Proposal for a possible path towards extracting QGP viscosities from experimental data
(Excerpts from an email exchange between B. Muller and U. Heinz, posted on 06/30/2009 for discussion at the 3rd TECHQM workshop at CERN, July 6-10, 2009)
The area where I believe things are ready to make a first serious attempt at a comprehensive model-data comparison is the shear (and bulk) viscosity, equation of state, and initial conditions. It is also extremely timely, because we saw at Quark Matter and elsewhere in the recent past several simplified attempts by various members of the community to deduce "values" for the shear viscosity of the quark gluon plasma from elliptic flow data. The controversial discussions surrounding these attempts show the need for a serious attack on the problem that properly accounts for the fireball dynamics and evolution history.
With the advent of validated 2-D viscous hydro codes, almost everything is in place to start to do such an analysis. We may require a final state hadron afterburner, but these exist, and if the project were given high priority, I am convinced that this could be added within a few months in collaboration with the experts. The number of relevant model parameters is limited: viscosity, EOS, initial energy density profile, equilibration time. So the theory/model side is perhaps sufficiently solidified to think of using it as a starting block for for a serious comparison with experimental data.
The range of observables on the data side is large, and to get such an analysis done in a comprehensive way will require the roping in a several members of the experimental community into the TECHQM activities.
We don't quite have all the required ingredients, but we are getting there. I think we have to narrow down the parameter space further for a first attempt. In order to establish a working machinery that can be used by more than one person (namely the one who wrote it) we should focus on a specific task with very limited freedom of fitting parameters (even if this doesn't get us close to a quantitatively reliable result for eta/s right away). Varying the EOS, initial conditions, thermalization time and freeze-out conditions all at the same time at this stage will be a waste of computing resources.
We absolutely need the hydro to hadron cascade interface. Without it we open up a considerable region of fit parameter space for the viscosities and freeze-out parameters in the late hadronic stage.
Pasi Huovinen has a mu=0 EoS which couples the latest lattice QCD data to a PCE hadron resonance gas. He has it for the BNL/Bielefeld/Livermore data with T_c = 195 MeV but promised to do a refit with a rescaled temperature scale that gives T_c=170 MeV. The first is available (we are collaborating on a paper which uses this EoS), the second a matter of a few weeks. We should ask Pasi to make this EoS available to TECHQM for development studies (publication of any results obtained with it must be discussed with Pasi). This will give us two choices for the EoS, and that's where I think we should leave it for now.
We should also limit the freedom of what to choose for the temperature dependence of \eta/s and \zeta/s. This limitation will induce unavoidable uncertainties in the extracted "average" viscosities, but one must start somewhere.
With some luck, a new graduate student at OSU will soon make some progress on exploring the effects of different assumptions for the pre-equilibrium collective dynamics on the subsequent hydro evolution, following up on recent work by Vredevoogd and Pratt. This will happen on a time scale of several months (the student, Daniel White, is just starting).
I don't know how to deal with the elephant in the room, namely the 30% uncertainty in the initial eccentricity. Until we figure that out, we have to deal with a 100% error on the extracted \eta/s, as shown by Luzum and Romatschke. TECHQM collaborators and others are invited to think about possible resolutions of this problem. This is important and deserves high priority.
So here is a suggestion: OSU provides the (2+1)-d viscous hydro code, accessible to TECHQM members on a password-protected area on this wiki. Its users will have to learn how to deal with its ideosyncracies, such as instabilities propagating inward from the boundary conditions at the grid corners whose elimination we haven't been able yet to fully automate -- it's a trial and error procedure at this point, but perhaps a dedicated user from the experimental community can fix up the code to increase its robustness against instability growth. OSU will collaborate on the hydro-cascade interface with Duke. We ask Pasi to provide the EoS. Someone from the experimental community within TECHQM will compile the data. Someone else will start running the code and start comparing with the data. Then we'll take it from there. The goal is to work towards developing an automated and user friendly protocol for doing these runs and comparisons, so that others can jump in.