A New Angle on the Ridge

The discovery of the “ridge” by the STAR Collaboration has proven stubbornly resistant to quantitative theoretical analysis. (See Berndt Mueller’s “Theorists Confront the Ridge” for a description of two recent attempts.) The discovery turns out to be nearly as resistant to historical analysis, at least for this outside observer.

To begin, the ridge is a structure on the “near”-side in various pair-correlation functions that remains after removal of the known correlation-inducing effects such as elliptic flow and “ordinary” jet correlations. It is termed the ridge because of its elongated shape in the pseudo-rapidity difference Δη ≡ η1 – η2 , where η1 and η2 are the pseudo-rapidities of the two particles in the pair analysis:

To the best of my knowledge, this feature was first shown in Kai Schweda’s talk at Quark Matter 2004, although I can no longer recall if he referred to it as “the ridge”. The first(?) STAR publication of such data

does not describe the ridge as such. Nor would the uninitiated be likely to puzzle this out from the “two-particle charge independent joint autocorrelation functions of correlated pairs per final state particle” considered there. What is important is that this study is an untriggered analysis – the illusion of a trigger particle near Δη=Δφ=0 is an artifact from conversions and (perhaps) HBT correlations. This is also true of the second STAR publication on this topic,

which does indeed mention the word “ridge”, but only in conjunction with the away-side structure, that is, not in the current context of the word (and the phenomena). These publications emphasize that the effect is present in minimum bias data, and attribute it to correlations induced by minijet production.

It would appear that the coming-out party for ridge phenomena associated with triggered events was Manuel Calderón’s talk at Quark Matter 2006 (see also pointers in that talk to those of Jörn Putschke and Jana Bielcikova at that meeting). For trigger particles satisfying 3 GeV/c < pT,trig < 4 GeV/c, the ridge was shown to be a significant near-side feature for associated particles with pT,assoc > 2 GeV/c, with a yield consistent with zero in the most peripheral events, but strongly increasing with centrality. That is, while the ridge might be visible in minimum bias event structure, it is a prominent structure in high pT events in nuclear collisions.

With each Quark Matter comes another surprise in this story, and Quark Matter 2008 was no exception. At that meeting, Ed Wenger’s talk for the PHOBOS Collaboration (in addition to having the world’s best cartoon illustration of disappearance of the away-side jet) made a striking observation: by utilizing PHOBOS’s very broad angular coverage, they were able to determine that the ridge structure extends to pseudo-rapidity differences (at least) as large as Δη=4. More accurately, low-pT associated particles showed a ridge-like structure in the very broad interval -4 < Δη < 2 with respect to a pT > 2.5 GeV/c trigger particle centered at η=1.

It is very hard to understand correlations over such a broad range if one insists on a space-time picture that maps “space-time rapidity” (pseudo-rapidity) onto true rapidity, as in the Bjorken model. Perhaps these data are reminding us that pseudo-rapidity in the end is just an angle, and that our ridge is in reality a “midriff bulge’ in these events. If so, this would be yet another observable begging for examination via realistic 3D hydrodynamic calculations.

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