Virtual Journal on QCD Matter

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(p_T,m) for different mass particles are substantially more alike when studied versus “transvese kinetic energy” KE_T = m_T -m. Plotting v₂ as as a function of KE_T collapses the data into one curve for KE_T < 1 GeV, while showing two distinct branches for mesons and baryons for larger values of KE_T. These two branches collapse into one curve when both v₂ and KE_T are divided by the quark content n_q (2 for mesons, 3 for baryons). These observations are discussed in

Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at √s_NN = 200 GeV

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 p_T-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

Centrality dependence of charged hadron and strange hadron elliptic flow from √s_NN = 200 GeV Au+Au collisions

which does not observe a scaling of v₂ with an explicitly calculated value of the ‘participant eccentricity’ ε_P. This is not in direct contradiction with the PHENIX paper- when performing the identical scaling of charged hadron v₂ with the p_T-integrated v₂ , a scaling behavior is observed by both collaborations. Nonetheless, there are least two puzzles here that require resolution:

1. Is there a substantial non-proportionality between p_T-integrated v₂ and participant eccentricity ε_P ? If so, what is the physical interpretation of the observed scaling pattern?
2. Why does the observed scaling behavior of v₂ with p_T-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 p_T studied have been observed for both K⁰_s 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

Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma

which examines the extent to which the n_q scaling is supported by hydrodynamic calculations, contaminated by resonances, and reconciliable (or not) with interpretations in terms of quasi-particles.

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