dense matter and QCD phase space

I came across some interesting information yesterday about the QCD phase diagram.

Last night I attended the retirement party of a legendary theoretical physicist Prof. J.W.A. Cleymans. There were a few talks about Cleymans work and his contributions to theoretical physics.

Anyway during one of the talks there was a slide of the QCD phase diagram

I had seem this diagram many times and thought that I understood generally all details of it but the surprising thing about this diagram is that Cleymans had been one of the pioneers at creating it. One of the speakers even called it the “Cleymans Plot”. Cleymans main contribution was the statistical hadronic model, which allowed physicists to realize that a phase boundary exists between hadronic and quarkonic matter seen clearly below

The line marked by the critical point is where the bulk of Cleymans work lays. Anyway on the way home his current PhD student Dawit and I were chatting about the origin of this line. Surprisingly there is no function in theoretical physics that describes this boundary line as yet! Much the work comes from analysis of that experimental data from RHIC, and FAIR and when the LHC starts running again(well actually it started running 2 days ago!) Also the line doesnt actually cross the T or \mu axes as yet. Maybe with data from the LHC  the boundary line can be shown to cross the T axis but for the crossing of the \mu axis data from superdense objects like possibly neutron and quark stars. I’m not certain whether its possibly to extract this data from black holes.