Coherent $\rho^0$ photoproduction in ultra-peripheral Pb-Pb collisions at $\mathbf{\sqrt{\textit{s}_{\rm NN}}} = 2.76$ TeV

We report the first measurement at the LHC of coherent photoproduction of $\rho^0$ mesons in ultra-peripheral Pb-Pb collisions. The invariant mass and transverse momentum distributions for $\rho^0$ production are studied in the $\pi^+ \pi^-$ decay channel at mid-rapidity. The production cross section in the rapidity range $|y|<0.5$ is found to be $\mathrm{d}\sigma/\mathrm{d}y = 425 \pm 10 \, (\mathrm{stat.})$ $^{+42}_{-50} \, (\mathrm{sys.})$ mb. Coherent $\rho^0$ production is studied with and without requirement of nuclear breakup, and the fractional yields for various breakup scenarios are presented. The results are compared with those from lower energies and with model predictions.


Introduction
Charged particle beams at the LHC generate an electromagnetic field which can be regarded as a beam of quasi-real photons; thus at the LHC, besides hadronic interactions, also photonuclear and photonphoton interactions occur. Collisions in which the impact parameter exceeds the sum of the radii of the incoming beam particles are called ultra-peripheral collisions (UPC). In UPC the cross section for hadronic processes is strongly suppressed, while the cross sections for two-photon and photonuclear interactions remain large. This is particularly the case for heavy ions, because the intensity of the photon flux grows with the square of the ion charge, Z. A number of reviews of UPC are available; e.g., [1,2]. The ALICE Collaboration has previously studied exclusive photoproduction of J/ψ in ultra-peripheral Pb-Pb and p-Pb collisions [3][4][5].
Exclusive photoproduction of ρ 0 vector mesons, Pb + Pb → Pb + Pb + ρ 0 , can be described as the fluctuation of a quasi-real photon into a virtual ρ 0 vector meson, which then scatters elastically off the target nucleus. Two cases can be distinguished. When the interaction involves the complete target nucleus, the process is called coherent. In this case the target nucleus normally remains intact. If the virtual ρ 0 vector meson scatters off only one of the nucleons in the target, then the process is called incoherent and in this case the target nucleus normally breaks up, emitting neutrons at very forward rapidities. For coherent processes, the size of the lead ion restricts the mean transverse momentum of the vector meson to be about 60 MeV/c corresponding to a de Broglie wavelength of the nuclear size, while it is of the order of 500 MeV/c for incoherent processes.
Because of the strong electromagnetic fields in ultra-peripheral collisions of heavy ions, multiple photons may be exchanged in a single event. The additional photons can lead to excitation of the nuclei. The dominant process is the excitation to a Giant Dipole Resonance [6]. As these photonuclear processes occur on a different time scale, they are assumed to be independent, so the probabilities factorize. The excited nucleus typically decays by the emission of neutrons at very forward rapidities. The signature of these processes is thus a ρ 0 vector meson with very low transverse momentum which may be accompanied by a few neutrons at very forward rapidities but no other particles.
The ρ 0 vector meson gives the dominant contribution to the hadronic structure of the photon. For proton targets, the process γ + p → ρ 0 + p contributes about 10% to 20% of the total γ + p cross section, depending on energy. Scaling from a nucleon target to a nuclear target is often done using the Glauber model assuming Vector Meson Dominance [12]. The large value of σ (γ + p → ρ 0 + p) means that for heavy nuclei one may reach the limit where the target appears like a black disk and the total ρ 0 + A cross section approaches 2πR 2 A (R A is the nuclear radius). The situation may, however, be more complicated for several reasons. The cross section σ (γ + p → ρ 0 + p) has contributions both from Reggeon and Pomeron exchange, and its energy dependence is therefore not monotonic. Furthermore, the nuclear medium might modify the Reggeon and Pomeron components differently. There may also be interference between the ρ and ρ ′ production amplitudes, and these amplitudes may be affected by the nuclear environment in a different way [13]. A detailed discussion of models for photoproduction of ρ 0 on complex nuclei based on data from fixed target experiments can be found in [12].
