Schwinger Pair Production in QCD from Flavor-Dependent Contact Interaction Model of Quarks

We study the Schwinger mechanism in QCD, which refers to the production of quark-antiquark pairs in the presence of a pure electric field strength eE, for a higher number of colors \(N_c\) and flavors \(N_f\). Our unified formalism is based on the Schwinger-Dyson equations, a flavor-dependent symmetry-preserving vector-vector contact interaction model of quarks, and an optimal time regularization scheme. For fixed \(N_c=3\) and \(N_f=2\), the dressed quark mass decreases as we increase eE, and near or above the pseudo-critical electric field \(eE_c\), the chiral symmetry is restored, and quarks become deconfined. The pair production rate \(\Gamma\) becomes stable and grows quickly above \(eE_c\). For fixed \(N_c=3\) and upon increasing \(N_f\), the dynamically generated mass suppresses, and as a result, the \(eE_c\) reduces to smaller values, and the pair production rate \(\Gamma\) tends to initiate and grow quickly for smaller values of \(eE_c\). In contrast, for fixed \(N_f=2\) and upon increasing \(N_c\), the chiral symmetry is restored for larger and larger values of \(eE_c\); and for \(N_c\ge 4\), the transition changes from smooth cross-over to the first order at some critical endpoint (\(N_{c,p}, eE_{c,p}\)). Consequently, the quark-antiquark production rate \(\Gamma\) requires higher values of \(eE_c\) for stable and quick growth as we increase \(N_c\). Our findings are satisfactory and in agreement with the already predicted results for the pair production rate (for fixed \(N_c=3\) and \(N_f=2\)) by other reliable effective models of QCD.