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QCD thermodynamics on the lattice

Final Report Summary - QCDTHERMO (QCD thermodynamics on the lattice)

The main goal of the project was to study quantum chromodynamics, in particular the thermodynamics of the quark-gluon plasma with lattice calculations. Different lattice discretizations were used. The results were first finalized using the staggered approach, then the theoretically more sound Wilson and chiral formulations were applied. For the computations, a graphics card (GPU) based PC cluster was installed with infiniband network for communication. During the lifetime of the project we achieved our planned goals, in some cases went significantly beyond the plans and also started new directions.

Various quantities have been determined in the continuum limit for the first time, using staggered fermions. These include the transition temperature, the equation of state, the phase diagram for small chemical potentials, fluctuations of conserved
charges. Since staggered fermions, when used to describe less than four quarks, suffer from a theoretically not well understood locality problem, it is desirable to perform calculations with a theoretically sound discretization. We used Wilson fermions and found nice agreement with staggered results. As a first step we determined the hadron spectrum. Then we studied the temperature dependence of three thermodynamic observables using three pion masses. We also determined
spectral functions of charmonium states at high temperature. Wilson fermions suffer from large discretization errors, especially close to the chiral limit where the explicit symmetry breaking of the discretization is most apparent. Therefore we started a pilot study with chiral (overlap) fermions. We were able to locate the finite temperature transition using two lattice spacings. We also studied the mass dependence of the transition in the three flavor theory.

Lattice QCD at non-vanishing density suffers from the infamous complex action problem. Nevertheless, several methods are available to study the phase diagram and the equation of state at small chemical potentials. We determined both of these in the continuum limit using staggered fermions. Recently the fluctuations of conserved charges (derivatives of the free energy with respect to chemical potentials) attracted serious interest from the community since these can also be measured by experiment. We have determined these fluctuations up to fourth order with staggered and second order with Wilson fermions. The former results made it possible to extract the freeze-out temperature of heavy-ion collisions without model assumptions.

Various new directions emerged during the lifetime of the project. In collaboration with colleagues in Regensburg and a recent team member who is a postdoc there we started studying QCD in the presence of a strong external magnetic field. This is relevant for non-central heavy-ion collisions. Several interesting, unexpected phenomena, such as inverse magnetic
catalysis and the decrease of the transition temperature were discovered.

Another new direction is the study of the spectrum of the Dirac operator at high temperatures which shows an interesting analogy with Anderson localization known from condensed matter physics.