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

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发表日期：

2024年9月3日

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Aftab Ahmad,
Akif Farooq

摘要

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 $N_c$ $N_{c}$ and flavors $N_f$ $N_{f}$ . 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 $N_c=3$ $N_{c} = 3$ and $N_f=2$ $N_{f} = 2$ , the dressed quark mass decreases as we increase eE, and near or above the pseudo-critical electric field $eE_c$ $e E_{c}$ , the chiral symmetry is restored, and quarks become deconfined. The pair production rate $\Gamma$ $Γ$ becomes stable and grows quickly above $eE_c$ $e E_{c}$ . For fixed $N_c=3$ $N_{c} = 3$ and upon increasing $N_f$ $N_{f}$ , the dynamically generated mass suppresses, and as a result, the $eE_c$ $e E_{c}$ reduces to smaller values, and the pair production rate $\Gamma$ $Γ$ tends to initiate and grow quickly for smaller values of $eE_c$ $e E_{c}$ . In contrast, for fixed $N_f=2$ $N_{f} = 2$ and upon increasing $N_c$ $N_{c}$ , the chiral symmetry is restored for larger and larger values of $eE_c$ $e E_{c}$ ; and for $N_c\ge 4$ $N_{c} \geq 4$ , the transition changes from smooth cross-over to the first order at some critical endpoint ( $N_{c,p}, eE_{c,p}$ $N_{c, p}, e E_{c, p}$ ). Consequently, the quark-antiquark production rate $\Gamma$ $Γ$ requires higher values of $eE_c$ $e E_{c}$ for stable and quick growth as we increase $N_c$ $N_{c}$ . Our findings are satisfactory and in agreement with the already predicted results for the pair production rate (for fixed $N_c=3$ $N_{c} = 3$ and $N_f=2$ $N_{f} = 2$ ) by other reliable effective models of QCD.