Dynamical mass generation and critical behavior in pseudo-Proca quantum electrodynamics

Abstract

We investigate dynamical mass generation in pseudo-Proca quantum electrodynamics (PPQED) using Schwinger–Dyson equations in rainbow-quenched and unquenched truncations. The pseudo-Proca screening scale m, together with the fine-structure constant \(\alpha \), the flavor number N, and the ultraviolet cutoff \(\varLambda \), controls the critical thresholds for chiral symmetry breaking in the reduced \((2 + 1)\)D theory. Within these truncation schemes, we obtain analytical estimates for both the critical coupling \(\alpha _c(m,\varLambda )\) and the critical number of fermion flavors \(N_c(m,\varLambda ,g)\), and show that increasing m suppresses dynamical mass generation through Yukawa screening. We further assess the robustness of this physical picture by incorporating a Ball–Chiu vertex construction; our results show that while vertex corrections modify the quantitative values of the critical parameters, they preserve the qualitative screening-driven suppression of dynamical mass generation. In addition, within the static approximation, our anisotropic extension shows that the critical coupling is a monotonically decreasing function of the ratio \(v_F/c\). Taken together, our results suggest that the scale m plays an important role in modulating criticality in PPQED.