arXiv:1106.6350v1 [nucl-th] 30 Jun 2011
The QGP shear viscosity – elusive goal or just
around the corner?
Chun Shen1, Steffen A Bass2, Tetsufumi Hirano3,4, Pasi
Huovinen5, Zhi Qiu1, Huichao Song6and Ulrich Heinz1
1Department of Physics, The Ohio State University, Columbus, Ohio 43026, USA
2Department of Physics, Duke University, Durham, North Carolina 27708, USA
3Department of Physics, Sophia University, Tokyo 102-8554, Japan
4Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
5ITP, J.W.Goethe-Universit¨ at, D-60438 Frankfurt a.M., Germany
6Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
VISHNU,a rather precise (O(25%)) extraction of the QGP shear viscosity (η/s)QGPfrom
heavy-ion elliptic flow data is possible if the initial eccentricity of the collision fireball
is known with < 5% accuracy. At this point, eccentricities from initial state models
differ by up to 20%, leading to an O(100%) uncertainty for (η/s)QGP. It is shown
that a simultaneous comparison of elliptic and triangular flow, v2and v3, puts strong
constraints on initial state models and can largely eliminate the present uncertainty in
(η/s)QGP. The variation of the differential elliptic flow v2(pT) for identified hadrons
between RHIC and LHC energies provides additional tests of the evolution model.
With the new viscous hydrodynamic + hadron cascade hybrid code
Prologue – how to measure (η/s)QGP: Hydrodynamics converts the initial spatial
deformation of the fireball created in relativistic heavy-ion collisions into final state
momentum anisotropies. Viscosity degrades the conversion efficiency εx=??y2−x2??
of the dynamically generated total momentum anisotropy εpis monotonically related to
the specific shear viscosity η/s. The observable most directly related to εpis the total
charged hadron elliptic flow vch
composition and pT-spectra of the various hadron species; the latter evolve in the
hadronic stage due to continuously increasing radial flow (and so does v2(pT)), even
if (as expected at top LHC energy ) εpfully saturates in the QGP phase. When (as
happens at RHIC energies) εpdoes not reach saturation before hadronization, dissipative
hadronic dynamics  affects not only the distribution of εpover hadron species and pT,
but even the final value of εpitself, and thus of vch
To isolate the QGP viscosity (η/s)QGPwe therefore need a hybrid code that couples
viscous hydrodynamics of the QGP to a realistic model of the late hadronic stage, such
as UrQMD , that describes its dynamics microscopically. VISHNU  is such a code.
?Txx+Tyy?of the fluid; for given initial fireball ellipticity εx, the viscous suppression
2 . Its distribution in pT depends on the chemical
2from which we want to extract η/s.
Extraction of (η/s)QGP from 200AGeV Au+Au collisions at RHIC: The
left panel in Fig. 1 shows that such an approach yields a universal dependence of