Measurements of long-range azimuthal anisotropies and associated Fourier coefficients in $pp$ collisions at $\sqrt{s}=5.02$ and 13 TeV and $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector

Results are presented from ATLAS measurements of two-particle correlations in $\sqrt{s} = 5.02$ and 13 TeV $pp$ collisions and in $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV $p$+Pb collisions at the LHC. The correlation functions are measured as a function of relative azimuthal angle, $\Delta \phi$, and pseudorapidity, $\Delta \eta$, using charged particles detected within the pseudorapidity interval $|\eta|{<}2.5$. Azimuthal modulation in the long-range component of the correlation function, with $|\Delta\eta|{>}2$, is studied using a template fitting procedure to remove a ``back-to-back'' contribution to the correlation function that primarily arises from hard-scattering processes. In addition to the elliptic, $\cos{(2\Delta\phi)}$, modulation observed in a previous measurement, the $pp$ correlation functions exhibit significant $\cos{(3\Delta\phi)}$ and $\cos{(4\Delta\phi)}$ modulation. The Fourier coefficients, $v_{n,n}$, associated with the $\cos{(n\Delta\phi)}$ modulation of the correlation functions for $n =$ 2--4 are measured as a function of charged-particle multiplicity, $N_{\mathrm{ch}}^{\mathrm{rec}}$, and charged particle transverse momentum, $p_{\mathrm{T}}$. The Fourier coefficients are observed to be compatible with $\cos{(n\phi)}$ modulation of per-event single-particle azimuthal angle distributions. The single particle Fourier coefficients, $v_n$, are measured as a function of charged particle multiplicity, $N_{\mathrm{ch}}^{\mathrm{rec}}$, and charged particle transverse momentum, $p_{\mathrm{T}}$ for $n {=} $ 2--4.