Central exclusive production of J/ψ and ψ(2S) mesons in pp collisions at √s=13 TeV

JHEP10(2018)167 Published for SISSA by Springer Received:June 15, 2018 Accepted:October 5, 2018 Published:October 26, 2018 Central exclusive production of J/ψ and ψ(2S) mesons in pp collisions at √s= 13 TeV The LHCb collaboration E-mail: [email protected] Abstract: Measurements are reported of the central exclusive production of J/ψ and ψ(2S) mesons in pp collisions at a centre-of-mass energy of 13 TeV. Backgrounds are significantly reduced compared to previous measurements made at lower energies through the use of new forward shower counters. The products of the cross-sections and the branching fractions for the decays to dimuons, where both muons are within the pseudorapidity range 2.0< η < 4.5, are measured to be σJ/ψ→µ+µ−= 435 ±18 ±11 ±17 pb σψ(2S)→µ+µ−= 11.1±1.1±0.3±0.4 pb . The first uncertainties are statistical, the second are systematic, and the third are due to the luminosity determination. The cross-sections are also measured differentially for meson rapidities between 2.0 and 4.5. Good agreement is observed with theoretical predictions. Photoproduction cross-sections are derived and compared to previous experiments, and a deviation from a pure power-law extrapolation of lower energy data is observed. Keywords: Charm physics, Forward physics, Hadron-Hadron scattering (experiments), Particle and resonance production, Quarkonium ArXiv ePrint: 1806.04079v2 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP10(2018)167 JHEP10(2018)167 Contents 1 Introduction 1 2 Detector, data samples and triggers 2 3 Event selection 3 3.1 HeRSCheL efficiency of selecting signal events 4 3.2 Purity of signal sample 6 3.3 Selection efficiency 8 4 Cross-section calculation 8 5 Systematic uncertainties 9 6 Results 11 7 Conclusions 14 A Additional material 17 The LHCb collaboration 22 1 Introduction Central exclusive production (CEP) [1] of a vector meson in pp collisions is a diffractive process in which the protons remain intact and the meson is produced through the fusion of a photon and a colourless strongly coupled object, the so-called pomeron. For charmonia production, the cross-section can be predicted in perturbative quantum chromodynamics (QCD) and at the leading order (LO) is proportional to the square of the gluon parton distribution function (PDF), which ensures a steep rise in the photoproduction cross-section with the centre-of-mass energy of the photon-proton system, W. Therefore, measurements of CEP of the J/ψ and ψ(2S) mesons provide not only a test of perturbative QCD but also probe the pomeron, and constrain the gluon PDF. Elastic photoproduction of charmonia has been measured in fixed target experiments [2–4], in electron-proton [5–8], p¯p[9], and proton-lead collisions [10]. The LHCb collaboration has previously measured the CEP of the J/ψ and ψ(2S) mesons in pp collisions at a centre-of-mass energy √s= 7 TeV [11]. In this paper, those results are extended to √s= 13 TeV and charmonia are measured up to W= 2 TeV, the highest energy yet explored. This corresponds to probing the gluon PDF down to a fractional momentum of the proton, described by the Bjorken variable x≈2×10−6, a scale at which saturation effects may become visible [12]. – 1 – JHEP10(2018)167 For diffractive processes, the dependence of the cross-section on the four-momentum transfer squared, t, is exponential with a slope brelated to the transverse size of the interaction region. In Regge theory [13,14], bvaries with Waccording to b=b0+ 4α0log(W/W0), where b0is the slope measured at an energy W0. Measurements at HERA determined α0= 0.164 ±0.041 GeV−2with b0= 4.63+0.07 −0.17 GeV−2for J/ψ photoproduction at W0= 90 GeV [6]. In pp collisions at √s= 7 TeV, LHCb measured b= 5.70±0.11 GeV−2at an average value of W= 750 GeV [11]. According to Regge theory, a value of b≈6.1 GeV−2 is expected for J/ψ production in pp collisions at √s= 13 TeV. In inelastic J/ψ production when proton dissociation occurs, the fall-off with tis more gradual. In contrast, the nonresonant ultraperipheral electromagnetic CEP of dimuons, produced through photon-photon fusion, peaks strongly at low tvalues. Therefore, the tdependence of the cross-section can be used to distinguish and study different production mechanisms. This paper presents measurements of the cross-section for central exclusive production of charmonia with rapidity, y, between 2.0 and 4.5, and follows the methodology of the LHCb analysis at √s= 7 TeV [11]. Exclusive charmonium candidates are selected through their characteristic signature at a hadron collider: a pp interaction devoid of any activity save the charmonium that is reconstructed from its decay to two muons. The addition of new forward shower counters (HeRSCheL) [15] extends the pseudorapidity region in which particles can be vetoed and roughly halves the number of background events compared to the previous measurement. The LHCb detector is outlined in section 2while the data and selection criteria are described in section 3. The cross-section calculation is detailed in section 4and systematic uncertainties are presented in section 5. The cross-section results for pp →pJ/ψp and pp →pψ(2S)pprocesses and derived photoproduction cross-sections for γp →J/ψ p and γp →ψ(2S)pare presented in section 6. Conclusions are given in section 7. 2 Detector, data samples and triggers The LHCb detector [16,17] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV.1Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad (SPD) and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [18]. The pseudorapidity coverage is extended by forward shower counters consisting of five planes of scintillators with three planes at 114, 19.7 and 7.5 m upstream of the interaction point, and two downstream at 20 and 114 m. At each location there are four quadrants 1Natural units with c= 1 are used throughout. – 2 – JHEP10(2018)167 of scintillators, whose information is recorded in every beam crossing by photomultiplier tubes, giving a total of 20 channels in HeRSCheL. These are calibrated using data taken without beams circulating at the end of each LHC fill. The pseudorapidity ranges covered by VELO and HeRSCheL are different. For VELO, the region is −3.5< η < −1.5 and 2< η < 5, and for HeRSCheL, the region is −10 < η < −5 and 5 < η < 10. A data set corresponding to an integrated luminosity of 204 ±8 pb−1in pp collisions at √s= 13 TeV is used in this analysis. The average number of pp interactions per beam crossing, µ, is 1.1, thus in about half of visible interactions there is only a single pp collision and the CEP process is uncontaminated by pile-up. The online event selection is performed by a trigger that consists of two different stages. First, there is a hardware stage, which requires less than 30 deposits in the SPD and at least one muon with a transverse momentum, pT, above 200 MeV. It is followed by a software stage, which applies a full event reconstruction and requires fewer than ten reconstructed tracks, at least one of which is identified as a muon. Simulated signal events are generated using SuperCHIC v2.02 [19], where the J/ψ and ψ(2S) mesons are transversely polarised. The J/ψ meson can also originate from exclusive χcdecays, which are also generated with SuperCHIC, or from ψ(2S) decays, which are handled by PYTHIA [20]. The LPAIR generator [21] is used to generate dimuons produced through the electromagnetic photon-photon fusion process. The interaction of the generated particles with the detector, and the detector response, are implemented using the Geant4 toolkit [22,23] as described in ref. [24]. 