The cross sections measured by STAR [8][9][10] at RHIC were found to be about a factor two less than that predicted by a Glauber calculation [14], while in agreement with STARLIGHT [15]. The reason for the difference between these two models will be discussed below. The many issues associated with calculating the photonuclear ρ 0 cross section and the discrepancies between models thus call for more data. In particular, it is important to establish if the trends seen at lower energies persist at higher energies.
Moreover, the total cross section for exclusive ρ 0 production is very large at LHC energies, with the models mentioned above predicting that it could be between 50-100% of the total hadronic inelastic cross section. It could thus constitute a significant background, e.g. at the trigger level, to low multiplicity peripheral hadronic interactions and to other types of ultra-peripheral collisions. It therefore has to be well understood. The high statistics in the ρ 0 sample allows the predictions for exclusive ρ 0 production accompanied by nuclear fragmentation to be tested with good precision.
This Letter presents the first measurement of the cross section for coherent photoproduction of ρ 0 vector mesons in Pb-Pb collisions at the LHC. The ρ 0 is reconstructed using the π + π − decay channel in the rapidity range |y| < 0.5. The rapidity interval corresponds to a γ-nucleon center of mass energy in the range 36 ≤ W γN ≤ 59 GeV with W γN = 48 GeV, about a factor of 4 higher than in any previous measurement [10]. The cross section is measured for the cases of no neutron emission and for at least one emitted neutron. The new data presented in this paper will hopefully help to clarify some of the theoretical uncertainties mentioned above.

The ALICE experiment and the UPC trigger
A full description of the ALICE detectors and their performance can be found in [16,17]; here, only the components relevant for this analysis will be briefly described. The Inner Tracking System (ITS) and Time Projection Chamber (TPC) are used to measure and identify the tracks of the decay products of the ρ 0 vector meson. The ITS consists of six layers of silicon detectors covering the full azimuthal angle.
The two innermost layers form the Silicon Pixel Detector (SPD) with a pseudorapidity acceptance of |η| < 1.4. The SPD also provides trigger information at the lowest level. Two layers of silicon drift and two of silicon strip detectors complement the ITS, and all six layers have an acceptance of |η| < 0.9. The TPC is the main tracking detector of ALICE. It has a Ne-CO 2 -N 2 gas mixture contained in a largealmost 90 m 3 -cylindrical drift detector with a central membrane at high voltage and two readout planes, composed of multi-wire proportional chambers, at the end caps. It covers the full azimuth and |η| < 0.9 for full length tracks. It also provides a measurement of the ionization energy loss, dE/dx, which allows the identification of particles. The TPC and ITS are situated inside a large solenoid magnet providing a B = 0.5 T field.
The measurement of neutrons emitted at forward rapidities is performed with a set of two neutron Zero Degree Calorimeters (ZDC) located 114 m away on each side of the interaction point. The ZDC has a 99% detection probability for neutrons with |η| > 8.8 [18]. Figure 1 illustrates the capabilities of the ZDC to separate the emission of zero, one or several neutrons at zero degrees. The sample appearing in this figure was obtained from events fulfilling the event selection described in Section 3.
In addition to the SPD, this analysis uses the Time of Flight (TOF) and VZERO detectors for triggering. TOF is a large cylindrical barrel surrounding the TPC. It has 18 sectors in azimuth, each made of multigap resistive plate chambers distributed in five gas-tight modules, with a total of 152928 read-out channels and an intrinsic time resolution better than 50 ps. The pseudorapidity acceptance is the same as for the TPC. The VZERO consists of two arrays of scintillators called VZERO-A and VZERO-C, covering the pseudorapidity ranges 2.8 < η < 5.1 (VZERO-A) and −3.7 < η < −1.7 (VZERO-C). Its time resolution, better than 500 ps [19], allows beam-beam collisions to be distinguished from beam-gas collisions.
