The Chiral Phase Transition in QCD: Mean-Field Versus the Functional Renormalisation Group
MetadataShow full item record
- Institutt for fysikk 
In this thesis we map out the phase diagram of the chiral phase transition of quantum chromodynamics (QCD) in the plane of temperature and quark chemical potential. We use the linear sigma model with quarks (LSMq) as a low energy effective theory of QCD. We first employ the mean-field approximation to calculate the phase diagram. With this approximation we find a first-order phase transition in the whole T-μ plane in the chiral limit. However at the physical point we find a crossover at zero chemical potential, which changes into a first-order transition as we increase μ, implying the existence of a critical endpoint.We then turn our attention to the more sophisticated functional renormalisation group and nonperturbative approximations. Using the local potential approximation (LPA), which is the simplest nonperturbative approximation, we found a second-order phase transition in the chiral limit at zero chemical potential. As we increased μ, the transition changed into a first-order one, which means that in contrast to the results from the mean-field approximation we found a critical endpoint also in the chiral limit. When comparing the phase diagrams obtained in the mean-field approximation with the phase diagrams from the LPA, we see that the latter phase diagram declines faster for high chemical potentials.While this work is primarily concerned with two-flavour QCD, we also introduce the three-flavour LSMq model and map out the phase diagram in the mean-field approximation. We find that the inclusion of the strange quark only has a minor effect on the phase diagram. The difference becomes more prominent as we increase the mass of the sigma particle to 800 MeV, but the difference is still small.