  Our research delves into the QCD phase diagram in the temperature $T$ and
quark chemical potential $\mu$ plane. We use a unique confining contact
interaction effective model of quark dynamics that maintains the QCD symmetry
intact. By embedding the model into a Schwinger-Dyson equations framework,
within a Landau gauge rainbow-ladder-like truncation, we derive the gap
equation. In order to accurately regulate the said equation, we utilize the
Schwinger optimal time regularization scheme. We further derive the effective
potential of the model by integrating the gap equation over the dynamical mass,
which along with the confining length scale serve as parameters for the chiral
and confinement deconfinement phase transitions, respectively. A cross-over
transition is observed at low $\mu$ and above a critical value of the
temperature $T_c$, whilst a first order phase transition is found for low $T$
at high density. The critical end point is estimated to be located at
$(\mu_{E}/T_{c,0}=1.6, T_{E}/T_{c,0}=0.42)$, which falls within the range of
other QCD effective models predictions. $T_{c,0} =208$ MeV is the critical
temperature at vanishing $\mu$. Screening effects of the medium which dilute
the strength of the effective coupling are considered by including the vacuum
polarization contribution due to quarks at high temperatures into the
framework. It locates the critical end point at $( \mu^{E}_{c}/T_c \approx2.6,
T^{E}_{c}/T_c \approx 0.57)$, which hints for a deeper analysis of screening
effects on models of this kind.
