Quark matter under strong electric fields in the Linear Sigma Model coupled with quarks

In this work we study the influence of external electric field and temperature on the chiral phase transition of Quantum Chromodynamics. We use the two-flavor Linear Sigma Model coupled with quarks (LSMq) in a thermal and electrized medium to evaluate the effective quark mass and the Schwinger pair production. To this end, we apply one-loop correction to the fermionic sector of the model and the simple tree-level approximation in the mesonic contributions. The electric fields strengthen the partial restoration of the chiral symmetry when applied with finite temperature in a crossover transition. The expected decrease of the pseudocritical temperature as a function of the electric field is observed until electric fields reach $eE\approx 13.5m_{\pi }^2$. For stronger electric fields, the effect is the opposite, which is in a very good agreement with previous results obtained with four-point non-renormalizable models, showing that this effect is independent of renormalizability issues. We also show the thermal and electric effects on the behavior of the Schwinger pair production.