We study two-particle long-range rapidity correlations arising in the early stages of heavy ion collisions in the saturation/Color Glass Condensate framework, assuming for simplicity that one colliding nucleus is much larger than the other. We calculate the two-gluon production cross section while including all-order saturation effects in the heavy nucleus with the lowest-order rescattering in the lighter nucleus. We find four types of correlations in the two-gluon production cross section: (i) geometric correlations, (ii) HBT correlations accompanied by a back-to-back maximum, (iii) away-side correlations, and (iv) near-side azimuthal correlations which are long-range in rapidity. The geometric correlations (i) are due to the fact that nucleons are correlated by simply being confined within the same nucleus and may lead to long-range rapidity correlations for the produced particles without strong azimuthal angle dependence. Somewhat surprisingly, long-range rapidity correlations (iii) and (iv) have exactly the same amplitudes along with azimuthal and rapidity shapes: one centered around ∆φ = π with the other one centered around ∆φ = 0 (here ∆φ is the azimuthal angle between the two produced gluons). We thus observe that the early-time CGC dynamics in nucleus-nucleus collisions generates azimuthal non-flow correlations which are qualitatively different from jet correlations by being long-range in rapidity. If strong enough, they have the potential of mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron correlators: one may need to take them into account in the experimental determination of the flow observables.PACS numbers: 25.75.Gz, 12.38.Bx, 12.38.Cy
I. INTRODUCTIONLong-range rapidity correlations between pairs of hadrons produced at small azimuthal angles with respect to each other were discovered recently in heavy ion (AA) [1-4], proton-proton (pp) [5], and proton-nucleus (pA) collisions [6]. Due to the particular shape of the corresponding correlation function, with a narrow correlation in the azimuthal angle ∆φ and a wide correlation in pseudo-rapidity separation ∆η, these correlations are often referred to as the "ridge".There appears to be a consensus in the community that the origin of these long-range rapidity correlations is in the very early-time dynamics immediately following the collision. A simple causality argument demonstrates that a correlation between two hadrons produced far apart in rapidity may arise only in their common causal past, that is, in the early stages of the collision [7,8]. However, the detailed dynamical origin of these "ridge" correlations is not completely clear.It has been proposed in the literature [7-15] that the "ridge" correlations may arise in the classical gluon field dynamics of the parton saturation physics/Color Glass Condensate (CGC). (For reviews of saturation/CGC physics see [16][17][18][19][20].) Indeed classical gluon fields, which in the McLerran-Venugopalan (MV) model [21][22][23] dominate gluon production in heavy ion collisions,...