ)σ, dσγp(W,t=0) dt =1 16πdσPγ(σ)σ2,(5) where Wis the invariant photon-nucleon center-of-massenergy. Further, in the small-σlimit, one can express Pγ(σ) in terms of the quark-antiquark component of the photon light-cone wave function and the color dipole cross section, which results in Pγ(σ)∝1/σ. In the opposite limit of large σ, the photon behaves as a superposition of the ρ,ω, and φ vector mesons in the spirit of the vector meson dominance model, and, hence, Pγ(σ) can be modeled using hadronic (cross section) fluctuations in ρmesons, which in turn are related to those for pions. Finally, the small-σand large-σ regimes can be smoothly interpolated. Note that this matching is achieved best when the light quark masses mqare taken to be those of the constituent quarks, mq∼300 MeV. For details, see [26,36]. The left panel of Fig. 1presents the resulting distribution Pγ(σ) as a function of σat W=100 GeV. Its shape and normalization are constrained by the procedure outlined above, the parametrization of σγp(W)[37], and the data on dσγp→Xp(W,t=0)/dt [38]. Since the Wdependence of Pγ(σ) is weak, the presented distribution is applicable to a wide range of energies probed in heavy-ion UPCs at the LHC. Note that the distribution Pγ(σ) parametrizes the so-called 025205-2
SLICING POMERONS IN ULTRAPERIPHERAL … PHYSICAL REVIEW C 110, 025205 (2024) FIG. 1. Left: The probability density Pγ(σ) for hadronic fluctuations of the real photon to interact with nucleons with the cross section σat W=100 GeV. Right: The P(ν) distribution over the number of wounded nucleons (inelastic interactions) νin inelastic photon-nucleus (Pb) scattering. The three curves correspond to the three models for Pγ(σ), see text for details. The inset emphasizes the region of large ν.The figures are adopted from [26]. resolved photon contribution to photon-induced scattering and does contain the direct photon contribution. Note that the notion of cross section (color) fluctuations in hadron-nucleus scattering has found important phenomenological applications and confirmation in jet production in proton-nucleus scattering at the LHC and deuteron-nucleus scattering at RHIC [39,40] as well as in pion and photon production in d+Au scattering at RHIC [41]. Using Eqs. (3) and (4), one can readily define the P(ν) probability distribution for the number of wounded nucleons νin inelastic photon-nucleus scattering as follows [26]: P(ν)=σν A ν=1σν ,(6) where σνis given by Eq. (4). To calculate it, we use a Monte Carlo generator for nucleon configurations in complex nuclei [42], which also includes nucleon-nucleon correlations in the nucleus wave function [43,44], and the Gribov-Glauber model for photon-nucleus scattering, where the hadronic structure of the photon is described by Pγ(σ). The resulting distribution P(ν) as a function of νfor lead (Pb) is shown by the curve labeled “Color Fluctuations” in the right panel of Fig. 1. Our modeling of small-σhadronic fluctuations of the photon is based on the quark-antiquark component of the photon wave function and corresponds to a weak nuclear shadowing, which disagrees with the observed strong gluon nuclear shadowing; see Eq. (2). To take it into account, we model the nuclear suppression of the dipoles with σ⩽σ0=20 mb by the factor of Rg A, which leads to the modified distribution ˜ Pγ(σ), ˜ Pγ(σ)=Rg Ax,Q2 eff θ(σ0−σ)+θ(σ−σ0)Pγ(σ),(7) where x=Q2 eff /W2and Pγ(σ) is shown in Fig. 1(left panel). The distribution P(ν) corresponding to σνcalculated using ˜ Pγ(σ) is given by the curve “Generalized CF” in the right panel of Fig. 1. Finally, to test the importance of cross section (color) fluctuations in the real photon, we calculated P(ν) neglecting these fluctuations and using Pγ(σ)=δ(σ−25 mb) (8) in Eq. (4). The result is given by the curve “Glauber” in Fig. 1. One can see from this figure that color fluctuations significantly increase the distribution P(ν) at small and especially large σ; the latter is emphasized in the insert. In the total inelastic photon-nucleus cross section, the AGK cancellations manifest themselves as the observation that the average number of wounded nucleons Ncollis inversely proportional to the nuclear shadowing factor. Generalizing the result of [34] for hadron-nucleus scattering to the case of photon-induced scattering, one obtains [26] Ncoll≡ A ν=1 P(ν)ν=A ν=1νσν A ν=1σν=AσγN inel σγA inel ,(9) where σγN inel is the photon-nucleon inelastic cross section. Considering a particular hard process in inelastic photon-nucleus scattering that probes the nuclear gluon distribution, e.g., inclusive charmonium (bottomonium) production γ+A→ J/ψ(ϒ)+Xor inclusive heavy-quark dijet production γ+ A→Q¯ Q+X, one obtains using Eq. (9) Ncoll≈ 1 Rg Pb(x,Q2)2.(10) In this estimate we used the following considerations. In general, the effect of nuclear shadowing for the nuclear inelastic cross section is somewhat larger than that for the total cross section. However, the theoretical uncertainties of the leading twist approximation [9] largely mask the differences and make the shadowing effects approximately equal (within uncertainties) in the two cases. Finally, in the last step, we used the results of Eq. (2). Figure 2shows predictions of the leading twist approximation (LTA) for the average number of wounded nucleons 025205-3
