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QCD at non-zero temperature with Wilson fermions on fine lattices

Subject Area Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Term from 2011 to 2020
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 206495355
 
Final Report Year 2019

Final Report Abstract

The project concerns strongly interacting matter at finite temperature, particularly the high-temperature phase called quark-gluon plasma (QGP). On the theory side, the only reliable tool to study the equilibrium properties of the QGP from first principles up to a few times the de-confining temperature is lattice QCD. The primary quantities computed are the thermodynamic potentials and other quantities that characterize a system of infinite size at perfect equilibrium. The calculations to date broadly support the picture of a hadron resonance gas up to fairly close to the transition, and a dominantly perturbative quark-gluon plasma above a few times the transition temperature. On the other hand, heavy-ion collision phenomenology indicates that the shear viscosity to entropy density ratio in the high-temperature phase is small, n/s <~ 0.2, suggesting that the system is very strongly coupled, perhaps similar to gauge theories with a gravity dual. It is therefore important to compute non-static observables using lattice QCD in order to establish a consistent picture of the quark-gluon plasma. During the first funding period of this project, the most interesting physics results obtained were the first calculation of the vector spectral function at vanishing spatial momentum in lattice QCD with dynamical quarks, the calculation and interpretation of non-static screening masses and the pion dispersion relation parameters in the low-temperature phase. The follow-up project was designed to consolidate and extend these pioneering results. A major outcome of the project is the first calculation of the vector correlator in the continuum limit of QCD with dynamical quarks. This has been achieved in the quark-gluon plasma at a temperature of 250 MeV thanks to simulations on fine lattices of size up to 24 x 96 3. This continuum correlator has been used to determine an important property of the QGP, namely the rate at which it produces photons. To do so, the difference of the transverse and longitudinal channels was studied. This difference vanishes in the QCD vacuum and was shown to obey an exact sum rule. The values of the photon rate that correspond to a good description of the Euclidean correlator are in line with the perturbative estimates for momenta of typical thermal magnitude. For smaller momenta, the Euclidean correlator at the present precision level does not constrain much the possible values of the photon rate. A second achievement of the project is the formulation of a dispersive relation for the vector correlator at fixed photon virtuality, rather than at fixed spatial momentum. In the near future, this will allow for lattice QCD studies of the photon rate with much reduced systematic uncertainty. Finally, the conceptual developments achieved as part of this project have led to methods to tackle dynamical properties of hadrons in the QCD vacuum. A prominent example is the study of vacuum spectral functions with the Backus-Gilbert method in the vector and axial-vector channels. Further proposed applications of this method are the study of nucleon structure functions and of the inclsive decay rates of heavy-flavour mesons.

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