Coherent $\psi$(2S) photo-production in ultra-peripheral Pb-Pb collisions at $\sqrt{s}_{\rm NN}$ = 2.76 TeV

We have has performed the first measurement of the coherent $\psi$(2S) photo-production cross section in ultra-peripheral Pb-Pb collisions at the LHC. This charmonium excited state is reconstructed via the $\psi$(2S) $\rightarrow l^{+}l^{-}$ and $\psi$(2S) $\rightarrow$ J/$\psi \pi^{+}\pi^{-}$ decays, where the J/$\psi$ decays into two leptons. The analysis is based on an event sample corresponding to an integrated luminosity of about 22 $\mu\rm{b}^{-1}$. The cross section for coherent $\psi$(2S) production in the rapidity interval $-0.9<y<0.9$ is $\mathrm{d}\sigma_{\psi{\rm(2S)}}^{\rm coh}/\mathrm{d}y =0.83\pm 0.19\big(\mathrm{\rm{stat}+{\rm syst}}\big)$ mb. The $\psi$(2S) to J/$\psi$ coherent cross section ratio is $0.34^{+0.08}_{-0.07}(\rm{stat}+{\rm syst})$. The obtained results are compared to predictions from theoretical models.


Introduction
Two-photon and photo-nuclear interactions at unprecedented energies can be studied in heavy-ion Ultra-Peripheral Collisions (UPC) at the LHC.In such collisions the nuclei are separated by impact parameters larger than the sum of their radii and therefore hadronic interactions are strongly suppressed.The cross sections for photon induced reactions remain large because the strong electromagnetic field of the nucleus enhances the intensity of the photon flux, which grows as the square of the charge of the nucleus.The physics of ultra-peripheral collisions is reviewed in [1,2].Exclusive photo-production of vector mesons at high energy, where a vector meson is produced in an event with no other final state particles, is of particular interest, since it provides a measure of the nuclear gluon distribution at low Bjorken-x.
Exclusive production of charmonium in photon-proton interactions at HERA [3][4][5], γ + p → J/ψ (ψ(2S)) + p, has been successfully modelled in terms of the exchange of two gluons with no netcolour transfer [6].Experimental data on this process from HERA have been used to constrain the proton gluon distribution at low Bjorken-x [7].Exclusive vector meson production in heavy-ion interactions is expected to probe the nuclear gluon distribution [8], for which there is considerable uncertainty in the low-x region [9].Exclusive ρ 0 [10] and J/ψ [11] production has been studied in Au-Au collisions at RHIC.The exclusive photo-production can be either coherent, where the photon couples coherently to almost all the nucleons, or incoherent, where the photon couples to a single nucleon.Coherent production is characterized by low transverse momenta of vector mesons (p T ≃ 60 MeV/c) where the target nucleus normally does not break up.However, the exchange of additional photons, radiated independently from the original one, may lead to the target nucleus breaking up or de-excite through neutron emission.Simulation models estimate this occurs in about 30% of the events [12].Incoherent production is characterized by a somewhat higher transverse momentum of the vector mesons (p T ≃ 500 MeV/c).In this case the nucleus interacting with the photon breaks up but, apart from single nucleons or nuclear fragments in the very forward region, no other particles are produced besides the vector meson.
We published the first results on the coherent photo-production of J/ψ in UPC Pb-Pb collisions at the LHC [13] in the rapidity region -3.6 < y <-2.6, which constrain the nuclear gluon distribution at Bjorken-x ≃ 10 −2 .Shortly afterwards, ALICE published a second paper measuring both the coherent and the incoherent J/ψ vector meson cross section at mid-rapidity [14], allowing the nuclear gluon distribution at Bjorken-x ≃ 10 −3 to be explored.The present analysis is performed in the same rapidity region with respect to the measurement reported in [14], and it is sensitive to Bjorken-x ≃ 10 −3 too.
There are very few studies of photo-production of ψ(2S) off nuclei.Incoherent photo-production, using a 21 GeV photon beam off a deuterium target, has been studied in [15]; non-exclusive photo-production, using bremstrahlung photons with an average energy of 90 GeV off a 6 Li target, have been reported in [16].However, no previous measurements of ψ(2S) coherent photo-production off nuclear targets, have been reported in the literature.

