We investigate the effect of a finite volume on the critical behavior of the theory of the strong interaction, Quantum Chromodynamics (QCD), by means of a quark-meson model for ${N}_{\mathrm{f}}=2$ quark flavors. In particular, we analyze the effect of a finite volume on the location of the critical point in the phase diagram existing in our model. In our analysis, we take into account the effect of long-range fluctuations with the aid of renormalization group techniques. We find that these quantum and thermal fluctuations, absent in mean-field studies, play an import role for the dynamics in a finite volume. We show that the critical point is shifted towards smaller temperatures and larger values of the quark chemical potential if the volume size is decreased. This behavior persists for antiperiodic as well as periodic boundary conditions for the quark fields as used in many lattice QCD simulations.
In this work, we present the first results on vector- and axial-vector meson spectral functions as obtained by applying the nonperturbative functional renormalization group approach to an effective low-energy theory motivated by the gauged linear sigma model. By using a recently proposed analytic continuation method, we study the in-medium behavior of the spectral functions of the $\ensuremath{\rho}$ and ${a}_{1}$ mesons in different regimes of the phase diagram. In particular, we demonstrate explicitly how these spectral functions degenerate at high temperatures as well as at large chemical potentials, as a consequence of the restoration of chiral symmetry. In addition, we also compute the momentum dependence of the $\ensuremath{\rho}$ and ${a}_{1}$ spectral functions and discuss the various timelike and spacelike processes that can occur.
We show how complex resonance poles and threshold energies for systems in hadron physics can be accurately obtained by using a method based on the Padé-approximant which was recently developed for the calculation of resonance poles for atomic and molecular auto-ionization systems. The main advantage of this method is the ability to calculate the resonance poles and threshold energies from \emph{real} spectral data. In order to demonstrate the capabilities of this method we apply it here to an analytical model as well as to experimental data for the squared modulus of the vector pion form factor, the S0 partial wave amplitude for $ππ$ scattering and the cross section ratio $R(s)$ for $e^+e^-$ collisions. The extracted values for the resonance poles of the $ρ(770)$ and the $f_0(500)$ or $σ$ meson are in very good agreement with the literature. When the data are noisy the prediction of decay thresholds proves to be less accurate but feasible.
We study fermionic excitations in a hot and dense strongly interacting medium consisting of quarks and (pseudo-)scalar mesons. In particular, we use the two-flavor quark-meson model in combination with the functional renormalization group (FRG) approach, which allows to take into account the effects from thermal and quantum fluctuations. The resulting fermionic excitation spectrum is investigated by calculating the quark spectral function at finite temperature, quark chemical potential, and spatial momentum. This involves an analytic continuation from imaginary to real energies by extending the previously introduced analytically continued FRG method to the present case. We identify three different collective excitations in the medium: the ordinary thermal quark, the plasmino mode, and an ultrasoft ``phonino'' mode. The dispersion relations of these modes are extracted from the quark spectral function. When compared to corresponding results from an FRG-improved one-loop calculation, a remarkable agreement has been found.
We present recent results on in-medium spectral functions of vector and axial-vector mesons, the electromagnetic (EM) spectral function and dilepton rates using the Functional Renormalization Group (FRG) approach. Our method is based on an analytic continuation procedure that allows us to calculate real-time quantities like spectral functions at finite temperature and chemical potential. As an effective low-energy model for Quantum Chromodynamics (QCD) we use an extended linear-sigma model including quarks where (axial-)vector mesons as well as the photon are introduced as gauge bosons. In particular, it is shown how the ρ and the a1 spectral function become degenerate at high temperatures or chemical potentials due to the restoration of chiral symmetry. Preliminary results for the EM spectral function and the dilepton production rate are discussed with a focus on the possibility to identify signatures of the chiral crossover and the critical endpoint (CEP) in the QCD phase diagram.
In this paper we explore practicable ways for self-consistent calculations of spectral functions from analytically continued functional renormalization group (aFRG) flow equations. As a particularly straightforward one we propose to include parametrizations of self-energies based on explicit analytic one-loop expressions. To exemplify this scheme we calculate the spectral functions of pion and sigma meson of the $O(4)$ model at vanishing temperature in the broken phase. Comparing the results with those from previous aFRG calculations, we explicitly demonstrate how self-consistency at all momenta fixes the tight relation between particle masses and decay thresholds. In addition, the two-point functions from our new semi-analytic FRG scheme have the desired domain of holomorphy built in and can readily be studied in the entire cut-complex frequency plane, on physical as well as other Riemann sheets. This is very illustrative and allows, for example, to trace the flow of the resonance pole of the sigma meson across an unphysical sheet. In order to assess the limitations due to the underlying one-loop structure, we also introduce a fully self-consistent numerical scheme based on spectral representations with scale-dependent spectral functions. The most notable improvement of this numerically involved calculation is that it describes the three-particle resonance decay of an off-shell pion, $\pi^* \to \sigma\pi\to3\pi$. Apart from this further conceptual improvement, overall agreement with the results from the considerably simpler semi-analytic one-loop scheme is very encouraging, however. The latter can therefore provide a sound and practicable basis for self-consistent calculations of spectral functions in more realistic effective theories for warm and dense matter.
We revisit the phase diagram of strong-interaction matter for the two-flavor quark-meson model using the Functional Renormalization Group. In contrast to standard mean-field calculations, an unusual phase structure is encountered at low temperatures and large quark chemical potentials. In particular, we identify a regime where the pressure decreases with increasing temperature and discuss possible reasons for this unphysical behavior.
In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard Källén-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $η_{0}$. As an example, we calculate $η_{0}$ in $ϕ^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.
