title: Covariant regularization for hot and dense QCD
Creators: name: Töpfel, Sebastian
Publisher: name: UNSPECIFIED
Year: 2025

description: We employ the functional renormalization group to study the chiral phase transition in the phase diagram of hot and dense QCD. In our phenomenological investigation of strongly interacting matter, we consider a low-energy effective model of two massless quark flavors that interact through a Yukawa term. Specifically, we work with a simple quark-meson model that includes quarks, the scalar sigma meson, and the pseudoscalar pions as its relevant field degrees of freedom. We compute meson curvature masses, which we use to determine the phase boundary associated with the chiral phase transition. Additionally, we calculate meson spectral functions, which provide information about, e.g., particle resonances and decay processes, thereby establishing a direct link between theory and experiment. Based on our calculations of chiral observables in different regularization schemes, we examine the scheme dependence of curvature masses and spectral functions. In particular, we focus on investigating the effects of regulator-induced symmetry breaking. To this end, we begin by employing canonical polynomial regulator functions, with and without explicit Lorentz symmetry breaking. Both the spatial and the covariant regulators respect chiral symmetry and the Silver-Blaze symmetry. We discuss the challenges associated with momentum-dependent covariant regulators at finite external parameters and demonstrate a procedure for their implementation. A comprehensive comparison of results obtained within the spatial and covariant schemes then allows us to assess the relevance of artificial Lorentz symmetry breaking at finite temperature and chemical potential. Furthermore, we make use of the Callan-Symanzik regulator, which is momentum-independent and thus inherently covariant. This regulator also respects the Silver-Blaze symmetry but breaks chiral symmetry. To allow for a meaningful implementation of this covariant regulator, we construct a symmetrization procedure based on Ward-Takahashi identities, which systematically eliminates the regulator-induced chiral symmetry breaking from the theory. Subsequently, we demonstrate the applicability of our symmetry-constrained Callan-Symanzik scheme through computations of curvature masses, spectral functions, and the phase diagram. In particular, we highlight the impact of artificial chiral symmetry breaking on chiral observables when our symmetrization procedure is not employed.

In addition to our investigation of regulator artifacts associated with explicit symmetry breaking, we collect and analyze various mathematical subtleties that arise in calculations of loop diagrams at finite temperature and/or chemical potential. In general, the calculation of correlation functions involves integration, differentiation, and the computation of limit processes. A priori, these mathematical operations do not commute. We present several scenarios in which the order of applying these operations is essential for obtaining consistent and unambiguous results. An understanding of these subtleties is of principal importance for quantum field theories and, in particular, underlies our calculations of chiral observables from the quark-meson model.