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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4208 Table 1 |The number of events accepted by the sequential selection requirements for data, compared with the number of background and signal events expected from the simulation. Selection

! eCe� CEP gg!

Hadronic fakes Other fakes T otal background Signal Data Preselection 74 4.7 6 19 104 9.1 105 NtrkD 0 4.0 4.5 6 19 33 8.7 39 p

T < 2 GeV 3.5 4.4 3 1.3 12.2 8.5 21 Aco< 0.01 1.3 0.9 0.3 0.1 2.6 7.3 13 Uncertainty 0.3 0.5 0.3 0.1 0.7 1.5 The signal simulation is based on calculations from ref. 28. In addition, the uncertainties on the expected number of events passing all selection requirements are given. give a negligible contribution to the signal region. The contribution from bottomonia production (for example,

!b!

or

Pb!!  b! 3 ) is calculated using parameters from refs 46, 47 and is found to be negligible. The contribution from other fake diphoton events (for example those induced by cosmic-ray muons) is estimated using photons that fail to satisfy the longitudinal shower-shape requirement. The total background due to other fake photons is found to be 0.1 0.1 events. As a further cross-check, additional activity in the muon spectrometer is studied. It is observed that out of 18 events satisfying the inverted p

T requirement, 13 have at least one additional reconstructed muon. In the regionp

T < 2 GeV , no events with muon activity are found, which is compatible with the above- mentioned estimate of 0.1 0.1. The contribution from UPC events where both nuclei emit a bremsstrahlung photon is estimated using calculations from ref. 13 and is found to be negligible for photons with jj< 2.4 and ET> 3 GeV . Results Photon kinematic distributions for events satisfying the selection criteria are shown in Fig. 3. The shape of the diphoton acoplanarity distribution for

! eCe� events in Fig. 3a reflects the trajectories of the electron and positron in the detector magnetic field, before they emit hard photons in their collisions with the ITD material. In total, 13 events are observed in data whereas 7.3 signal events and 2.6 background events are expected. In general, good agreement bet- ween data and MC simulation is observed. The eect of sequential selection requirements on the number of events selected is shown in Table 1, for each of the data, signal and background samples. T o quantify an excess of events over the background expectation, a test statistic based on the profile likelihood ratio 48 is used. The p value for the background-only hypothesis, defined as the probability for the background to fluctuate and give an excess of events as large or larger than that observed in the data, is found to be 5 10�6. The p value can be expressed in terms of Gaussian tail probabilities, which, given in units of standard deviation (  ), corresponds to a significance of 4.4  . The expected p value and significance (obtained before the fit of the signal-plus-background hypothesis to the data and using standard model predictions from ref. 28) are 8 10�5 and 3.8 , respectively. The cross-section for the Pb C Pb (

)! Pb./C Pb./

process is measured in a fiducial phase space defined by the pho- ton transverse energy ET> 3 GeV , photon absolute pseudorapidity jj< 2.4, diphoton invariant mass greater than 6 GeV , diphoton transverse momentum lower than 2 GeV and diphoton acoplanarity below 0.01. Experimentally, the fiducial cross-section is given by fidD Ndata� Nbkg C R Ldt (1) where Ndata is the number of selected events in data, Nbkg is the expected number of background events and R Ldt is the integrated Table 2 | Summary of systematic uncertainties. Source of uncertainty Relative uncertainty Trigger 5% Photon reco. efficiency 12% Photon PID efficiency 16% Photon energy scale 7% Photon energy resolution 11% T otal 24% The table shows the relative systematic uncertainty on detector correction factor C broken into its individual contributions. The total is obtained by adding them in quadrature. luminosity. The factor C is used to correct for the net eect of the trigger eciency, the diphoton reconstruction and PID eciencies, as well as the impact of photon energy and angular resolution. It is defined as the ratio of the number of generated signal events satisfying the selection criteria after particle reconstruction and detector simulation to the number of generated events satisfying the fiducial criteria before reconstruction. The value of C and its total uncertainty is determined to be 0.31  0.07. The dominant systematic uncertainties come from the uncertainties on the photon reconstruction and identification eciencies. Other minor sources of uncertainty are the photon energy scale and resolution uncertain- ties and trigger eciency uncertainty. T o check for a potential model dependence, calculations from ref. 28 are compared with predictions from ref. 20, and a negligible impact on the C-factor uncertainty is found. Table 2 lists the separate contributions to the systematic uncertainty. The uncertainty on the integrated luminosity is 6%. It is derived following a methodology similar to that detailed in refs 49,50, from a calibration of the luminosity scale using xy beam-separation scans performed in December 2015. The measured fiducial cross-section is fidD 70 24 (stat.)17 (syst.) nb, which is in agreement with the predicted values of 45 9 nb (ref. 20) and 49 10 nb (ref. 28) within uncertainties. Conclusion In summary, this article presents evidence for the scattering of LbyL in quasi-real photon interactions from 480 b�1 of ultra-peripheral PbC Pb collisions atpsNND 5.02 T eV by the ATLAS experiment at the LHC. The statistical significance against the background-only hypothesis is found to be 4.4 standard deviations. After background subtraction and analysis corrections, the fiducial cross-section for the PbC Pb (

