Time-Scales and Flavor Dependence of (Elliptic) Flow

Elliptic flow at ultra-relativistic energies, the preferential emission of matter along the impact parameter axis of the overlap zone of the two colliding nuclei, was first mentioned in our Hydro Primer. The main relevance of elliptic flow lies in the short timescales over which it is generated and its resulting sensitivity to the equation of state of the (QGP) medium. The short timescale of elliptic flow buit-up was first discussed in detail in:

Anisotropic transverse flow and the quark hadron phase transition

Hoever, the hadronic phase contributes significantly to the ellliptic flow phenomenology: one of the most compelling signatures of hydrodynamic behavior is the mass ordering of the anisotropy coefficient v2 versus transverse momentum. Hydrodynamics does not know anything about the flavor or quark content of a particular hadron, but it knows its mass. Since the hadron mass is the guiding scale, this ordering (or splitting) can only develop at or after hadronization, even though the overall magnitude of the elliptic flow is determined far earlier in the deconfined phase. This picture was recently confirmed in a very elegant way in the following paper:

Mass ordering of differential elliptic flow and its violation for phi mesons

In particular figure #5 of that paper demonstrates nicely how the magnitude of the elliptic flow is set in the deconfined phase, the mass splitting, however, first develops in the hadronic phase.

The other point raised in this paper involves the phi meson, which due to its strangeness-suppressed hadronic cross section does not partake in the mass-splitting of the hadronic phase. Therefore the elliptic flow seen in the phi should closely reflect the elliptic flow imprinted on the system at hadronization. The violation of the mass ordering by the phi is a good prediction which allows for an experimental confirmation of the the underlying physics picture, namely that of a hydrodynamically evolving QGP, followed by a dissipative hadronic expansion with flavor-dependent sequential freeze-out.

One should note, however, that the early freeze-out of multi-strange hadrons and its potential applications to the analysis of the early reaction phase is an idea that has been around for a decade, both in the context of a purely microscopic transport model as well as in the context of a hybrid Hydro+Micro approach:

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