ARTICLES PUBLISHED ONLINE: 14 AUGUST 2017 | DOI: 10.1038/NPHYS4208 Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC ATLAS Collaboration† Light-by-light scattering (γ γ →γ γ ) is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. This reaction is accessible at the Large Hadron Collider thanks to the large electromagnetic field strengths generated by ultra-relativistic colliding lead ions. Using 480 µb−1 of lead–lead collision data recorded at a centre-of-mass energy per nucleon pair of 5.02 TeV by the ATLAS detector, here we report evidence for light-by-light scattering. A total of 13 candidate events were observed with an expected background of 2.6 ± 0.7 events. After background subtraction and analysis corrections, the fiducial cross-section of the process Pb + Pb (γ γ ) →Pb(∗)+ Pb(∗)γ γ , for photon transverse energy ET >3 GeV, photon absolute pseudorapidity |η|<2.4, diphoton invariant mass greater than 6 GeV, diphoton transverse momentum lower than 2 GeV and diphoton acoplanarity below 0.01, is measured to be 70 ± 24 (stat.) ±17 (syst.) nb, which is in agreement with the standard model predictions. O ne of the key features of Maxwell’s equations is their linearity in both the sources and the fields, from which follows the superposition principle. This forbids effects such as light-by-light (LbyL) scattering, γ γ →γ γ , which is a purely quantum-mechanical process. It was realized in the early history of quantum electrodynamics (QED) that LbyL scattering is related to the polarization of the vacuum1. In the standard model of particle physics, the virtual particles that mediate the LbyL coupling are electrically charged fermions or W ± bosons. In QED, the γ γ →γ γ reaction proceeds at lowest order in the fine-structure constant (αem) via virtual one-loop box diagrams involving fermions (Fig. 1a), which is an O(α4 em ≈3×109) process, making it challenging to test experimentally. Indeed, the elastic LbyL scattering has remained unobserved: even the ultra-intense laser experiments are not yet powerful enough to probe this phenomenon2. LbyL scattering via an electron loop has been precisely, albeit indirectly, tested in measurements of the anomalous magnetic moment of the electron and muon3,4 where it is predicted to contribute substantially, as one of the QED corrections5. The γ γ →γ γ reaction has been measured in photon scattering in the Coulomb field of a nucleus (Delbrück scattering) at fixed photon energies below 7 GeV (refs 6–9). The analogous process, where a photon splits into two photons by interaction with external fields (photon splitting), has been observed in the energy region of 0.1–0.5 GeV (ref. 10). A related process involving only real photons, in which several photons fuse to form an electron–positron pair (e+e−), has been measured in ref. 11. Similarly, the multiphoton Compton scattering, in which up to four laser photons interact with an electron, has been observed12. An alternative way by which LbyL interactions can be studied is by using relativistic heavy-ion collisions. In ‘ultra-peripheral collision’ (UPC) events, with impact parameters larger than twice the radius of the nuclei13,14, the strong interaction does not play a role. The electromagnetic (EM) field strengths of relativistic ions scale with the proton number (Z). For example, for a lead (Pb) nucleus with Z = 82 the field can be up to 1025 V m−1 (ref. 15), much larger than the Schwinger limit16 above which QED corrections become important. In the 1930s it was found that highly relativistic charged particles can be described by the equivalent photon approximation (EPA)17–19, which is schematically shown in Fig. 1b. The EM fields produced by the colliding Pb nuclei can be treated as a beam of quasi-real photons with a small virtuality of Q2 < 1/R2, where R is the radius of the charge distribution and so Q2 < 10−3 GeV2. Then, the cross-section for the reaction Pb + Pb (γ γ ) →Pb + Pb γ γ can be calculated by convolving the respective photon flux with the elementary cross-section for the process γ γ →γ γ . Since the photon flux associated with each nucleus scales as Z 2, the cross-section is extremely enhanced as compared with proton–proton (pp) collisions. In this article, a measurement of