3 Event selection The selection of candidate signal events is similar to that used in the previous LHCb analysis [11]. Two reconstructed muons are required in the region 2.0< η < 4.5, with an invariant mass within ±65 MeV of the known J/ψ or ψ(2S) mass [25] and p2 Tof the reconstructed meson below 0.8 GeV2. The mass and p2 Trequirements are both chosen to reject background while ensuring good signal efficiency, the evaluations of which are described in section 3.2 and 3.3. Events with additional VELO tracks or photons with transverse energies above 200 MeV are vetoed. Events with significant deposits in HeRSCheL are removed. The HeRSCheL response is described using a variable χ2 HRC that quantifies the activity above noise, taking account of correlations between the counters. The invariant mass, M, of all candidates without the mass-window requirement applied is shown in figure 1. The data in the nonresonance regions (when 1500 < M < 2700 MeV, 3200 < M < 3500 MeV and 3800 < M < 8000 MeV) are candidates for electromagnetic CEP dimuons produced by photon-photon fusion and constitute an important calibration sample. The p2 Tdistribution of these dimuons with and without the requirement on χ2 HRC is shown in figure 2and is significantly peaked towards low values due to the long-range electromagnetic interaction. The fraction of electromagnetic CEP events in this sample is determined from a fit to the p2 Tdistribution with two components: a signal shape taken from simulated events and an inelastic background modelled with the sum of two exponential functions. – 3 – JHEP10(2018)167 2000 3000 4000 ) [MeV] − µ + µ Mass( 1 10 2 10 3 10 4 10 Candidates per 10 MeV =13 TeV)sLHCb ( Total fit Nonresonant background Figure 1. Invariant mass distribution of dimuon candidates. The J/ψ and ψ(2S) mass windows of the signal regions are indicated by the vertical lines. The power of HeRSCheL to discriminate CEP events can be seen in figure 3, which shows the distributions of χ2 HRC for three classes of low-multiplicity-triggered events. The first class is CEP-enriched dimuons: events in the nonresonant dimuon sample with p2 T<0.01 GeV2, which has a purity of 97% for electromagnetic CEP events. The second class, inelastic-enriched J/ψ , applies the nominal J/ψ selections but requires p2 T>1 GeV2, thus selecting inelastic events with proton dissociation. The third class consists of events with more than four tracks reconstructed. Figure 3shows that CEP-enriched events have lower values of χ2 HRC. To select exclusive J/ψ and ψ(2S) candidates, it is required that log(χ2 HRC)<3.5; this value is chosen in order to minimise the combined statistical and systematic uncertainty on the total cross-sections. After the event selections, there are 14 753 J/ψ signal candidates and 440 ψ(2S) signal candidates remaining. The estimation of the signal efficiency, H, for the requirement log(χ2 HRC)<3.5 is described in section 3.1. Using this, section 3.2 explains how the purity of the signal sample is estimated. The signal efficiency of all selection requirements is detailed in section 3.3. 3.1 HeRSCheL efficiency of selecting signal events The efficiency for the veto on HeRSCheL activity is estimated from data using the nonresonant calibration sample. The fits to the p2 Tdistributions in figure 2give the numbers of electromagnetic CEP events with and without the HeRSCheL veto. The ratio of these gives the efficiency of the veto, which is determined to be H= 0.723 ±0.008. The signal loss includes in particular a contribution from events where there is an additional primary interaction only seen in the HeRSCheL detector, as well as spill-over from previous collisions, electronic noise and calibration effects, as discussed in ref. [15]. This efficiency, measured using the nonresonant sample, is applicable to any CEP process, with the same veto, collected in this data-taking period. – 4 – JHEP10(2018)167 0 0.5 1 1.5 2 ] 2 [GeV) − µ + µ ( 2 T p 10 2 10 3 10 4 10 2 Candidates per 0.04 GeV =13 TeV)sL (HE RSCE LHCb w/o H =13 TeV)sL (HE RSCE LHCb w/ H Total fit Inelastic background Figure 2. Transverse momentum squared for dimuons in the nonresonant region. The upper distributions are without any requirement on HeRSCheL: the lower are with the HeRSCheL veto applied. The total fit includes the electromagnetic CEP signal events as described by the LPAIR generator as well as the inelastic background. 