)! Pb./C Pb./

process was measured and is compatible with standard model predictions. The analysis is mostly limited by the amount of data available and the lower limit on transverse energy for reconstructed photons (ETD 3 GeV), below which more signal is expected. Advancements on these two points would also allow for reconstruction of low-mass mesons decaying into two photons, which in turn could be used to improve detector calibration. The heavy-ion data yield is expected to double at the end of 2018 (and again increase tenfold after 856 © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. NATURE PHYSICS | VOL 13 | SEPTEMBER 2017 | www.nature.com/naturephysics NATURE PHYSICS DOI: 10.1038/NPHYS4208 ARTICLES LHC Run 4, scheduled to start in 2026), which would significantly reduce the statistical uncertainty. Future upgrades of ATLAS, such as extended tracking acceptance fromjj< 2.5 tojj< 4.0, will further improve this. Data availability. The experimental data that support the findings of this study are available in HEPData with the identifier http://dx.doi.org/10.17182/hepdata.77761. Received 9 February 2017; accepted 15 June 2017; published online 14 August 2017 References

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ATLAS Computing Acknowledgements 20162017, ATL-GEN-PUB-2016-002 (2016); https://cds.cern.ch/record/2199109 Acknowledgements W e thank CERN for the very successful operation of the LHC, as well as the support sta from our institutions without whom ATLAS could not be operated eciently. W e acknowledge the support of ANPCyT , Argentina; Y erPhI, Armenia; ARC, Australia; BMWFW and FWF , Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP , Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT , Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF , Georgia; BMBF , HGF and MPG, Germany; GSRT , Greece; RGC, Hong Kong SAR, China; ISF , I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST , Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT , Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZ’, Slovenia; DST/NRF , South Africa; MINECO, Spain; SRC and W allenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST , Taiwan; TAEK, T urkey; STFC, United Kingdom; DOE and NSF , United States of America. In addition, individual groups and members have received support from BCKDF , the Canada Council, CANARIE, CRC, Compute NATURE PHYSICS | VOL 13 | SEPTEMBER 2017 | www.nature.com/naturephysics © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. 857 ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4208 Canada, FQRNT , and the Ontario Innovation Trust, Canada; EPLANET , ERC, ERDF , FP7, Horizon 2020 and Marie Skªodowska-Curie Actions, European Union; Investissements d' Avenir Labex and Idex, ANR, Région Auvergne and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF; BSF , GIF and Minerva, Israel; BRF , Norway; CERCA Programme Generalitat de Catalunya, Generalitat V alenciana, Spain; the Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in ref. 51. Author contributions All authors have contributed to the publication, being variously involved in the design and the construction of the detectors, in writing software, calibrating subsystems, operating the detectors and acquiring data, and finally analysing the processed data. The ATLAS Collaboration members discussed and approved the scientific results. The manuscript was prepared by a subgroup of authors appointed by the collaboration and subject to an internal collaboration-wide review process. All authors reviewed and approved the final version of the manuscript. Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Publisher' s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional aliations. Correspondence and requests for materials should be addressed to ATLAS Collaboration. Competing financial interests The authors declare no competing financial interests. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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