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Correlations in azimuthal angle extending over a long range in pseudorapiditybetween particles, usually called the "ridge" phenomenon, were discovered inheavy-ion collisions, and later found in pp and p$-$Pb collisions. In largesystems, they are thought to arise from the expansion (collective flow) of theproduced particles. Extending these measurements over a wider range inpseudorapidity and final-state particle multiplicity is important to understandbetter the origin of these long-range correlations in small-collision systems.In this Letter, measurements of the long-range correlations in p$-$Pbcollisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV are extended to a pseudorapiditygap of $\Delta\eta \sim 8$ between particles using the ALICE, forwardmultiplicity detectors. After suppressing non-flow correlations, e.g., from jetand resonance decays, the ridge structure is observed to persist up to a verylarge gap of $\Delta\eta \sim 8$ for the first time in p$-$Pb collisions. Thisshows that the collective flow-like correlations extend over an extensivepseudorapidity range also in small-collision systems such as p$-$Pb collisions.The pseudorapidity dependence of the second-order anisotropic flow coefficient,v2({\eta}), is extracted from the long-range correlations. The $v_{2}(\eta)$results are presented for a wide pseudorapidity range of $-3.1 < \eta < 4.8$ invarious centrality classes in p$-$Pb collisions. To gain a comprehensiveunderstanding of the source of anisotropic flow in small-collision systems, the$v_{2}(\eta)$ measurements are compared to hydrodynamic and transport modelcalculations. The comparison suggests that the final-state interactions play adominant role in developing the anisotropic flow in small-collision systems.

Measurements of long-range two-particle correlation over a wide pseudorapidity range in p$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.0$ TeV