Flow equations for spectral functions at finite external momenta

Abstract

In this work we study the spatial-momentum dependence of mesonic spectral functions obtained from the quark-meson model using a recently proposed method to calculate real-time observables at finite temperature and density from the Functional Renormalization Group. This non-perturbative method is thermodynamically consistent, symmetry-preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations for 2-point functions. Results on the spatial-momentum dependence of the pion and sigma spectral function are presented at different temperatures and densities, in particular near the critical endpoint in the phase diagram of the quark-meson model.Comment: 13 pages, 7 figure

Second look to the Polyakov loop Nambu–Jona-Lasinio model at finite baryonic density

“…Expression (26) demonstrates that |Φ| approaches unity at high densities only if d4 d2 = − b4 3b2 → 0 in full agreement with values found for κ 2 and κ 4 . On the other hand, this limiting value of the Polyakov loop modulus should be reached from below.…”

“…Further extension remains impossible at present due to the sign problem [20,21]. Thermodynamics of QCD was also studied within the Functional Renormalization Group approach, which allowed to take under control quantum quark-meson fluctuations in the deep infrared limit [22][23][24][25][26][27]. At the same time, a pure Yang-Mills potential for the Polyakov loop being an order parameter of the deconfinement transition does not provide a phase transition in a perturbative regime, see e.g.…”

Low-temperature behavior of the quark-meson model

“…[5,6]. In the present case, the constituent quark mass is higher so as to shift the critical end-point (CEP) to higher temperatures and to induce a change of curvature of the critical first-order line.…”

“…The latter will be needed to obtain the spectral properties of the inmedium sigma and pion modes, which will aid the physical interpretation of the results at low temperatures T and large quark chemical potentials μ. For details of the numerical implementation, we refer to our previous work [5,6].…”

“…These are obtained from the Euclidean two-point functions by the method proposed in Refs. [5,6], which entails an analytic continuation from imaginary to real energies. The flow equations for the two-point functions Γ For initial conditions for the retarded two-point functions at the UV scale, we use…”