M. ALVIOLI, V. GUZEY, AND M. STRIKMAN PHYSICAL REVIEW C 110, 025205 (2024) FIG. 2. The LTA predictions for the average number of wounded nucleons Ncollin inelastic photon-nucleus (Pb) scattering as a function of xat Q2=3, 20, and 1000 GeV2. Ncoll=1/Rg Pb(x,Q2) in inelastic photon-nucleus (Pb) scattering as a function of xat Q2=3, 20, and 1000 GeV2. These values of Q2correspond to photoproduction J/ψ,ϒ, and high-pTdijets, respectively. One can see from the figure that, in the discussed kinematics, the average number of wounded nucleons is modest. As a result, the series in Eq. (9) converges rather rapidly. In particular, we have checked that it is saturated by first six terms with a 5% precision. Note, however, that the convergence slows down in the limit of small x. Measurements of Ncollpresent a new method to study nuclear shadowing in inelastic photon-nucleus scattering. Unlike the observables used so far, the constraint of Eq. (10) indicates that one can perform a “Pomeron surgery” of nuclear shadowing by cutting a small number of Pomeron exchanges controlling the number of inelastic interactions with target nucleons. As a result, it gives an opportunity for an experimental determination of a small number of parameters quantifying nuclear shadowing, which leads to a systematic improvement of its theoretical description. We elaborate on it in the following section. III. THE DISTRIBUTIONS OVER THE NUMBER OF WOUNDED NUCLEONS AND FORWARD NEUTRONS FROM NUCLEAR BREAKUP The average number of inelastic interactions Ncollencodes information on the energy and scale dependence of nuclear shadowing. To obtain a more microscopic description of nuclear shadowing, one needs to determine not only Ncoll, but also the entire distribution over the number of wounded nucleons. This can be done using experimental data on the neutron emission resulting from nucleus fragmentation in a given UPC process, e.g., in inclusive quarkonium or dijet photoproduction in heavy-ion UPCs with an additional condition of Xn neutrons in the zero degree calorimeter (ZDC) on the nuclear target side [18,19]. Very little is known about the dynamics of neutron emission in high energy scattering off heavy nuclei. The ALICE Collaboration measured the distribution over the number of collisions Ncoll(ET)in proton-nucleus scattering as determined by the energy release (ET) at central rapidities and the neutron multiplicity as a function of ET[45]. It was observed that Ncoll(ET)is linearly proportional to the number of evaporation neutrons Mn(ET)for the same ETbins at least up to Ncoll∼10. Note that in our case Ncollis much lower; see Eq. (10). Another important observation made by the E665 experiment at Fermilab is that in muon-nucleus deep inelastic scattering (DIS) in coincidence with detection of slow neutrons, μ−+A→n+X, the average neutron multiplicity Mn for the lead target is [46] Mn≈5.(11) This result has been understood in the framework of cascade models of nuclear DIS [47,48], where soft neutrons are produced either directly in DIS on a bound nucleon or through a statistical decay (deexcitation) of the excited residual nucleus, leading to neutron evaporation.1The latter mechanism depends strongly on the hadron formation time: to describe the energy spectrum of emitted neutrons, one has to assume that only nucleons and pions with momenta ⩽1GeV/ccould be involved in final-state interactions. A similar conclusion was reached by Baker (private communication) using the BEAGLE Monte Carlo generator [50]. This suggests the following space-time picture of forward neutron production in high energy photon-nucleus scattering. Well before the target, the incoming photon fluctuates into long-lived hadronic components, which pass through the nucleus and interact inelastically with several nucleons. It leads to the creation of holes in the nucleus (particle-hole excitations in the terminology of a nuclear shell model), which de-excite and cool the nucleus by evaporating neutrons. It also produces a number of soft particles with momenta less than 1GeV/c, which in turn generate more neutrons. The nucleon fragmentation weakly depends on the incident energy due to Feynman scaling, and, hence, it is not significantly affected by the energy conservation constraint, which is important in the case when one uses hadron multiplicities at central rapidities [51]. In this case, the energy transferred to the rest of the nucleus, which heats the residual