The data used for this analysis were collected during the 2010 Pb-Pb run of the LHC at an energy of √ s NN = 2.76 TeV. Two different triggers were used. At the beginning of the run, when the luminosity was low, the trigger requirement was at least two hits in the TOF detector. When the luminosity was increased the trigger selection was strengthened to improve the purity by additionally requiring at least two hits in the outer layer of the SPD, and no activity in any of the VZERO arrays.

Track and event selection
In addition to the trigger selection, the events used for the analysis are required to fulfill the following requirements: i) a primary vertex has to be identified within 10 cm of the nominal interaction point position, along the beam direction; ii) the event is required to have exactly two tracks reconstructed in the TPC and ITS satisfying the track selections discussed below; iii) the VZERO arrays are required to be empty (the difference between the offline and online VZERO selection will be discussed below); iv) the energy loss in the TPC has to be consistent with that for pions within 4 standard deviations from the Bethe-Bloch expectations, i.e., ∆σ 2 π + + ∆σ 2 π − < 16 (see Fig. 2); v) the track pairs used to define the coherent signal have to have a transverse momentum below 150 MeV/c and rapidity |y| < 0.5, the latter requirement being imposed to avoid edge effects; vi) the track pairs used to define the coherent signal are required to have tracks of opposite charge.
The background estimated from like-sign pairs (π + π + and π − π − ) is below 2% and it is subtracted from the final sample bin-by-bin in invariant mass.
The track selection requires that each track has at least 70 space points, out of a maximum of 159, in the TPC and a χ 2 per degree of freedom from the Kalman fit procedure better than 4. Each track has at least one hit in the SPD with a χ 2 per ITS hit less than 36. The distance of closest approach between the track and the primary vertex has to be less than 2 cm along the beam direction and less than 0.0182 + 0.035/p 1.01 T cm (p T in GeV/c) in the plane perpendicular to the beam direction. These track selection cuts are based on studies of the detector performance [17].
Three other track selections are used in order to estimate systematic errors. These differ from the default track selection described above in the following ways: (a) accepting tracks reconstructed only in the ITS in addition to combined ITS-TPC tracks satisfying the default track selection; (b) using only TPC information and accepting tracks having at least 50 space points in the TPC; (c) using the default track cuts with stronger requirements on TPC variables. The latter requirements meant that the tracks had to pass at least 120 of the 159 TPC pad rows and have a cluster in more than 80% of the crossed pad rows. For the cross section calculation, the mean of the results of the four different track selection methods is used. The systematic error related to the track selection is estimated from the deviation from the mean. This contributes +3.7 −3.0 % to the systematic error.
-BB line  The ionization energy loss for the selected tracks is shown in Fig. 2. The scale on both axes is in units of the number of standard deviations from the Bethe-Bloch expectation in the TPC; in this way the dependence on track momentum is removed. Pions can be clearly identified by the 4σ circle centered on (0, 0), while the events above and to the right of the pions are mostly e + e − pairs from γγ → e + e − . This figure shows that any possible contamination from kaons or protons in the sample is negligible. There could, however, be a contamination from muons from the process γγ → µ + µ − , which cannot be distinguished from pions using the energy loss. This contribution can be estimated from the number of e + e − pairs in the data sample, as the cross sections for γγ → µ + µ − and γγ → e + e − are about the same at midrapidity for invariant masses well above threshold. It can also be calculated from STARLIGHT [21,22]. Both methods give an expected number of muon pairs of about 5%, which is not corrected for, but added to the systematic error.