LbyL scattering in Pb + Pb collisions at the Large Hadron Collider (LHC) is reported, following the approach recently proposed in ref. 20. The final-state signature of interest is the exclusive production of two photons, Pb + Pb (γ γ ) →Pb(∗)+ Pb(∗)γ γ , where a possible EM excitation of the outgoing ions21 is denoted by (∗). Hence, the expected signature is two photons and no further activity in the central detector, since the Pb(∗) ions escape into the LHC beam pipe. Moreover, it is predicted that the background is relatively low in heavy-ion collisions and is dominated by exclusive dielectron (γ γ →e+e−) production20,22. The misidentification of electrons as photons can occur when the electron track is not reconstructed or the electron emits a hard- bremsstrahlung photon. The fiducial cross-section of the process γ γ →γ γ in Pb + Pb collisions is measured, using a data set recorded at a nucleon–nucleon centre-of-mass energy (√sNN) of 5.02 TeV. This data set was recorded with the ATLAS detector at the LHC in 2015 and corresponds to an integrated luminosity of 480 ± 30 µb−1. In addition to the measured fiducial cross-section, the significance of the observed number of signal candidate events is given, assuming the background-only hypothesis. Experimental set-up ATLAS is a cylindrical particle detector composed of several sub- detectors23. ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z axis along the beam pipe. The x axis points from the interaction point to the centre of the LHC ring, and the y © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. †A full list of authors and affiliations appears at the end of the paper. 852 NATURE PHYSICS | VOL 13 | SEPTEMBER 2017 | www.nature.com/naturephysics

NATURE PHYSICS DOI: 10.1038/NPHYS4208 ARTICLES

X X X Pb82+ Pb82+ X v ≈ c v ≈ −c EM fields EM fields Pb Pb a b Figure 1 | Diagrams illustrating the QED LbyL interaction processes and the equivalent photon approximation. a, Diagrams for Delbrück scattering (left), photon splitting (middle) and elastic LbyL scattering (right). Each cross denotes external field legs, for example, an atomic Coulomb field or a strong background magnetic field. b, Illustration of an ultra-peripheral collision of two lead ions. Electromagnetic interaction between the ions can be described as an exchange of photons that can couple to form a given final state X. The flux of photons is determined from the Fourier transform of the electromagnetic field of the ion, taking into account the nuclear electromagnetic form factors. axis points upwards. Cylindrical coordinates (r,φ) are used in the transverse plane, with φ being the azimuthal angle around the z axis. The pseudorapidity is defined in terms of the polar angle θ as η=−ln tan(θ/2). Angular distance is measured in units of 1R≡√(1η)2 +(1φ)2. The photon or electron transverse energy is ET =E sin(θ), where E is its energy. The inner tracking detector (ITD) consists of a silicon pixel system, a silicon microstrip detector and a straw-tube tracker immersed in a 2T magnetic field provided by a superconducting solenoid. The ITD track reconstruction efficiency is estimated in ref. 24 for minimum-bias pp events that, like UPC Pb + Pb events, have a low average track multiplicity. For charged hadrons in the transverse momentum range 100 < pT < 200 MeV the efficiency is about 50% and grows to 80% for pT > 200 MeV. Around the tracker there is a system of EM and hadronic calorimeters, which use liquid argon and lead, copper or tungsten absorbers for the EM and forward (|η| > 1.7) hadronic components of the detector, and scintillator-tile active material and steel absorbers for the central (|η| < 1.7) hadronic component. The muon spectrometer consists of separate trigger and high-precision tracking chambers measuring the trajectory of muons in a magnetic field generated by superconducting air-core toroids. The ATLAS minimum-bias trigger scintillators (MBTSs) consist of scintillator slabs positioned between the ITD and the endcap calorimeters with each side having an outer ring of four slabs segmented in azimuthal angle, covering 2.07<|η|<2.76 and an inner ring of eight slabs, covering 2.76<|η|<3.86. The ATLAS zero-degree calorimeters (ZDCs), located along the beam