Detector description
The main components of the ALICE detector are a central barrel placed in a large solenoid magnet (B = 0.5 T), covering the pseudo-rapidity region |η| < 0.9, and a muon spectrometer at forward rapidity, covering the range -4.0 < η < -2.5 [23].Three central barrel detectors are used in this analysis.The ALICE Internal Tracking System(ITS) is made of six silicon layers, all of them used in this analysis for particle tracking.The Silicon Pixel Detector (SPD) makes up the two innermost layers of the ITS, covering pseudo-rapidity ranges |η| < 2 and |η| < 1.4, for the inner (radius 3.9 cm) and outer (average

Data Analysis
The event sample considered for the present analysis was collected during the 2011 Pb-Pb run, using a dedicated Barrel Ultra-Peripheral Collision trigger (BUPC), selecting events with the following characteristics: (i) at least two hits in the SPD detector; (ii) a number of fired pad-OR (N on ) in the TOF detector [25] in the range 2 ≤ N on ≤ 6, with at least two of them with a difference in azimuth, ∆φ , in the range 150 • ≤ ∆φ ≤180 • ; (iii) no hits in the V0-A and no hits in the V0-C detectors.The integrated luminosity used in this analysis was 22.4 +0.9 −1.2 µb −1 .Luminosity determination and systematics are discussed in Sec.3.1 In the present analysis, coherent ψ(2S) photo-production was studied in four different channels: ψ(2S)→ l + l − and ψ(2S)→ J/ψ π + π − , followed by the J/ψ→ l + l − decay, where l + l − can be either a e + e − or µ + µ − pair.