Data analysis
Using the event and track selection described in the previous section, the four-momenta of the two tracks are constructed and pair variables are extracted. The resulting distribution of the pair transverse momentum is shown in Fig. 3 for events with 0.4 ≤ M ππ ≤ 1.1 GeV/c 2 and |y| < 0.5. A peak at low transverse momentum (p T < 0.15 GeV/c), corresponding to coherent production, is clearly seen. The distribution is compared with the corresponding distributions from STARLIGHT [15,22] events for coherent and incoherent ρ 0 production, processed through the detector response simulation based on GEANT 3. The coherent peak is shifted to slightly lower p T in data than that predicted by STARLIGHT. A similar trend has been observed by STAR at lower energies [23]. The shape of the coherent peak in the p T distribution is determined by the nuclear form factor. The form factor used in STARLIGHT is consistent with what is obtained from elastic electron-nucleus scattering, which probes the charge content of the nucleus. Since the ρ 0 couples to both neutrons and protons, a possible explanation of this difference could thus be the presence of a "neutron skin". The effect, however, appears larger than what the current limit on the difference between neutron and proton radius in 208 Pb (0.3 fm) allows [24], and is thus not fully understood. Data also show a dip around p T = 0.12 GeV/c, which is not present in the the model. In a Glauber calculation, the transverse momemtum distribution is determined from a Fourier transform of the nuclear profile function, see e.g. [2], and the direct dependence on the form factor is only an approximation; this could also contribute to explaining the difference between STARLIGHT and data. The high-p T tail of the distribution is very well described by the incoherent p T spectrum from STARLIGHT.    . 3: Transverse momentum distributions for π + π − -pairs with a linear (upper) and logarithmic (lower) scale on the y-axis. The dashed (red) and dash-dotted (blue) histograms show the normalized p T distribution from STARLIGHT passed through the detector response simulation for coherent and incoherent ρ 0 production, respectively. The solid (black) histogram is the sum of the two.
The final sample of coherent ρ 0 → π + π − candidates is corrected for acceptance and efficiency in invariant mass bins. The event sample used to determine the corrections has uniform distributions in invariant mass, rapidity, transverse momentum, and azimuthal angle over the ranges 2m π ≤ M ππ ≤ 1.5 GeV/c 2 , |y| ≤ 1.0, p T ≤ 0.15 GeV/c, and 0 ≤ φ ≤ 2π. Using a flat distribution in transverse momentum is justified over the narrow range p T ≤ 0.15 GeV/c, where the acceptance and efficiency are constant. All models predict only a very small variation of the cross section over the range |y| < 0.5 (see Fig. 5 below) so also for rapidity a uniform input distribution is justified. The advantage of using a flat input distribution in invariant mass is to obtain sufficient statistics in the tails of the distribution. If one were to use a ρ 0 -shape as input, one would need enormous statistics to cover the high and low invariant mass ranges.
The ρ 0 candidates are assumed to be transversely polarized. This is expected from helicity conservation and has been confirmed by photoproduction measurements [10,25]. This polarization translates into a dn/dΩ ∝ sin 2 (θ ) angular distribution of the π + π − decay products in their center of mass system (θ is here measured relative to the direction of flight of the ρ 0 in the γ-nucleon center of mass system). All generated samples serve as input to a full detector simulation using GEANT 3 for the propagation of particles through the detector. Selection criteria are applied in the same way as done for real events. The variation of the detector configuration during the data taking period is included in the detector response simulations. The product of acceptance and efficiency varies from about 2% at the low end of the studied invariant mass interval (M ππ = 0.6 GeV/c 2 ) to about 12% at the high end (M ππ = 1.5 GeV/c 2 ).   The uncertainty in the trigger efficiency is obtained by comparing the measured trigger efficiency with the one in the detector response simulation in a data sample taken with a ZDC trigger [4]. The result is a trigger efficiency uncertainty of +3.8 −9.0 %. In addition, a correction is applied for the trigger dead time resulting from after pulses in the TOF. The systematic error on this correction is estimated to be ±1.3%.
