The finite temperature QCD phase transition and the thermodynamic equation of state

Abstract

Heavy ion collision experiments at the Relativistic Heavy Ion Collider (RHIC) at BNL or at the Large Hadron Collider (LHC) at CERN are routinely performed today and provide insight into a new phase of strongly interacting matter that is created for a short time after the collision the quark gluon plasma. Its theoretical description requires the knowledge of the thermodynamic equation of state (EoS) of the plasma. It is calculable within the lattice approach to quantum chromodynamics, the established theory of strong interactions. The lattice discretisation however requires the complete control of the continuum limit to be taken in the end. Current discrepancies in results from different lattice collaborations suggest this to be very crucial for the EoS. In this work we report about an evaluation of the trace anomaly providing the pressure and energy density. We employ the Wilson twisted mass discretisation of the quark action. This formulation is known to have an automatic improvement of lattice artifacts that are proved to occur only in the second order of the lattice spacing. Including two dynamical light quark flavours the twisted mass discretisation has been applied very successfully at zero temperature. This work presents first robust results for the non-vanishing temperature case. Due to the missing strange quark flavour, the results for the EoS are of qualitative nature useful to disentangle its strange quark contribution. The continuum limit of the trace anomaly is studied using several values ofNτ and the tree-level correction technique. From the corrected and interpolated trace anomaly the EoS is obtained from the temperature integral method. Moreover, we are able to contribute to the yet unresolved question of the order of the two flavour phase transition in the chiral limit, for which two possibilities usually are discussed: a second order transition in the universality class of an O(4) symmetric 3-dimensional spin model or alternatively a first order transition. For our currently simulated pion masses in the range of 300-700 MeV we present evidence that the finite temperature transition we observe is a crossover transition. For these masses the chiral condensate as the order parameter in the chiral limit is analysed in comparison with the O(4) universal scaling function which characterises a second order transition. It is found to agree with the collected numerical data, however only if several scaling violating contributions are considered, thus prohibiting a final conclusive statement. Further, we investigate the chiral limit by comparing the scaling of the observed crossover temperature with the mass considering several possibilities among them above alluded ones. For the O(4) scenario we find the transition temperature Tc = 152 (26) MeV in the chiral limit.