The ψ(2S)
For the di-muon and di-electron decay channels the following selection criteria were applied: (i) a reconstructed primary vertex.The primary vertex position is determined from the tracks reconstructed in the ITS and TPC as described in ref. [27].The vertex reconstruction algorithm is fully efficient for events with at least one reconstructed primary charged particle in the common TPC and ITS acceptance; (ii) only two good tracks with at least 70 TPC clusters and at least 1 SPD cluster each.Moreover, particles originated in secondary hadronic interactions or conversions in the detector material, were removed using a distance of closest approach (DCA) cut.The tracks extrapolated to the reconstructed vertex should have a DCA in the beam direction DCA L ≤ 2 cm, and in the plane orthogonal to the beam direction DCA T ≤ 0.0182 + 0.0350/p 1.01  T , where p T is the transverse momentum in (GeV/c) [28]; (iii) at least one of the two good tracks selected in criterion (ii) should have p T ≥ 1 GeV/c; this cut reduces the background, while it marginally affects the genuine leptons from J/ψ decays; (iv) The V0 trigger required no signal within a time window of 25 ns around the collision time in any of the scintillator tiles of both V0-A and V0-C.Signals in both V0 detectors were searched offline in a larger window according to the prescription described in [14]; (v) the specific energy loss dE/dx for the two tracks is compatible with that of electrons or muons (     Coherent ψ(2S) photo-production at √ s NN = 2.76 TeV ALICE Collaboration coherent and incoherent events were simulated for each decay channel.The event total transverse momentum reconstruction is obtained adding the p T of the two leptons.The selection of coherent events requires a threshold on the reconstruction of the event total transverse momentum, obtained by adding the p T of the two decay leptons.Transverse momentum carried away by the bremhstralung photons reflects in a broadening of the event total p T .Bremhstralung effects are more important for the di-electron decay and the corresponding p T threshold has to be larger in this case.Consequently a p T cut p T <0. 15 GeV/c for di-muons and p T <0.3 GeV/c for di-electrons: 98 (77)% of the coherent signal is retained for di-muons and di-electrons respectively.Figure 1 (top panel) shows the invariant mass(left) and the p T distribution(right) for these decay channels.The p T distributions clearly show a coherent peak at low p T .No events are found with a transverse momentum exceeding 1.5 GeV/c, as expected for a negligible hadronic contamination, characterized by a much larger event p T .The number of ψ(2S) candidates are obtained by fitting the invariant mass distribution of both channels to an exponential function describing the underlying continuum and to a Crystal Ball function to extract the ψ(2S) signal.The Crystal Ball ψ(2S) resonance mass and width were left free, while the tail parameters (α and n) were fixed to the values obtained by Monte Carlo simulation.The mass (width calculated from the standard deviation) value from the fit is 3.664 ± 0.013 GeV/c 2 (22±9 MeV/c 2 ) in good agreement with the known value of the ψ(2S) mass and compatible with the absolute calibration accuracy of the barrel.The obtained yield (see Table 1) was N yield =(18.4±9.3).
The product of the acceptance and efficiency correction (Acc × ε) ψ(2S) was calculated as the ratio of the number of simulated events that satisfy the conditions i) to vi), to the number of generated events with the ψ(2S) in the rapidity interval −0.9 < y < 0.9.Transverse polarization of the ψ(2S) is expected from helicity conservation for a quasi-real photon.In addition, for the coherent sample, a reconstructed ψ(2S) transverse momentum condition p T < 0.15 GeV/c (p T < 0.3 GeV/c) was required for di-muons (dielectrons) in the final state.The values for the combined acceptance and efficiency are reported in Table 1.
According to STARLIGHT the fraction ( f I ) of incoherent over coherent events in the low p T region is 4.4% for di-muons and 16.6% for di-electrons.Another theoretical model, described in [22], predicts a much higher coherent over incoherent cross section ratio, resulting in a f I prediction 50% smaller.
Taking the average of these two predictions, (3.3±1.1)% for di-muons and (11.1±3.4)% for di-electrons is obtained.The uncertainty was obtained by requiring the used value to agree with the two models within 1σ .The final f I (see Table 1) is the average of the f I for di-electrons and di-muons, weighted with the corresponding acceptance and efficiency (Acc x ε).The remaining background (N back ) was estimated studying the wrong-sign event sample, obtained by applying cuts (i) to (v).For di-muon and di-electron channels no wrong-sign events were found in the invariant mass range considered and therefore N back =0.
The coherent ψ(2S) yield is obtained using the formula giving N coh ψ(2S) =17.5±9.0.The coherent ψ(2S) differential cross section can be written as: where (Acc × ε) ψ(2S) corresponds to the acceptance and efficiency as discussed above.BR(ψ(2S) → l + l − ) is the branching ratio for ψ(2S) decay into leptons [29], ∆y = 1.8 the rapidity bin size, and L int the total integrated luminosity.These values are listed in Table 1.The systematic uncertainty on the yield for the di-lepton channel is obtained by varying the bin size and by replacing the exponential with a polynomial to fit the γγ process.In addition, the Crystal Ball function parameters can be also obtained by fitting a simulated sample made of ψ(2S) and γγ event cocktail and then used to fit the coherentenriched data sample too.By applying the different methods reported above, the maximum difference in Coherent ψ(2S) photo-production at √ s NN = 2.76 TeV ALICE Collaboration the obtained yield is 12%: this value is used as systematic uncertainty on the yield.The STARLIGHT model predicts a dependence of the ψ(2S) cross section on the rapidity, giving a ≈10% variation over the rapidity range −0.9 < y < 0.9.In order to evaluate the systematic uncertainty on the acceptance coming from the generator choice, a flat dependence of dσ ψ(2S) /dy in the interval −0.9 < y < 0.9, as predicted by other models, was used.The relative differences in (Acc × ε) between the input shapes was 1.0 %, and are taken into account in the systematic uncertainty calculation.The systematic uncertainty on the tracking efficiency was estimated by comparing, in data and in Monte Carlo, the ITS (TPC) hit matching efficiency to tracks reconstructed with TPC (ITS) hits only.
The trigger efficiency was measured relying on a data sample collected in a dedicated run triggered by the ZDCs only.Events with a topology having the BUPC conditions, given at the beginning of Section 3, were selected.The resulting trigger efficiency was compared to that obtained by the Monte Carlo simulation, showing an agreement within +4.0% −9.0% .The e/µ separation was obtained by using two methods: a) a sharp cut in the scatter plot of the first lepton dE/dx as a function of the second lepton dE/dx, where all the particles beyond a given threshold are considered as electrons; b) using the average of the electron (muon) dE/dx and considering as electrons (muons) the particles within three sigmas from the Bethe-Block expectation.The difference between the two methods was used as an estimate of the systematic uncertainty, giving ±2%.The systematic uncertainty related to the application of the V0 offline decision (cut iv) on Sec.3.1, was evaluated repeating the analysis with this cut excluded.This results in a more relaxed event selection, increasing the cross section by 6%.The integrated luminosity was measured using a trigger for the most central hadronic Pb-Pb collisions.The cross section for this process was obtained with a van der Meer scan [30], giving a cross section σ = 4.10 +0. 22 −0.13 (syst) b [31].The integrated luminosity for the BUPC trigger sample, corrected for trigger live time, was L int = 22.4 +0.9 −1.2 µb −1 , where the uncertainty is the quadratic sum of the cross section uncertainty quoted above and the trigger dead time uncertainty.An alternative method based on using neutrons detected in the two ZDCs was also used.The ZDC trigger condition required a signal in at least one of the two calorimeters, thus selecting single electromagnetic dissociation as well as hadronic interactions.The cross section for this trigger was also measured with a van der Meer scan [26].The integrated luminosity obtained for the BUPC by this method is consistent with the one quoted above within 2.5%.The sources and the values of the systematic uncertainties are listed in Table 2.As a result in the rapidity interval − 0.9 < y < 0.9 a cross section dσ coh ψ(2S) /dy = 0.76 ± 0.40(stat) +0.12 −0.13 (syst) mb is obtained.