The invariant mass distribution of the ρ 0 candidates, corrected for acceptance and efficiency, is shown in Fig. 4. It is well known that the shape of the ρ 0 in photoproduction deviates from a pure Breit-Wigner resonance [7][8][9][10]25]. Several different parameterizations exist to describe the shape, with one of the most often used being a formula due to Söding, where a continuum amplitude, B, is added to the Breit-Wigner resonance [26]: Here, A is the amplitude of the Breit-Wigner function, B is the amplitude of the direct non-resonant π + π − production, and the mass dependent width is given by with m π the mass of the pion. Eq The ratio |B/A| is lower than what was found by STAR with Au targets, |B/A| = 0.81-0.89 (GeV/c 2 ) −1/2 for W γN in the range 7-12 GeV [8][9][10]. The result from ZEUS with proton targets for W γN in the range 55-90 GeV shows that |B/A| varies with the γ-proton momentum tranfer [25]. The average is |B/A| = 0.67± 0.02 (stat.)± 0.04 (syst.), while for momentum transfers of the same order as for coherent production |B/A| ≈ 0.8. The lower value of |B/A| observed by ALICE may indicate that the nonresonant contribution is more strongly absorbed in heavy nuclei at high energies, as had been previously suggested [28].
Other parameterizations of the ρ 0 shape are possible, and as a cross check the invariant mass distribution was also fit to a Ross-Stodolsky function [25,29]: with a slightly different definition of the mass dependent width As can be seen in Fig. 4, this parameterization also described the observed shape of the invariant mass distribution well and gave a ρ 0 mass (M ρ 0 = 769.2 ± 2.8 (stat.) +8.0 −5.2 (syst.) MeV/c 2 ) and width (Γ ρ 0 = 156.9 ± 6.1 (stat.) +17.3 −5.9 (syst.) MeV/c 2 ) consistent with the PDG values. The deviation from a pure Breit-Wigner shape is given by the parameter k, which was found to be k = 4.7± 0.2 (stat.) +0. 8 −0.6 (syst.). This can be compared to the corresponding value for proton targets from ZEUS [25] and H1 [30] at HERA. ZEUS finds k = 5.13 ± 0.13 averaged over all momentum transfers and k ≈ 6 for t = 0, while H1 reports k = 6.84±1.00 averaged over all momentum transfers. The larger value of k for proton targets again indicates that the invariant mass distribution for Pb-targets deviates less from a pure Breit-Wigner resonance, as was also found using the Söding formula.
As can be seen in the lower part of Fig. 4, there is a hint of a resonance around 1.3 GeV/c 2 . This may be understood from two-photon production of the f 2 (1270) meson followed by its decay into two pions, γ + γ → f 2 (1270) → π + π − . This meson is a "standard candle" in two-photon interactions with a well known γγ coupling, but it has so far not been observed in ultra-peripheral collisions because of the large background from photonuclear processes. The significance of the excess over the ρ 0 Breit-Wigner distribution is estimated to be 4 +2 −1 , where the error comes from the uncertainty in the skewness of the Breit-Wigner distribution (parameter k in the Ross-Stodolsky formula).
The normalized yield of ρ 0 s (N yield ) is obtained by integrating the resonant part of Eq. 1 (obtained by setting B = 0 and taking the other parameters from the fit) from 2m π to 1.5 GeV/c 2 . The systematic error on the number of extracted ρ 0 s is obtained by varying the fitting method (χ 2 or log likelihood minimization) and fitting range, resulting in an error of +0.8 −1.4 %. The uncertainty in the track selection gives an additional error of +3.7 −3.0 % as discussed above. Both Eq. 1 and 3 describe the observed shape equally well, so no additional systematic error was added to the yield because of the choice of fitting function.
It is worth noting that the shape of the resonant contribution (shown by the dashed curve in Fig. 4) is quite different from the shape of the measured π + π − invariant mass distribution. However, the integrated yield between 2m π and 1.5 GeV/c 2 does not deviate by more than around 1% if the non-resonant amplitude is included in the integration.
