# What’s the basic procedure to draw a QCD phase diagram?

Could someone recommend a book/resource where I can find a detailed way of sketching out a QCD temperature-chemical potential phase diagram using gap equations (eg. equations 35-37 or 39-40 as given here)?

P.S- Other similar questions on QCD phase diagrams focus more on their characteristics and not so much much on the basic method of obtaining them.

• Mar 23 at 8:25

It is rather a complicated question and still an area of active research. The most reliable and direct way to plot the phase diagram with the axes $$\mu, B, T$$, where $$\mu$$ is baryon potential, $$B$$ is magnetic field is by means of Lattice QCD.
However, there is a important limitation - that the theory with baryon chemical potential suffers from notorious sign problem. This makes the direct simulation not feasible and results are obtained with imaginary chemical potential $$i \mu$$, and then analytically continued to the real axis. There also exist different approaches for handling the sign problem - reweighting, complex Langevin, but none of the gives fully satisfactory results.
• thanks for sharing the paper. I am not looking for a "good" phase diagram, rather, how does one reach 'any' T-$\mu$ curve starting from gap equations (eg. equations 35-37 or 39-40 as given in [ift.uni.wroc.pl/~blaschke/maestro/B+AnnPhys2014.pdf]? The gap equations in principle have 2 unknowns - mass $m$ & $\triangle$ (for $\mu=0$) but how to plot the T-$\mu$ curve? So, I 'm not looking for the physics as much as the steps to sketch out a phase diagram. Dec 18, 2020 at 17:13