3.2
The ψ(2S)→ π + π − J/ψ, J/ψ→ l + l − (l + l − = e + e − , µ + µ − ) channels The analysis criteria used to select these channels are similar to those described in Sec.3.1, with the requirements on the track quality slightly relaxed to keep the efficiency at an acceptable level.Such a cut softening was allowed by the smaller QED background in four track events, compared to the channels described in Sec.3.1.Selection (ii) is modified so that four good tracks with at least 50 TPC clusters each are required.In addition to cuts i) to vi), the invariant mass of di-muons(di-electrons) was required to match that expected by leptons from J/ψ decay, i.e. 3.0 < M π + π − µ + µ − < 3.2 GeV/c 2 for di-muons (2.6 < M π + π − e + e − < 3.2 GeV/c 2 for di-electrons).
The acceptance and the efficiency were estimated with similar techniques.Due to the coupling to the photon, the ψ(2S)is transversely polarized.According to previous experiments [32], J/ψ and two pions from ψ(2S) decay are in s-wave state and thus the ψ(2S) polarization fully transfers to the J/ψ.When computing the efficiency and acceptance the ψ(2S) is therefore assumed transversely polarized.A coherentenriched sample can be obtained by selecting appropriate regions on invariant mass and p T , tuned by using a Monte Carlo simulation, as described in Sec.GeV/c 2 ) for the ψ(2S)→ π + π − µ + µ − (ψ(2S)→ π + π − e + e − ) channel, 95% (87%) of the signal was retained.The striped area in the invariant mass(left) plots on Fig. 1(central and bottom panels) shows the ψ(2S) candidates satisfying the p T cut for the two channels.To extract the coherent ψ(2S) yield, the contribution from incoherent ψ(2S) was subtracted as shown in Eq.( 1).The background was estimated by looking at events with all the possible combination of wrong-sign tracks.One event was found in the di-muon sample and no events in the di-electron sample.The fraction of the incoherent sample contaminating the coherent sample was estimated as in Sec.3.1, and was found to be 3.4% in the ψ(2S)→ π + π − µ + µ − channel and 13.2% in the ψ(2S)→ π + π − e + e − channel.The systematic uncertainty on the yield was obtained by using an alternative set of cuts.According to the kinematics of the ψ(2S)→ π + π − J/ψ decay channel, pions are characterized by a small transverse momentum (p T <0.4 GeV/c), while the lepton transverse momentum exceeds 1.1 GeV/c.Instead of selecting events where the di-lepton invariant mass is close to that of the J/ψ, events were selected according to the kinematics of the decay products of the ψ(2S).All the other cuts were kept as described in Sec.3.1.Two alternative selections were considered: (i) a sample where both leptons have a transverse momentum larger than 1.1 GeV/c; and (ii) a sample without any decay product with transverse momentum in the range 0.4< p T <1.2 GeV/c.The ψ(2S) yield was unchanged for both these selections while a small change applies to the acceptance and efficiency in the π + π − J/ψ decay, giving a negligible systematic uncertainty.The relative difference in (Acc × ε) between the STARLIGHT rapidity shape and a flat rapidity one was 2.0 % for ψ(2S)→ π + π − J/ψ channel, and is taken into account in the systematic uncertainty calculation.As a result the obtained cross sections in the rapidity interval −0.9 < y < 0.9 are dσ coh ψ(2S) /dy = 0.81 ± 0.22(stat) +0.09 −0.10 (syst) mb for the ψ(2S)→ π + π − J/ψ, J/ψ → µ + µ − channel and dσ coh ψ(2S) /dy = 0.89 ± 0.31(stat) +0.13 −0.12 (syst) mb for the ψ(2S)→ π + π − J/ψ, J/ψ → e + e − channel.

