Dynamical mass generation and critical behavior in pseudo-Proca quantum electrodynamics
We investigate dynamical mass generation in pseudo-Proca quantum electrodynamics (PPQED) by means of 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 $\Lambda$, control 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 $\alpha_c(m,\Lambda)$ and the critical number of fermion flavors $N_c(m,\Lambda,g)$, 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, which modifies the quantitative values of the critical parameters while preserving their qualitative dependence on the screening scale $m$. In addition, within the static approximation, the anisotropic extension indicates that the critical coupling decreases as the ratio $v_F/c$ increases. Taken together, our results suggest that the scale $m$ plays an important role in modulating criticality in PPQED. Furthermore, the Ball-Chiu vertex construction shows that vertex corrections modify the quantitative values of the critical parameters while preserving the screening-driven suppression of dynamical mass generation in $(2+1)$D.