0 5 10 ) HRC 2 χlog( 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Normalised candidates Selected LHCb CEP-enriched dimuons ψ J/Inelastic-enriched More than 4 tracks Figure 3. Distributions, normalised to unit area, of the logarithm of the discriminating variable χ2 HRC that is related to activity in HeRSCheL. The response to three classes of events, as described in the text, is shown. The selection requirement for the analysis is indicated by the red vertical line and the arrow. – 5 – JHEP10(2018)167 3.2 Purity of signal sample Three background sources are considered: nonresonant dimuon production; feed-down of CEP χcJ (1P) or ψ(2S) to J/ψ mesons and other undetected particles; and nonexclusive events where the proton dissociates but the remnants remain undetected. The amount of nonresonant background is determined from the fit shown in figure 1, where the signals are modelled with two Crystal Ball functions [26] and the nonresonant background with the sum of two exponential functions. This background is estimated to contribute a fraction of 0.009 ±0.001 to the J/ψ and 0.161 ±0.018 to the ψ(2S) samples. The ψ(2S) feed-down background in the J/ψ selection is determined using simulated events that have been normalised to have the same yield as the ψ(2S)→µ+µ−signal in data and is estimated to contribute a fraction 0.015±0.001 to the J/ψ samples. The χcJ (1P) feed-down background is determined using a data calibration sample, which contains events that pass the nominal J/ψ selection, except instead of zero photons, it is required that there is exactly one reconstructed photon with a transverse energy above 200 MeV. The numbers of χc0(1P), χc1(1P), and χc2(1P) candidates in this calibration sample are determined from a fit to the invariant mass of the dimuon plus photon system. These are scaled by the ratio of J/ψ to J/ψ +γcandidates in the corresponding simulated χcJ (1P) sample from which it is esimated that a fraction of 0.005 ±0.001 of the J/ψ candidate sample is due to feed-down from χc0(1P) mesons, 0.002 ±0.001 from χc1(1P) mesons, and 0.038 ± 0.002 from χc2(1P) mesons. The total feed-down ratio from ψ(2S) and χcJ (1P) mesons is 0.060±0.002, to be compared to 0.101±0.009 in the previous analysis [11]: the addition of HeRSCheL suppresses events with proton dissociation, which are more numerous in the double-pomeron-exchange process that mediates χcJ (1P) production. The fraction of nonexclusive events due to proton dissociation is determined through the p2 Tdistribution of the J/ψ and the ψ(2S) candidates, after a background subtraction to remove contributions coming from the electromagnetic nonresonant and feed-down backgrounds. The electromagnetic component is shown in figure 2, while the feed-down shape is taken from the J/ψ +γcalibration sample. The background-subtracted p2 Tdistribution consists of two remaining components: signal and proton dissociation background. Since t≈ −p2 T, approximately exponential distributions with different slopes are expected for each. In the previous analysis [11], each was modelled by an exponential function whose slope was a free parameter. The presence of the HeRSCheL detector however now allows these shapes to be determined from data, thus reducing the model dependence of the result. The background subtracted distribution without HeRSCheL veto applied is split into two distributions: SHif log(χ2 HRC)<3.5 (corresponding to the signal selection), and S¯ H otherwise. Since Hand (1 −H) are the respective efficiencies for a CEP event to enter the distributions SHand S¯ H, the distribution, β=S¯ H−((1 −H)/H)SH, by construction has no contribution coming from exclusive events. The distribution for βapproximates to the shape of the proton dissociation in the candidate distribution SH, but is not