Abstract
We present the first calculation of fermion spectral function at finite temperature in quark-meson model in the framework of the functional renormalization group (FRG). We compare the results in two truncations, after first evolving flow equation of effective potential, we investigate the spectral function either by taking the IR values as input to calculate one-loop self-energy or by taking the scale-dependent values as input to evolve the flow equation of the fermion two-point function. The latter one is a self-consistent procedure in the framework of FRG. In both truncations, we find a multi-peak structure in the spectral function, indicating quark collective excitations realized in terms of the Landau damping. However, in contrast to fermion zero-mode in the one-loop truncation, we find a fermion soft-mode in the self-consistent truncation, which approaches the zero-mode as temperature increases.
Highlights
The QCD phase transitions at finite temperature and density provide deep insight into the strong interacting matter created in high-energy nuclear collisions and compact stars
We present the first calculation of the fermion spectral function at finite temperature in the quark-meson model in the framework of the functional renormalization group
We compare the results in two truncations; after first evolving the flow equation of effective potential, we investigate the spectral function either by taking the IR values as input to calculate one-loop self-energy or by taking the scale-dependent values as input to evolve the flow equation of the fermion two-point function
Summary
The QCD phase transitions at finite temperature and density provide deep insight into the strong interacting matter created in high-energy nuclear collisions and compact stars. To calculate the spectral function in the usually used imaginary time formalism with the FRG, an analytical continuation is required to bring the imaginary time in the Euclidean two-point function at finite temperature to the real time in the Minkowski space [20,21,22,23,24,25,26] This method has been applied to the study of realtime observables such as shear viscosity [26] and soft modes [27] near the QCD critical point. When the FRG is put to use to investigate the quark spectral function, the most crucial difference is that one takes into account the scale dependence of the meson masses, and the thresholds of each decay, creation, and scattering channel.
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