nuclear system, is proportional to Ncoll. Since the Fermilab data [46] correspond to the average momentum fraction x=0.015, where the nuclear shadowing effect is small, one finds that Ncoll≈1; see Eq. (9). Thus, every inelastic photon-nucleon interaction results on average in 5 forward neutrons. We use this hypothesis and perform the following numerical test study. First, we consider a simple model, which assumes that the probability density of neutron emission is given by the Poisson distribution and that each hole created 1The geometry of the heating is very different from the case of AA collisions, where in each collision a large portion of nucleons in each nucleus interacts and deexcitation of the spectators only occurs close to the interaction surface [49]. 025205-4
SLICING POMERONS IN ULTRAPERIPHERAL … PHYSICAL REVIEW C 110, 025205 (2024) FIG. 3. Left: The probability distribution of forward neutron emission Pcomb (N)(13) as a function of the number of emitted neutrons N for Mn=5. The three curves correspond to the three models for Pγ(σ) discussed in text. Right: The contributions of ν=1,2,3 wounded nucleons to Pcomb(N) in the Glauber model for Pγ(σ) chosen to correspond to Ncoll=2. The black dotted curve labeled “Sum” gives the total Pcomb(N). in the target nucleus generates independently on average Mn neutrons. Therefore, the neutron probability distribution for ν=Ncollwounded nucleons is PPoisson(N;λ=νMn)=(νMn)Ne−νMn N!,(12) where Nis the number of produced neutrons (neutron multiplicity). Then, we combine the distribution over the number of wounded nucleons P(ν) discussed in Sec. II with the Poisson distribution of produced neutrons (12). The resulting probability distribution of forward neutrons is given by the following expression: Pcomb(N)= A ν=1 P(ν)PPoisson(N;νMn).(13) The left panel of Fig. 3presents Pcomb(N) as a function of forward neutrons Nfor Mn=5. The three curves correspond to the three models for the hadronic (color) fluctuations of the real photon; see the right panel of Fig. 1. One can see from the figure that cross section fluctuations of the real photon noticeably affect the shape of the neutron distribution: its maximum at small Nis more pronounced compared to the “Glauber” result and is also somewhat suppressed by the leading twist shadowing in the “Generalized CF” case. Extraction of the contributions of individual ν(deconvolution) from the distribution Pcomb(N) is feasible for not very large values of σγN inel . This is illustrated in the right panel of Fig. 3, which shows the contributions of ν=1,2,3 wounded nucleons to Pcomb(N) in the case when Pγ=δ(σ−¯σ) with ¯σchosen to correspond to Ncoll=2; see Fig. 2. The black dotted curve labeled “Sum” gives the total Pcomb(N)inthis model. One can see from the figure that the peaks of these contributions are sufficiently separated, which gives a principal possibility to reconstruct the distribution over wounded nucleons P(ν). Then one can use an iterative procedure to find individual σν. Indeed, assuming that the series in Eq. (3)is dominated by the ν=1,2 terms (the limit of weak nuclear shadowing), one obtains Ncoll −1≈σ2 σ1≈A−1 2σ2 inel σineld2 bT2 A( b),(14) where, in the second approximation, we used Eq. (4). The ratio σ2 inel/σinelplays a central role in the leading twist approach to nuclear shadowing, where it determines its magnitude in the weak shadowing limit. Working along these lines, one can determine higher moments σn inel/σinel(see [52]), which built up a full-fledged LTA shadowing correction. The shape of the neutron distributions in Fig. 3strongly depends on the magnitude of nuclear shadowing, which in turn is correlated with Ncolland the x-dependence (energy dependence) of nuclear modification of nuclear PDFs in LTA: an increase of nuclear shadowing leads to the proportional increase of Ncoll) [see Eq. (10) and Fig. 2], and, hence, to a wider distribution Pcomb(N) with important contributions of large ν. This is illustrated by the left panel of Fig. 4, which shows Pcomb(N) as a function of Nfor Ncoll=3. A comparison with the right panel of Fig. 3demonstrates that Pcomb(N) has become wider (the black dotted curve) because of an important contribution of ν⩾2 wounded nucleons. Note that, to reach a high accuracy in deconvolution of Pcomb(N), one needs to calibrate the theoretical description against the kinematics, where only one target nucleon is struck, e.g., using γ+A→2jets+Xor quasi-elastic J/ψ production for xA⩾0.01, where the effect of nuclear shadowing is small and Ncoll≈1. It is supported by the results in the right panel of Fig. 4, which show that Pcomb(N)at Ncoll=1.2 is dominated by the ν=1 contribution. In summary, an important qualitative effect predicted by our model is a strong increase of the multiplicity of neutrons detected in ZDCs with a decrease of xfrom x∼0.05 corresponding to the right panel of Fig. 4, where nuclear shadowing is small, to x∼10−3corresponding to the left panel of Fig. 4, where the shadowing effect is large. After measurements of the neutron multiplicity for large xare performed, it would be 025205-5