The number of extracted ρ 0 s is corrected for the following 3 contributions: incoherent events with p T < 0.15 GeV/c ( f incoh ), events which have one or more additional SPD tracklets ( f SPD ), and the number of coherent ρ 0 events lost by the VZERO offline timing requirement ( f VZERO ).
The number of incoherent events with p T < 0.15 GeV/c is estimated in two different ways: first fitting the sum of two exponentials in p 2 T to the the p T distributions and integrating the fitted functions over the interval chosen for the coherent selection (p T < 0.15 GeV/c), and second using the fit to the STARLIGHT templates shown in Fig. 3. The correction for incoherent events is found to be 5.1% in both cases with an uncertainty estimated from using different track selections of ±0.7%.
The track selection (a) above allows one to check the events for any additional activity in the ITS, for example from tracks with low momenta, which do not reach the TPC, using SPD tracklets, defined as any combination of hits from the two SPD layers. Rejecting events with one or more extra tracklets, not associated with the two good tracks coming from the primary vertex, removes 3.0% of the events in the signal region. Since true UPC events should have no additional tracks, the extracted yield is corrected for this. In the Monte Carlo samples of coherently produced ρ 0 s, the same cut removes only 0.5% of the events which is taken as the systematic error associated with this cut.
The events selected by the SPD+TOF+VZERO trigger are required to have no online signal in the VZERO detector. A similar cut is also applied offline to the events triggered by TOF only. The VZERO offline selection is further refined using the timing information. This selection has been tuned to work well for hadronic interactions, which typically have a non-zero signal in the VZERO on both sides. In the ultra-peripheral events studied here, where the VZERO is required to be empty, the offline selection is less reliable, and a coherent signal can be observed in the events with 2 tracks rejected by the offline VZERO requirement. The increase in the coherent signal when the offline VZERO selection is not used amounts to 10.0%. The systematic error of this number is obtained from the estimated contamination from hadronic events following from this looser cut. This contamination is determined from the fraction of the events which have a signal in the ZDCs, resulting in a systematic error of +0.0 −3.1 %.  The corrected number of coherent ρ 0 s is then obtained from with f incoh = 0.051 ± 0.007, f SPD = 0.030 ± 0.005, and f VZERO = −0.100 +0.031 −0.000 . From this number the differential cross section is calculated as The systematic errors discussed above are summarized in Table 1. They have been evaluated for the SPD+TOF+VZERO trigger sample, which contains more than 80% of the total integrated luminosity. The total error is obtained by adding the individual errors following the description in [31]. The two trigger samples, with appropriate errors, are compared as a cross check. They use different trigger combinations and were taken under quite different running conditions, with the typical hadronic minimum bias interaction rate being around 10 Hz during the early part of the run when the TOF only trigger was used and around 200 Hz during the later part of the run when the SPD+TOF+VZERO trigger was used. The correction factor for trigger dead time due to after pulses was thus very different for the two samples (≈1 during the early part and ≈5 during the later part).
To make a comparison of the cross sections measured under the different trigger conditions, the systematic errors are separated into correlated and uncorrelated errors for the two trigger samples. The fully correlated errors are those related to luminosity, incoherent contribution, trigger efficiency, and particle identification. The fully uncorrelated errors are those related to the VZERO offline selection (different VZERO thresholds were used for the two data samples), the cut on SPD tracklets, and trigger dead time.
