The detailed dependence of the elliptic flow parameter v2 on the particle masses and transverse momentum has provided strong evidence for the applicability of hydrodynamics for describing the bulk motion of final-state particles at RHIC. (For a partial list of references, see the Hydro Primer elsewhere in this journal.) Equally intriguing have been various scaling patterns observed in the flow data: The separate curves v2(pT,m) for different mass particles are substantially more alike when studied versus “transvese kinetic energy” KET = mT -m. Plotting v2 as as a function of KET collapses the data into one curve for KET < 1 GeV, while showing two distinct branches for mesons and baryons for larger values of KET. These two branches collapse into one curve when both v2 and KET are divided by the quark content nq (2 for mesons, 3 for baryons). These observations are discussed in
by the PHENIX Collaboration, who also observed that the v2 data for different centralities and for different species (Au+Au and Cu+Cu) could also be cast into a universal distribution when scaled by the pT-integrated v2 for each centrality and/or species. Since the integrated v2 at a given centrality is expected to be proportional to the initial eccentricity ε, the implication was that v2 scaled by ε scaled as expected from hydrodynamic simulations.
This last observation has been called into question by a recent STAR publication
which does not observe a scaling of v2 with an explicitly calculated value of the ‘participant eccentricity’ εP. This is not in direct contradiction with the PHENIX paper- when performing the identical scaling of charged hadron v2 with the pT-integrated v2 , a scaling behavior is observed by both collaborations. Nonetheless, there are least two puzzles here that require resolution:
- Is there a substantial non-proportionality between pT-integrated v2 and participant eccentricity εP ? If so, what is the physical interpretation of the observed scaling pattern?
- Why does the observed scaling behavior of v2 with pT-integrated v2 fail for identified hadrons? Is the observed scaling simply an ‘accident’ when summing over particle species?
As an aside, note that the STAR paper shows, and states in the conclusions but not the abstract “For the most central collisions (0-10%), negative values of v2 at the lowest pT studied have been observed for both K0s and Λ . This is the first time one found a negative v2 in Au + Au collisions at RHIC. It is consistent with the strong expansion observed in hadron spectra analysis.”
On the general issue of empirical scaling trends in data that are stronger than those suggested by the underlying theory, see the analysis in
which examines the extent to which the nq scaling is supported by hydrodynamic calculations, contaminated by resonances, and reconciliable (or not) with interpretations in terms of quasi-particles.