Viscosity and the soft ridge at RHIC

Abstract

Abstract. Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.Jet correlation measurements display a ridge of enhanced particle emission that is broad in pseudorapidity η and narrow in azimuthal angle φ [1]. Many have attributed this 'hard ridge' to the passage of the jet through the high-density environment produced by the nuclear collision; see e.g. [2]. Interestingly, a similar ridge feature is exhibited in untriggered correlation studies where no jet tag is present [3]. As with the hard ridge, the width of the untagged 'soft ridge' broadens in η and narrows in φ for collisions of higher centrality (smaller impact parameter).We ask whether the (η, φ) dependence of the soft ridge in untagged correlations can be a consequence of radial flow and viscous diffusion. The connection between radial flow and momentum correlations has been stressed elsewhere [4,5,6]. In ref. [7] we attributed the rapidity broadening of untriggered momentum correlations to viscous diffusion, extracting an estimate of the viscosity-to-entropy ratio in the range from 0.08 to 0.32. In this paper we show that viscous diffusion together with flow can explain the centrality dependence of the soft ridge; see fig. 1 (right).The soft ridge has been observed both in momentum fluctuation studies [8] and multiplicity correlation measurements [9]. Here, we focus on the momentum correlation results, which we argue depend strongly on the viscosity of the high density liquid produced in collisions. Our hope is to eventually reduce the rather large uncertainty in the viscosity estimate in [7] by using the full landscape of η − φ correlations, rather than just the η dependence. In this paper, we first recall the role of shear viscosity in the evolution of momentum fluctuations. We survey the hydrodynamic formulation of [7], extending it to include transverse flow. We then confront the soft ridge.Central nuclear collisions produce a fluid that flows outward with an average transverse velocity v ⊥ . In the hydrodynamic description of these collisions, we typically assume that v ⊥ varies smoothly with spacetime (t, x) and is the same for all collisions of a fixed impact parameter. More realistically, small deviations relative to v ⊥ occur throughout the fluid, varying with each collision event. Such deviations occur, e.g., because the number and location of nucleon-nucleon subcollisions varies in each event.Viscous friction arises as neighboring elements of the fluid flow past one another. This friction drives the stress-energy tensor toward the local average T 0r = γ 2 ( +p)v ⊥ , arXiv:0806.4366v1 [nucl-th]

Momentum kick model description of the near-side ridge and jet quenching

“…Similar ∆φ-∆η correlations associated with a near-side jet have also been observed by the PHENIX Collaboration [16,17] and the PHOBOS Collaboration [18]. While many theoretical models [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] have been proposed to discuss the jet structure and related phenomena, the ridge phenomenon has not yet been fully understood.…”

Methods for the study of transverse momentum differential correlations

“…Additionally, one can also use the measureC, defined in Sect. 2, to study the transverse momentum correlations [3,11,12]. We argue that a differential version of all the observables, as defined in the previous section, may provide an equivalent or even better way to estimate the medium viscosity.…”

“…Gavin suggested recently [12] that the width of transverse momentum fluctuation distributions measured as a function of pseudorapidity may be used to estimate the viscosity of the matter formed in A + A collisions studied at RHIC and LHC.…”

“…Extensions of fluctuation variables Φ pt [9] and σ pt [10] are also possible. In this work, we study three differential observables namely, inclusive and event-wise correlation functions and a differential version of the measureC, used by Gavin [11,12] to estimate the viscosity per unit entropy of the matter formed in A + A collisions. The observable definitions and notation used in this work are presented in Sect.…”

High energy factorization in nucleus-nucleus collisions. III. Long range rapidity correlations

“…Further, the LO Glasma fields have the spatial structure of flux tubes stretching between the two nuclei, each localized transversely in a region of size 1/Q s . This geometrical picture naturally explains the rapidity correlations observed in the near side ridge in heavy ion collisions [11,12]. However, the boost invariance of the Glasma configurations at LO is broken by quantum effects and it is important to understand their impact on multiparticle correlations.…”