The errors related to the signal extraction and track selection are found to be partly correlated, but are decorrelated for the comparison. This gives a cross section dσ /dy = 466 +25 −25 mb for the sample taken with the TOF only trigger and dσ /dy = 414 +14 −16 mb for the sample taken with the SPD+TOF+VZERO trigger. The error is obtained from the squared sum of the statistical and uncorrelated systematic error. The difference of 12% corresponds to 1.8 standard deviations. The final cross section is obtained as the weighted mean of the cross sections of the two samples, giving dσ /dy = 425 ± 10 (stat.) +42 −50 (syst.) mb. 10 In addition to the ρ 0 cross section, the cross section for two-photon production of e + e − pairs in the range 0.6 ≤ M ee ≤ 2.0 GeV/c 2 and |η 1,2 | < 0.9 (η 1,2 are the pseudorapidities of the two tracks) was measured. The analysis is similar to the one for ρ 0 but the PID requirement was modified to accept electrons rather than pions. The result is σ (0.6 ≤ M ee ≤ 2.0 GeV, |η 1,2 | < 0.9) = 9.8 ± 0.6 (stat.) +0.9 −1.2 (syst.) mb, which is in good agreement with the STARLIGHT [21] prediction for the same selection in invariant mass and pseudorapidity (σ = 9.7 mb). The cross sections for the individual trigger samples are 11.8 ± 1.6 (stat.) +1.1 −1.4 (syst.) mb (TOF only trigger) and 9.4 ± 0.7 (stat.) +0.9 −1.1 (syst.) mb (SPD+TOF+VZERO trigger).
As discussed above, photoproduction of vector mesons may occur in interactions where additional photons are exchanged between the nuclei, leading to neutron emission in the forward region. These neutrons may be detected in the ALICE ZDCs. Four Gaussian distributions centered around each peak with means and variances constrained to x n = nx 0 and σ n = √ nσ 1 have been fitted to the ZDC energy distribution shown in Fig. 1. In order to separate different cases of neutron emission, the minima between the first three Gaussians are used. The minimum between zero and one-neutron emission lies at half the energy per nucleon and it is roughly three sigma away from the adjacent peaks. A given event is considered to have no neutron in the ZDC if the energy registered in the calorimeter is less than 600 GeV, one neutron if the energy lies between 600 GeV and 2000 GeV and more than one neutron if the energy is above 2000 GeV.
The events are divided into different groups as follows: no neutrons emitted in any direction (0n0n), at least one neutron emitted in any direction (Xn), at least one neutron emitted in one direction and no neutron emitted in the other direction (0nXn), at least one neutron emitted in both directions (XnXn).
The corrections applied in obtaining the cross section from the measured yield are independent of the ZDC signal. The fractional yield for each fragmentation selection thus reflects the relative ρ 0 production cross section. The only exception to this is the correction for the incoherent contribution ( f incoh ), which is expected to be higher when a signal is required in the ZDCs. This correction is thus calculated for each ZDC selection separately, using the same method as described above.

Results and discussion
The coherent ρ 0 photoproduction cross section, dσ /dy, is shown and compared with model predictions in Fig. 5. The measured cross section is in agreement with STARLIGHT [15] and the calculation by Gonçalves and Machado (GM) [32], while the GDL (Glauber-Donnachie-Landshoff) prediction [14,33] is about a factor of 2 higher than data. The calculation by GM is based on the Color Dipole model, while STARLIGHT and GDL use the photon-proton cross section σ (γ + p → ρ 0 + p) constrained from data as input. In STARLIGHT, the γ-nucleon cross section is given by the parameterization σ = 5.0W 0.20 γN + 26.0W −1.23 γN µb (W γN in GeV), while GDL use the Donnachie-Landshoff model [34] for the total ρN cross section. All calculations use the Glauber model to scale the cross section from γ-nucleon to γ-nucleus.
The STAR Collaboration has published the total coherent ρ 0 photoproduction cross section at three different energies [8][9][10]. To be able to compare the current result to those, one has to integrate dσ /dy over the whole phase space, which can only be done using models. The extrapolation factor from |y| < 0.5 to all rapidities is calculated as the mean of the values obtained from the STARLIGHT (10.6) and GM (9.1) models, and the deviation of the two from the mean (≈ 8%) is added to the systematic error. This gives σ (Pb + Pb → Pb + Pb + ρ 0 ) = 4.2 ± 0.1(stat.) +0.5 −0.6 (syst.) b at √ s NN = 2.76 TeV. The total cross section as a function of √ s NN is shown in Fig. 6, where the results from ALICE and STAR Collaborations are compared with the STARLIGHT and GDL calculations. The total cross section increases by about a factor of 5 between the top RHIC energy and √ s NN = 2.76 TeV.