Combining the cross sections
The ψ(2S) coherent production cross sections reported in the Sections 3.1 and 3.2 (Fig. 2) were combined, using the statistical and the uncorrelated systematic uncertainty as a weight.Finally the correlated systematic uncertainty was added.Asymmetric uncertaintys were combined according to the prescriptions given in [33].The average cross section in the rapidity interval −0.9 < y < 0.9 is dσ coh ψ(2S) /dy = 0.83 ± 0.19 stat + syst mb.

Coherent production with nuclear break up or nucleus de-excitation followed by neutron emission
In UPC one or both nuclei may get excited due to the exchange of additional photons.This excitation may lead to break up of the nucleus via emission of one or more neutrons.The neutron emission was measured by using the ZDC detector, for the events studied in the decay channel, ψ(2S) → l + l − π + π − .We found 20 events (71 +9 −11 )% with no neutrons on either side (0n,0n), 8 events (29 +11 −9 )% with at least one neutron on either side (Xn), 7 events (25 +10 −8 )% with no neutron on one side and at least one neutron on the other one (0n Xn) and 1 event (4 +8 −3 )% with at least one neutron on both sides (Xn Xn).Uncertainties on the fraction are obtained assuming a binomial distribution.These fractions are in agreement with predictions by STARLIGHT [12] and RSZ [8], as shown in Table 3.

The ψ(2S) to J/ψ cross section ratio
In order to compare the coherent ψ(2S) cross section to the previously measured J/ψ cross section [14], we report on the ψ(2S)/ J/ψ cross section ratio.Many of the systematic uncertainties of these measurements are correlated and cancel out in the ratio.Since the analysis relies on the same data sample and on the same trigger, the systematic uncertainties for the luminosity evaluation, trigger efficiency, and dead time were considered as fully correlated.Several uncertainties, corresponding to the same quantity, measured at slightly different energies (corresponding to the different masses), are partially Coherent ψ(2S) photo-production at √ s NN =2.76 TeV at −0.9 < y < 0.9 in three different channels.The square represents the systematic uncertainties while the bar represents the statistic uncertainty.The combined cross section uncertainty (shaded area) was obtained using the prescription from reference [33].correlated, while the uncorrelated part is small.Namely, the systematic uncertainties for e/µ separation and the measurement of the neutron number are strongly correlated and hence can be neglected in the ratio.The systematic uncertainties connected to the signal extraction and the branching ratio are considered uncorrelated between the two measurements.The quadratic sum of these sources together with the statistic uncertainty was used to combine different channels in both measurements.For the combination of asymmetric uncertainties the prescription from reference [33] was used.The value of the ratio is (dσ coh ψ(2S) /dy)/(dσ coh J/ψ /dy) = 0.34 +0.08 −0.07 (stat + syst).

