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We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel technique based on algorithmic differentiation has been developed. Results for thermodynamic observables as well as the phase structure obtained through the series expansion up to 24th order are compared to the full model solution at finite chemical potential. The available higher order coefficients also allow for resummations, e.g. Padé series, which improve the convergence behavior. In view of our results we discuss the prospects for locating the QCD phase boundary and a possible critical endpoint with the Taylor expansion method.
As a first step towards a realistic phenomenological description of vector and axial-vector mesons in nuclear matter, we calculate the spectral functions of the ρ and the a1 meson in a chiral baryon-meson model as a low-energy effective realization of QCD, taking into account the effects of fluctuations from scalar mesons, nucleons, and vector mesons within the functional renormalization group (FRG) approach. The phase diagram of the effective hadronic theory exhibits a nuclear liquid-gas phase transition as well as a chiral phase transition at a higher baryon-chemical potential. The in-medium ρ and a1 spectral functions are calculated by using the previously introduced analytically-continued FRG (aFRG) method. Our results show strong modifications of the spectral functions—in particular near the critical endpoints of both phase transitions—which may well be of relevance for electromagnetic rates in heavy-ion collisions or neutrino emissivities in neutron-star merger events.
We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark–meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu–Gorkov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above , 2Δ0 where Δ0 is its on-shell value. We find Δ0 ≈ 40 MeV close to the chiral phase transition.
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.