M. ALVIOLI, V. GUZEY, AND M. STRIKMAN PHYSICAL REVIEW C 110, 025205 (2024) FIG. 4. The probability distribution of forward neutron emission Pcomb(N) as a function of the number of emitted neutrons Nfor Mn=5. The left and right panels correspond to the strong nuclear shadowing with Ncoll=3 and weak shadowing with Ncoll=1.2, respectively. See Fig. 3for the legend. possible to test LTA predictions for the probabilities of 1,2,3 wounded nucleons as well as the assumption that emissions of neutrons generated by a removal of nucleons can be treated as independent. IV. CONCLUSIONS AND OUTLOOK In this paper, we suggest using measurements of forward neutrons from nuclear breakup in inclusive high energy photon-nucleus scattering in heavy-ion UPCs, e.g., charmonium (bottomonium) production γ+A→J/ψ(ϒ)+Xor heavy-quark dijet production γ+A→Q¯ Q+X, as a novel way to study the QCD dynamics at small x. The key quantity is the number of inelastic photon-nucleon interactions (the number of wounded nucleons): its average value Ncollis proportional to inverse of the gluon nuclear shadowing and its distribution is sensitive to details of nuclear shadowing. Our numerical analysis suggests that the number of forward neutrons from nuclear breakup detected in the ZDC on the nuclear target side is rather unambiguously proportional to the number of wounded nucleons, which provides a practical opportunity for novel studies of nuclear shadowing and its x dependence. Using these processes, it would be possible to explore effects related to proximity to the black disk limit of the strong interaction. For example, one can study fragmentation of leading hadrons in γAscattering and look for suppression of their multiplicity as a function of Feynman xFand Was well as for broadening of their transverse momentum distribution [3]. These effects should be more pronounced for central collisions characterized by an enhanced activity in the ZDC. It should be possible to construct from the data an analog of the central-to-peripheral RCP ratio of yields, which would probe the density dependence of fragmentation. It would also be useful to construct similar quantities for low-pTcharm production. Another interesting application is for multiparton interactions in proton-nucleus (pA) scattering. It was argued in [53] that the single and double scattering can be separated using their dependence on the impact parameter: the former is proportional to A, while the latter ∝A4/3. However, since both hard interactions are typically detected in a limited range of rapidities |y|⩽3−4, centrality is difficult to determine from the transverse energy ETsignal because multiparton interactions also contribute to ET. The use of forward neutrons in ZDCs would alleviate this problem. Note that the neutrons detected in ZDCs can be a promising complementary way to determine centrality of various photon-nucleus and proton-nucleus inelastic collisions, expanding the use of ZDCs beyond their current use in vector meson diffractive production and for determining of centrality of heavy-ion collisions. The main advantage of using forward neutrons rather than the transverse energy ETfor the determination of centrality is a much larger distance in rapidity between the rapidity of the hard process and that of the process used for determination of the centrality. One of the principal problems of using UPCs for studies of small-xphenomena is a lack of the nucleon reference data at similar energies with the precision necessary to observe nuclear effects with a better than 10% accuracy (J/ψ exclusive photoproduction is a notable exception). Below we outline a possible strategy for overcoming this problem. Note that we are not aiming to optimize cuts or to account for the energy resolution of ZDCs since this would require a dedicated Monte Carlo study. One can separate events into two classes: peripheral events corresponding to Ncoll⩽2 (we call it class “L”) and more central events corresponding to Ncoll⩾1.5–2 and Mn∼ 7–10 (class “H”). If statistics is sufficient, the lower limit for class “H” can be gradually increased, which will push up the average number of wounded nucleons. Then, the ratio of the number of events in the two classes, ˆ R=Yield(H)/Yield(L), should quantify the effect of nuclear shadowing at small and large impact parameters, which in principle probes the dependence of nuclear shadowing on the thickness of nuclear matter. The promising channels for such an analysis include inclusive charm production with the transverse momentum in the range pT=5–20 GeV/cand production of soft particles 025205-6
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