Discussion
We have previously measured the coherent photo-production cross section for the J/ψ vector meson at mid and forward rapidities [13,14].The results showed that the measured cross section was in good agreement with models that include a nuclear gluon shadowing consistent with the EPS09 parametrization [9].Models based on the colour dipole model or hadronic interactions of the J/ψ with nuclear matter were disfavoured.The ψ(2S) is similar to the J/ψ in its composition (cc) and mass, but it has a more complicated wave function as a consequence of it being a 2S rather than a 1S state, and has a larger radius.There is a consensus view about the presence of a node in the ψ(2S) wavefunction: few authors pointed out that this node gives a natural explanation of the ψ(2S) smaller cross section compared to the J/ψ one; in addition it was argued that the node may give strong cancellations in the scattering amplitude in γ-nucleus interactions [34,35].
In Pb-Pb collisions the poor knowledge of the ψ(2S)  √ s NN =2.76 TeV at −0.9 < y < 0.9.The uncertainty was obtained using the prescription from reference [33].The theoretical calculations described in the text are also shown.
There are predictions by five different groups for coherent ψ(2S) production in ultra-peripheral Pb-Pb collisions; some of them published several different calculations (see Fig. 3).The model by Adeluyi and Nguyen (AN) is based on a calculation where the ψ(2S) cross section is directly proportional to the gluon distribution squared [18].It is essentially the same model used by Adeluyi and Bertulani [36] to calculate the coherent J/ψ cross section, which was found to be in good agreement with the ALICE data, when coupled to the EPS09 shadowing parametrization.The calculations are done for four different parameterizations of the nuclear gluon distribution: EPS08 [37], EPS09 [9], HKN07 [38], and MSTW08 [39].The last one (MSTW08) corresponds to a scaling of the γ p cross section neglecting any nuclear effects (impulse approximation).It is worth noting they used for the ψ(2S) the same wave function used for the J/ψ.The model by Gay Ducati, Griep, and Machado (GDGM) [19] is based on the colour dipole model and is similar to the model by Goncalves and Machado for coherent J/ψ production [20].The latter calculation could not reproduce the ALICE coherent J/ψ measurement.The new calculation has, however, been tuned to correctly reproduce the ALICE J/ψ result.The model by Lappi and Mantysaari (LM) is based on the colour dipole model [21].Their prediction for the J/ψ was about a factor of two above the cross section measured by ALICE.The current ψ(2S) cross section has been scaled down to compensate for this discrepancy.The model by Guzey and Zhalov (GZ) is based on the leading approximation of perturbative QCD [22].They used different gluon shadowing predictions, using the dynamical leading twist theory or the EPS09 fit.Finally, STARLIGHT uses the Vector Meson Dominance model and a parametrization of the existing HERA data to calculate the ψ(2S) cross section from a Glauber model assuming only hadronic interactions of the ψ(2S) [17].This model does not implement nuclear gluon shadowing.
It is worth noting that removing all nuclear effects in STARLIGHT gives a cross section for J/ψ production almost identical to the Adeluyi-  4: Ratio of the ψ(2S) to J/ψ cross section for pp and γp interactions compared to theoretical predictions.The ALICE ratio measured in Pb-Pb collisions is shown as well.The uncertainty was obtained using the prescription from reference [33].ing all nucleons contributing to the scattering (impulse approximation).Conversely, when applying the same procedure to the ψ(2S) vector meson production, the comparison shows that STARLIGHT cross section is ≃50% smaller with respect to the Adeluyi-Nguyen one.This result may indicate that the γ+p→ψ(2S)+p cross section is parametrized in a different way in the two models, due to the limited experimental data, making it difficult to tune the models.For J/ψ, a wealth of γ + p → J/ψ + p cross section data has been obtained by ZEUS and H1, while the process γ + p → ψ(2S) + p was measured by H1 at four different energies only.This makes it much harder to constrain the theoretical cross section to the experimental data.Since the effect of gluon shadowing decreases the vector meson production cross section, this may explain why the ψ(2S) STARLIGHT cross section is close to the AN-EPS09 model, while it is a factor of two larger for J/ψ.The coherent ψ(2S) photo-production cross section is compared to calculations from twelve different models in Fig. 3. Since a comprehensive model uncertainty is not provided by the model authors, the comparison with the experimental results is quantified by dividing the difference between the value of each model at y = 0 and the experimental result, by the uncertainty of the measurement itself.The present measurement disfavours the EPS08 parametrization when implemented in the AN model and the GDGM models with a strong shadowing.Similarly the models that neglect any nuclear effect are disfavoured at a level between 1.5 and 3 sigmas.The systematic uncertainties on the cross section parametrization and the experimental statistical uncertainties do not allow a preference to be given between the models implementing moderate nuclear gluon shadowing (as AN-EPS09) and those taking into account Glauber nuclear effects only (as STARLIGHT).
Figure 4 shows the ψ(2S) to J/ψ cross section ratio measured in Pb-Pb collisions by ALICE and those obtained in pp collisions by CDF [40], and in pp collisions by LHCb [41].Both STARLIGHT and the GDGM model predict correctly the experimental pp results.The figure also shows the ratio measured  5: Ratio of the ψ(2S) to J/ψ cross section measured by ALICE in Pb-Pb collisions.The uncertainty was obtained using the prescription from reference [33].The predictions from different theoretical models are also shown.by H1 in γp collisions.The H1 result is compatible with the pp measurements, while the ALICE point is 2σ larger than the average of the pp measurements, although still with sizable uncertainties.This difference may indicate that the nuclear effects and/or the gluon shadowing modify the J/ψ and the ψ(2S) production in a different way, since other effects, as the different photon flux, due to the larger ψ(2S) mass, could not explain such a difference.
Figure 5 shows the comparison of the ψ(2S) to J/ψ cross section ratio between measurements and predictions in Pb-Pb UPC.Most models predict a ψ(2S) to J/ψ cross section ratio in Pb-Pb collisions smaller by 2-2.5 σ than the one measured by ALICE.It is worth noting the same models which reproduced correctly the pp ratio, fail in describing the Pb-Pb ratio.It is surprising that the AN model, although it assumes a ψ(2S) wave function identical to the J/ψ one, describes in a satisfactory way this ratio.

