The ATLAS CollaborationThis letter describes the observation of the light-by-light scattering process, γγ → γγ, in Pb+Pb collisions at √ s NN = 5.02 TeV. The analysis is conducted using a data sample corresponding to an integrated luminosity of 1.73 nb −1 , collected in November 2018 by the ATLAS experiment at the LHC. Light-by-light scattering candidates are selected in events with two photons produced exclusively, each with transverse energy E γ T > 3 GeV and pseudorapidity |η γ | < 2.4, diphoton invariant mass above 6 GeV, and small diphoton transverse momentum and acoplanarity. After applying all selection criteria, 59 candidate events are observed for a background expectation of 12 ± 3 events. The observed excess of events over the expected background has a significance of 8.2 standard deviations. The measured fiducial cross section is 78 ± 13 (stat.) ± 7 (syst.) ± 3 (lumi.) nb.Light-by-light scattering, γγ → γγ, is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics [1, 2]. In the Standard Model (SM), the γγ → γγ reaction proceeds at one-loop level at order α 4 (where α is the fine-structure constant) via virtual box diagrams involving electrically charged fermions (leptons and quarks) or W ± bosons. However, in various extensions of the SM, extra contributions are possible, making the measurement of γγ → γγ scattering sensitive to new physics. Relevant examples are magnetic monopoles [3], vector-like fermions [4] and axion-like particles [5,6]. The light-by-light cross section is also sensitive to the effect of possible non-SM operators in an effective field theory [7][8][9]. Light-by-light scattering graphs with electron loops also contribute to the anomalous magnetic moment of the electron and muon [10,11].Strong evidence for this process in relativistic heavy-ion (Pb+Pb) collisions at the Large Hadron Collider (LHC) has been reported by the ATLAS [12] and CMS [13] collaborations with observed significances of 4.4 and 4.1 standard deviations, respectively. Exclusive light-by-light scattering can occur in these collisions at impact parameters larger than about twice the radius of the ions, as demonstrated for the first time in Ref. [14]. The strong interaction becomes less significant and the electromagnetic (EM) interaction becomes more important in these ultraperipheral collision (UPC) events. In general, this allows to study processes involving nuclear photoexcitation, photoproduction of hadrons, and two-photon interactions [15,16]. The EM fields produced by the colliding Pb nuclei can be described as a beam of quasi-real photons with a small virtuality of Q 2 < 1/R 2 , where R is the radius of the charge distribution and so Q 2 < 10 −3 GeV 2 [17, 18]. The cross section for the elastic reaction Pb+Pb (γγ) → Pb+Pb γγ can then be calculated by convolving the appropriate photon flux with the elementary cross section for the process γγ → γγ. Since the photon flux associated with each nucleus scales with the square of the number of protons, the cross section is strongl...

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (r δr δ L > 0.5 for k 1 h/Mpc) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping initiatives.

This paper presents measurements of W AE Z production in pp collisions at a center-of-mass energy of 8 TeV. The gauge bosons are reconstructed using their leptonic decay modes into electrons and muons. The data were collected in 2012 by the ATLAS experiment at the Large Hadron Collider and correspond to an integrated luminosity of 20.3 fb −1 . The measured inclusive cross section in the detector fiducial region is σ W AE Z→l 0 νll ¼ 35.1 AE 0.9ðstatÞ AE 0.8ðsysÞ AE 0.8ðlumiÞ fb, for one leptonic decay channel. In comparison, the next-to-leading-order Standard Model expectation is 30.0 AE 2.1 fb. Cross sections for W þ Z and W − Z production and their ratio are presented as well as differential cross sections for several kinematic observables. Limits on anomalous triple gauge boson couplings are derived from the transverse mass spectrum of the W AE Z system. From the analysis of events with a W and a Z boson associated with two or more forward jets an upper limit at 95% confidence level on the W AE Z scattering cross section of 0.63 fb, for each leptonic decay channel, is established, while the Standard Model prediction at next-to-leading order is 0.13 AE 0.01 fb. Limits on anomalous quartic gauge boson couplings are also extracted.