axis at 140 m from the interaction point on both sides, detect neutral particles (including neutrons emitted from the nucleus). The ATLAS trigger system25 consists of a Level-1 trigger implemented using a combination of dedicated electronics and programmable logic, and a software-based high-level trigger. Monte Carlo simulation and theoretical predictions Several Monte Carlo (MC) samples are produced to estimate background contributions and corrections to the fiducial measurement. The detector response is modelled using a simulation based on GEANT4 (refs 26,27). The data and MC simulated events are passed through the same reconstruction and analysis procedures. LbyL signal events are generated taking into account box diagrams with charged leptons and quarks in the loops, as detailed in ref. 28. The contributions from W-boson loops are omitted in the calculations since they are mostly important for diphoton masses mγ γ >2mW (ref. 29). The calculations are then convolved with the Pb + Pb EPA spectrum from the STARlight 1.1 MC generator30. Next, various diphoton kinematic distributions are cross-checked with predictions from ref. 20 and good agreement is found. The theoretical uncertainty on the cross-section is mainly due to limited knowledge of the nuclear electromagnetic form factors and the related initial photon fluxes. This is studied in ref. 20 and the relevant uncertainty is conservatively estimated to be 20%. Higher-order corrections (not included in the calculations) are also part of the theoretical uncertainty and are of the order of a few per cent for diphoton invariant masses below 100 GeV (refs 31,32). The sources of background considered in this analysis are: γ γ →e+e−, central exclusive production (CEP) of photon pairs, exclusive production of quark–antiquark pairs (γ γ →q¯q) and other backgrounds that could mimic the diphoton event signatures. The γ γ →e+e−background is modelled with STARlight 1.1 (ref. 30), in which the cross-section is computed by combining the Pb + Pb EPA with the leading-order formula for γ γ →e+e−. This process has been recently measured by the ALICE Collaboration, and a good agreement with STARlight is found33. The exclusive diphoton final state can be also produced via the strong interaction through a quark loop in the exchange of two gluons in a colour-singlet state (see Supplementary Fig. 2). This CEP process, gg →γ γ , is modelled using SUPERCHIC 2.03 (ref. 34), in which the pp cross- section has been scaled by A2R4 g as suggested in ref. 20, where A = 208 and Rg ≈0.7 is a gluon shadowing correction35. This process has a large theoretical uncertainty, of O (100%), mostly related to incomplete knowledge of gluon densities36. The γ γ →q¯q contribution is estimated using Herwig++ 2.7.1 (ref. 37) where the EPA formalism in pp collisions is implemented. The γ γ →q¯q sample is then normalized to the corresponding cross-section in Pb + Pb collisions30. Event selection Candidate diphoton events were recorded in the Pb + Pb run in 2015 using a dedicated trigger for events with moderate activity in the calorimeter but little additional activity in the entire detector. At Level-1 the total ET registered in the calorimeter after noise suppression was required to be between 5 and 200 GeV. Then at the high-level trigger, events were rejected if more than one hit was found in the inner ring of the MBTS (MBTS veto) or if more than ten hits were found in the pixel detector. The efficiency of the Level-1 trigger is estimated with γ γ →e+e− events passing an independent supporting trigger. This trigger is designed to select events with mutual dissociation of Pb nuclei and small activity in the ITD. It is based on a coincidence of signals in both ZDC sides and a requirement on the total ET in the calorimeter below 50 GeV. Event candidates are required to have only two reconstructed tracks and two EM energy clusters. Furthermore, to reduce possible backgrounds, each pair of clusters (cl1, cl2) is required to have a small acoplanarity (1 −1φcl1,cl2/π < 0.2). The extracted Level-1 trigger efficiency is provided as a function of the NATURE PHYSICS | VOL 13 | SEPTEMBER 2017 | www.nature.com/naturephysics © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. 853