exactly the same since the efficiency to veto nonexclusive events has a weak dependence on p2 T. Consequently, the proton dissociation in the distribution SHis estimated by scaling the distribution βby f(p2 T)≡SH(p2 T)/β(p2 T). – 6 – JHEP10(2018)167 0 0.5 1 1.5 2 ] 2 [GeV 2 T p ψ J/ 0 500 1000 1500 2000 2500 3000 2 Candidates per 0.04 GeV =13 TeV)sLHCb ( Proton dissociation Feed-down Nonresonant 0 0.5 1 1.5 2 ] 2 [GeV 2 T p (2S) ψ 0 50 100 150 200 250 300 2 Candidates per 0.20 GeV =13 TeV)sLHCb ( Proton dissociation Nonresonant 0 0.5 1 1.5 2 ] 2 [GeV 2 T p ψ J/ 0 500 1000 1500 2000 2500 2 Yield per 0.04 GeV =13 TeV)sLHCb ( Exponential fit 0 0.5 1 1.5 2 ] 2 [GeV 2 T p (2S) ψ 0 50 100 150 200 2 Yield per 0.20 GeV =13 TeV)sLHCb ( Exponential fit Figure 4. Top: transverse momentum squared distribution of (left) J/ψ and (right) ψ(2S) candidates when data is below the HeRSCheL threshold. Bottom: CEP signal for the (left) J/ψ and (right) ψ(2S) selections. The single exponential fit of the signal is shown by the curve superimposed on the data points. The scale factor f(p2 T) is known from data for values of p2 T&0.8 GeV2, since there is little signal in this region as the signal distribution is expected to follow exp(−bsigp2 T) with bsig ≈6 GeV−2. An extrapolation of f(p2 T) is performed to the region p2 T<0.8 GeV2using functions which fit the data well in the region p2 T>0.8 GeV2. The default is an exponential function for the J/ψ analysis and a constant for the ψ(2S) analysis. A linear dependence is used to estimate the systematic uncertainty. The p2 Tcandidate distributions in data with the estimated backgrounds superimposed are shown in the upper row of figure 4. The lower row shows the signal components after subtracting the proton dissociation background. These are fitted with a single exponential function, exp(−bsigp2 T), to test the hypothesis that the signal has this dependence. The J/ψ signal contribution is well described with bsig = 5.93 ±0.08 GeV−2, consistent with extrapolations from previous pp measurements at 7 TeV and from H1 results [5,11]. The corresponding slope, in the ψ(2S) analysis, is bsig = 5.06±0.45 GeV−2. Fits to the derived proton dissociation components show that these are also consistent with a single exponential. In the region 0 < p2 T<0.8 GeV2, 0.175±0.015 of the J/ψ candidate sample is estimated to be due to proton-dissociation events, while for the ψ(2S) sample the contamination is estimated to be 0.11 ±0.06. The uncertainties are statistical, and the correlation between – 7 – JHEP10(2018)167 the HeRSCheL efficiency and the proton-dissociation contamination is taken into account. The current analysis shows an approximate halving of the proton-dissociation background compared to the analysis at √s= 7 TeV, due to the additional HeRSCheL veto. The overall purities are 0.755±0.015 and 0.726±0.061 for the J/ψ and ψ(2S) selections, respectively. 3.3 Selection efficiency The efficiency for selecting signal events is the product of the reconstruction efficiency, rec, and selection efficiency, sel. The reconstruction efficiency is the product of trigger, tracking, muon chamber acceptance and muon identification efficiencies. The acceptance is determined from simulation. The other quantities are determined from simulation and scaled using a data calibration sample. The trigger efficiency is calibrated through the fraction of events where both muons pass the trigger, in a sample collected with the requirement that at least one muon passes the trigger. The muon identification efficiency is calibrated using a sample enriched in J/ψ mesons that has been selected requiring a single identified muon. The tracking efficiency is calibrated using low-multiplicity events where the dimuon hardware was triggered by two objects having an absolute azimuthal angular difference close to π. The efficiency for the selection requirements on the mass and transverse momentum of the J/ψ candidate, and the veto on