The cross section and its energy dependence is well described by STARLIGHT, while the GDL calculation overpredicts the cross section by about a factor of 2. The agreement with STARLIGHT is somewhat surprising since its Glauber calculation does not include the elastic part of the total cross section, which is included in the GDL model. It has been argued that coherent ρ 0 production off heavy nuclei may probe the onset of the Black Body Limit, in which the total ρ 0 -nucleus cross section approaches 2πR 2 A at high energies [14]. The results from STAR and ALICE do not favour this picture. The cross section is instead reduced by about a factor of 2 compared with the GDL model [33], independent of energy, indicating that further work is needed to understand this process. It should be noted that none of the models in Fig. 5 include cross terms such as ρ + N → ρ ′ + N.
The photonuclear cross section, σ (γ + Pb → ρ 0 + Pb), in STARLIGHT is almost energy independent for W γN > 10 GeV. The increase in the Pb-Pb cross section, σ (Pb + Pb → Pb + Pb + ρ 0 ), with √ s NN is thus  The number of events that satisfy various selections on the number of neutrons detected in the ZDCs. 0n0n corresponds to no neutrons emitted in any direction; Xn to at least one neutron emitted in any direction; 0nXn to no neutrons in one direction and at least one neutron in the other direction; XnXn to at least one neutron in both directions. For the relative yield the systematic error is estimated, as explained in the text.
almost entirely due to the increase in the photon flux at higher collision energies.
The model by GM, although in agreement with the current result, has been criticized for using the Color Dipole model for a soft probe like the ρ 0 [33]. A recent publication shows that the calculation indeed has large uncertainties arising from the choice of ρ 0 wave function and dipole cross section [35].
The number of events satisfying the different fragmentation scenarios as well as the ratio to the total number of events are shown in Table 2. The table also shows the expected fractions from the STARLIGHT [36] and GDL [33] models. These models assume that the probabilities for exchange of multiple photons in a single event factorize in impact parameter space. One should note that some of the fractions are correlated: the sum of (0n0n) and (Xn) should be 100%, and the sum of (0nXn) and (XnXn) should be equal to (Xn). This is the case within errors, but the sum is not exact, since the incoherent contribution is subtracted for each selection separately. The results in Table 2 are consistent with both the STARLIGHT and GDL calculations within three standard deviations, but seem to favour the GDL results.

Conclusions
The first LHC measurement on coherent photoproduction of ρ 0 in Pb-Pb collisions at √ s NN = 2.76 TeV has been presented. Comparisons with model calculations show that a straightforward scaling of the γnucleon cross section using the Glauber model [14,33] overpredicts the cross section by about a factor of two. Comparisons with results from Au-Au collisions at RHIC energies indicate that this factor of two discrepancy is independent of collision energy in the range √ s NN = 62.4-2760 GeV. The measured cross section at midrapidity is found to be consistent with the STARLIGHT [15] and GM [32] models.
The relative yields for different fragmentation scenarios are found to be in agreement with predictions from the STARLIGHT and GDL models. This is important not only to confirm the assumptions in the two models but also because some experiments, e.g. PHENIX [37], have relied on a ZDC signal to trigger on ultra-peripheral collisions. To be able to relate such measurements to a photonuclear cross section, it is imperative that the probabilities for exchange of multiple photons are well understood.
The total cross section is found to be about half the total hadronic inelastic cross section. This is an increase of about a factor of 5 from Au-Au collisions at √ s NN = 200 GeV, where the fraction was about 10%. If the increase of the coherent ρ 0 photoproduction cross section continues to follow STARLIGHT, one can expect it to exceed the total hadronic production cross section of heavy ions such as lead or gold at a √ s NN of about 20 TeV.