ATLAS has measured two-particle correlations as a function of the relative azimuthal angle, Δϕ, and pseudorapidity, Δη, in ffiffi ffi s p ¼ 13 and 2.76 TeV pp collisions at the LHC using charged particles measured in the pseudorapidity interval jηj < 2.5. The correlation functions evaluated in different intervals of measured charged-particle multiplicity show a multiplicity-dependent enhancement at Δϕ ∼ 0 that extends over a wide range of Δη, which has been referred to as the "ridge." Per-trigger-particle yields, YðΔϕÞ, are measured over 2 < jΔηj < 5. For both collision energies, the YðΔϕÞ distribution in all multiplicity intervals is found to be consistent with a linear combination of the per-trigger-particle yields measured in collisions with less than 20 reconstructed tracks, and a constant combinatoric contribution modulated by cos ð2ΔϕÞ. The fitted Fourier coefficient, v 2;2 , exhibits factorization, suggesting that the ridge results from per-event cos ð2ϕÞ modulation of the single-particle distribution with Fourier coefficients v 2 . The v 2 values are presented as a function of multiplicity and transverse momentum. They are found to be approximately constant as a function of multiplicity and to have a p T dependence similar to that measured in p þ Pb and Pb þ Pb collisions. The v 2 values in the 13 and 2.76 TeV data are consistent within uncertainties. These results suggest that the ridge in pp collisions arises from the same or similar underlying physics as observed in p þ Pb collisions, and that the dynamics responsible for the ridge has no strong ffiffi ffi s p dependence. DOI: 10.1103/PhysRevLett.116.172301 Measurements of two-particle angular correlations in high-multiplicity proton-proton (pp) collisions at a centerof-mass energy ffiffi ffi s p ¼ 7 TeV at the LHC showed an enhancement in the production of pairs at small azimuthal-angle separation, Δϕ, that extends over a wide range of pseudorapidity differences, Δη, and which is often referred to as the "ridge" [1]. The ridge has also been observed in proton-lead (p þ Pb) collisions [2][3][4][5][6][7], where it is found to result from a global sinusoidal modulation of the per-event single-particle azimuthal angle distributions [3][4][5][6] TeV data recorded during LHC run 2 and run 1, respectively, to address these issues. The maximum number of inelastic interactions per crossing was 0.04 and 0.5 for the 13 and 2.76 TeV data, respectively. Two-particle angular correlations are measured as a function of Δη and Δϕ in different intervals of the measured charged-particle multiplicity and different p T intervals spanning 0.3 < p T < 5 GeV: 0.3-0.5 GeV, 0.5-1 GeV, 1-2 GeV, 2-3 GeV, 3-5 GeV. Separate p T -integrated results use 0.5 < p T < 5 GeV. Per-trigger-particle yields are obtained from the long-range (jΔηj > 2) component of the correlation. A new template-fitting method is applied to these yields to test for sinusoidal modulation similar to that observed in p þ Pb collisions. The measurements were performed using the ATLAS inner detector (ID), min...