Long range correlations and the soft ridge in relativistic nuclear collisions

Abstract

Relativistic Heavy Ion Collider experiments exhibit correlations peaked in relative azimuthal angle and extended in rapidity. Called the ridge, this peak occurs both with and without a jet trigger. We argue that the untriggered ridge arises when particles formed by flux tubes in an early Glasma stage later manifest transverse flow. Combining a blast wave model of flow fixed by single-particle spectra with a simple description of the Glasma, we find excellent agreement with current data. Correlation measurements of high transverse momentum particles provided the first striking experimental evidence of jet quenching. Further studies of the correlation of high p t particles with more typical particles reveal a complex pattern of correlations as a function of relative pseudorapidity η = η 1 − η 2 and azimuthal angle φ = φ 1 − φ 2 . In particular, a "hard ridge" of enhanced correlation is observed near η = φ = 0 that is narrow in φ and broad in η [1]. Interestingly, the STAR collaboration reports a similar ridge in correlations of particles of any p t , i.e., without a jet trigger [2,3,4]. As with the hard ridge, the width of the untriggered soft ridge is broad in η and narrow in φ. Preliminary PHOBOS data suggests that the hard ridge and possibly the soft ridge may extend over the broad range −4 < η < 2 [5].We argue that the soft ridge is a consequence of earlystage rapidity correlations in concert with late-stage transverse flow. Correlations over several rapidity units can only originate at the earliest stages of an ion collision when the first partons are produced [6]. Hydrodynamics and other later-stage effects can modify these correlations, but are limited to a horizon of ∼ 1−2 rapidity units. Analogous to super-horizon fluctuations in the cosmos, these long range correlations can therefore reveal the 'little bang' in each nuclear collision at its birth.Almost instantaneously after a collision of two nuclei, Color Glass Condensate (CGC) theory predicts that the transverse fields of each nucleus are transformed into longitudinal fields that are approximately uniform in rapidity [7,8]. The fields, which are random over transverse distances larger than Q −1 s where Q s ∼ 1 − 2 GeV is the saturation scale, comprise a series of flux tubes. Long range rapidity correlations arise because particles from the same flux tube start at nearly the same transverse position, regardless of rapidity.Pressure builds as the flux tubes fragment to form particles. The resulting transverse flow modifies these long range correlations by focusing particles into a narrow region in φ. Suppose that the transverse fluid velocity has the Hubble-like form γ t v t = λr t . A fluid cell a distance r t from the center of the collision volume will then have a mean speed v t . When this cell freezes out, it releases particles into an opening angle φ ∼ v th /v t ∝ (λr t ) −1 , for a thermal velocity v th ∼ 1. This modifies the correlations, since particles near the center of the collision volume have a large opening angle, while those from a large...

Challenging claims of nonjet “higher harmonic” components in 2D angular correlations from high-energy heavy-ion collisions

“…The various harmonic flows were attributed to fluctuations in the initial-state A-A geometry coupled to radial expansion of the bulk medium [12,13]. In an alternative scheme the elongated SS 2D peak was explained in terms of glasma flux tubes coupled to radial flow [14,15].…”

On multiplicity correlations in the STAR data

“…It has been indicated that the "hydrodynamical" type models with fluctuations in the initial volume and/or saturation effects may be relevant for the correlations discussed here [11][12][13]. Such models may also relate these correlations to the famous "ridge" effect [14,15]. However, collective effects are absent in PYTHIA and in our naïve model.…”

“…This will not change if we average the numerator and denominator in (14) separately. We see that this simplified model disagrees strongly with the pp data: the values of are always negative, whereas in the data they are positive.…”

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.…”

“…Furthermore, both J z and α 3 commute with the operator acting on ψ(r, φ, z, t) in Eq. (35). Upon using the representation in Ref.…”