additional tracks, photon activity, or HeRSCheL activity is obtained from data. The fits to the mass distributions in figure 1determine the fraction of signal inside the mass window and give a signal efficiency of 0.967 ±0.002. No dependence on rapidity is found. The efficiency for the requirement on the meson candidates that p2 T<0.8 GeV2is 0.993 ±0.001 and is determined from the fitted slope to the signal components shown in figure 4as described in the previous section. A small dependence on rapidity yis introduced through the Regge extrapolation of the exponential slope: b=b0+ 4α0log(W/W0), where W2=Mψey√s. The signal efficiency of vetoing events with additional VELO tracks or photons is obtained using the same technique described in section 3.1 to determine the HeRSCheL veto efficiency. When vetoing events with additional VELO tracks, no dependence on rapidity is found in simulation, while a slight dependence is observed for the photon veto, which is due to material effects in the detector whose density varies with rapidity. The shape of the rapidity dependence is taken from simulation and normalised to data. The efficiency of vetoing events with VELO tracks is determined to be 0.969 ±0.004 and of vetoing events with photons is on average 0.983 ±0.003. 4 Cross-section calculation The products of the cross-sections and the branching fractions of the decays to two muons, σψ→µµ, are measured differentially in ten equally spaced bins of J/ψ rapidity and three unequal bins of ψ(2S) rapidity in the range y∈(2.0,4.5). The measurements are limited to the fiducial region where both muons have pseudorapidities between 2.0 and 4.5. – 8 – JHEP10(2018)167 2 3 4 rapidity ψ J/ 0 1 2 3 4 5 6 7 8 9 [nb] p ψ pJ/ → pp dy σd JMRT LO JMRT NLO =13 TeV)sLHCb ( 2 3 4 rapidity(2S) ψ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 [nb] (2S)p ψ p → pp dy σd JMRT LO JMRT NLO =13 TeV)sLHCb ( Figure 5. Differential cross-sections compared to LO and NLO theory JMRT predictions [28,29] for the J/ψ meson (top) and the ψ(2S) meson (bottom). The inner error bar represents the statistical uncertainty; the outer is the total uncertainty. Since the systematic uncertainty for the ψ(2S) meson is negligible with respect to the statistical uncertainty, it is almost not visible in the lower figure. addition of new scintillators in the forward region has resulted in lower backgrounds in pp collisions at a centre-of-mass energy √s= 13 TeV compared to the previous measurement at √s= 7 TeV. As a consequence, the systematic uncertainty on the J/ψ cross-section is reduced from 5.6% at √s= 7 TeV to 2.7% at √s= 13 TeV, reflecting an improved understanding of the background proton-dissociation process. After correcting for the muon acceptance, the cross-sections for the J/ψ and ψ(2S) mesons are compared to theory and found to be in better agreement with the JMRT NLO rather than LO predictions. The derived cross-section for J/ψ photoproduction shows a deviation from a pure powerlaw extrapolation of H1 data, while the ψ(2S) results are consistent although more data are required in this channel to make a critical comparison. – 15 – JHEP10(2018)167 2 10 3 10 W [GeV] 10 2 10 3 10 [nb] p ψ J/ → p γ σ = 13 TeV)sLHCb ( = 7 TeV)sLHCb ( ALICE H1 ZEUS Fixed target exp. Power law fit to H1 data JMRT NLO prediction 2 10 3 10 W [GeV] 1− 10 1 10 2 10 [nb] (2S)p ψ → p γ σ = 13 TeV)sLHCb ( = 7 TeV)sLHCb ( H1 power law scaled by 0.166 ψ J/H1 Figure 6. Compilation of photoproduction cross-sections for various experiments. The upper (lower) plot uses the J/ψ (ψ(2S)) data. Acknowledgments We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.A.). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (U.S.A.). We are indebted to the communities behind the multiple open-source software packages on which we depend. Individual groups – 16 – JHEP10(2018)167 or members have received support from AvH Foundation (Germany), EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union), ANR, Labex P2IO and OCEVU, and R´egion Auvergne-Rhˆone-Alpes (France), Key Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China), RFBR, RSF and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, the Royal Society, the English-Speaking Union and the Leverhulme Trust (United Kingdom). A Additional material 1.00 0.58 0.58 0.57 0.57 0.57 0.56 0.54 0.51 0.40 1.00 0.71 0.71 0.71 0.71 0.70 0.67 0.62 0.49 1.00 0.74 0.74 0.74 0.73 0.69 0.64 0.50 1.00 0.76 0.75 0.74 0.71 0.65 0.50 1.00 0.76 0.74 0.71 0.65 0.50 1.00 0.74 0.71 0.65 0.50 1.00 0.69 0.64 0.49 1.00 0.61 0.46 1.00 0.43 1.00 1.00 0.74 0.88 0.78 0.68 0.69 0.71 0.64 0.77 0.76 1.00 0.91 0.96 0.95 0.95 0.96 0.94 0.96 0.93 1.00 0.94 0.88 0.89 0.91 0.86 0.94 0.92 1.00 0.97 0.97 0.98 0.95 0.98 0.95 1.00 0.99 0.99 0.99 0.97 0.93 1.00 0.99 0.98 0.98 0.94 1.00 0.99 0.99 0.95 1.00 0.97 0.93 1.00 0.96 1.00 Table 5. (Top) Statistical and (bottom) systematic correlation matrices for J/ψ, where each column corresponds to one rapidity bin in increasing order. As the matrix is symmetric, only the top triangle is shown. 1.00 0.55 0.56 1.00 0.52 1.00 1.00 0.95 0.96 1.00 1.00 1.00 Table 6. (Top) Statistical and (bottom) systematic correlation matrices for ψ(2S), where each column corresponds to one rapidity bin in increasing order. As the matrix is symmetric, only the top triangle is shown. – 17 – JHEP10(2018)167 J/ψ y bin 2.0−2.25 2.25−2.5 2.5−2.75 2.75−3.0 3.0−3.25 W+(GeV) 581 658 746 845 958 k+dn/dk+(×10−3) 22.7 21.6 20.4 19.2 18.0 r(W+) 0.786 0.774 0.762 0.748 0.732 W−(GeV) 69.4 61.2 54.0 47.7 42.1 k−dn/dk−(×10−3) 42.5 43.7 44.9 46.0 47.2 r(W−) 0.885 0.888 0.891 0.893 0.896 σγp→J/ψp(W−)(nb) Power law 68.0 62.6 57.6 52.9 48.7 JMRT NLO 65.3 59.5 54.1 49.1 44.5 Calculated: σγp→J/ψp(W+)(nb) Power law 291 335 321 339 358 JMRT NLO 297 343 330 350 371 J/ψ y bin 3.25−3.50 3.50−3.75 3.75−4.0 4.0−4.25 4.25−4.5 W+(GeV) 1085 1230 1394 1579 1790 k+dn/dk+(×10−3) 16.8 15.7 14.5 13.3 12.1 r(W+) 0.715 0.695 0.672 0.647 0.618 W−(GeV) 37.1 32.8 28.9 25.5 22.5 k−dn/dk−(×10−3) 48.3 49.5 50.7 51.8 53.0 r(W−) 0.898 0.901 0.903 0.905 0.907 σγp→J/ψp(W−)(nb) Power law 44.8 41.2 37.9 34.8 32.0 JMRT NLO 40.2 36.3 32.7 29.5 26.4 Calculated: σγp→J/ψp(W+)(nb) Power law 395 403 403 456 524 JMRT NLO 411 423 427 485 560 ψ(2S)ybin 2.0−3.0 3.0−3.5 3.5−4.5 W+(GeV) 772 1115 1634 k+dn/dk+(×10−3) 21.5 18.5 14.4 r(W+) 0.787 0.762 0.677 W−(GeV) 63.4 43.2 29.9 k−dn/dk−(×10−3) 45.3 49.9 52.4 r(W−) 0.911 0.942 0.926 σγp→ψ(2S)p(W−)(nb) Power law 10.6 8.2 6.4 Calculated: σγp→ψ(2S)p(W+)(nb) Power law 64 55 88 Table 7. Values used in evaluating the photo-production cross-section using eq. (6.1) for the J/ψ and ψ(2S) analysis with gap survival factors for the production of J/ψ and ψ(2S) mesons at √s= 13 TeV [31]. For the J/ψ analyis, σγp→J/ψp(W+)is calculated using the power-law description of HERA or the JMRT NLO description for σγp→J/ψp(W−). – 18 – JHEP10(2018)167 J/ψ y bin 2.00−2.25 2.25−2.50 2.50−2.75 2.75−3.00 3.00−3.25 r(W+) 0.766 0.752 0.736 0.718 0.698 r(W−) 0.882 0.885 0.888 0.891 0.894 J/ψ y bin 3.25−3.50 3.50−3.75 3.75−4.00 4.00−4.25 4.25−4.50 r(W+) 0.676 0.650 0.620 0.587 0.550 r(W−) 0.897 0.899 0.902 0.904 0.906 ψ(2S)ybin 2.00−2.25 2.25−2.50 2.50−2.75 2.75−3.00 3.00−3.25 r(W+) 0.757 0.741 0.724 0.705 0.683 r(W−) 0.879 0.882 0.886 0.889 0.892 ψ(2S)ybin 3.25−3.50 3.50−3.75 3.75−4.00 4.00−4.25 4.25−4.50 r(W+) 0.658 0.630 0.598 0.562 0.522 r(W−) 0.895 0.898 0.900 0.903 0.905 Table 8. Gap survival factors for the production of J/ψ and ψ(2S) mesons at √s= 7 TeV. 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Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France 5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France 7LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, Orsay, France 8LPNHE, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, Paris, France 9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany 10 Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany – 24 –