Conclusions
We performed the first measurement of the coherent ψ(2S) photo-production cross section in Pb-Pb collisions, obtaining dσ coh ψ(2S) /dy = 0.83±0.19stat + syst mb in the interval −0.9 < y < 0.9.This result disfavours models considering all nucleons contributing to the scattering and those implementing strong shadowing, as EPS08 parametrization.The ratio of the ψ(2S) to J/ψ cross section ratio in the rapidity interval −0.9 < y < 0.9 is 0.34 +0.08 −0.07 (stat + syst).Most of the models underpredict this ratio by 2-2.5 σ .The current models of the ψ(2S) production in ultra-peripheral collisions require further efforts; the data shown in the present analysis may help to improve the understanding of this process and to refine the theory behind the exclusive vector meson photo-production.

Fig. 1 :
Fig. 1: Invariant mass (left) and p T distributions (right) for ultra-peripheral Pb-Pb collisions at √ s NN = 2.76 TeV and −0.9 < y < 0.9 for events satisfying the event selections in Sec.3.The channels ψ(2S)→ l + l − are shown on the top panel (l + l − = e + e − and µ + µ − ), the ψ(2S)→ π + π − µ + µ − channel is shown in the central and the channel ψ(2S)→ π + π − e + e − in the bottom one.The number of event is obtained by the fit (top panel) or by event counting in a selected invariant mass region (central and bottom panel), see text.

Fig. 2 :
Fig.2: Measured differential cross section of ψ(2S) photo-production in Pb-Pb ultra-peripheral collisions at √ s NN =2.76 TeV at −0.9 < y < 0.9 in three different channels.The square represents the

Fig. 3 :
Fig.3: Measured differential cross section of ψ(2S) photo-production in ultra-peripheral Pb-Pb collisions at √ s NN =2.76 TeV at −0.9 < y < 0.9.The uncertainty was obtained using the prescription from Fig.5: Ratio of the ψ(2S) to J/ψ cross section measured by ALICE in Pb-Pb collisions.The uncertainty was obtained using the prescription from reference[33].The predictions from different theoretical models are also shown.

Table 1 :
see below); it is worth noting that the TPC resolution does not allow muon and charged pion discrimination; → µ + µ − π + π − ψ(2S) → e + e − π + π − Summary of the main experimental results and correction parameters used in the cross section evaluation.The bottom line shows the cross section for the three ψ(2S) decay channels.

Table 2 :
Systematic uncertainties per decay channel.
wave function as a function of the transverse quark pair separation d makes it difficult to estimate the nuclear matter effects.