  We use the linear sigma model coupled to quarks to explore the location of
the phase transition lines in the QCD phase diagram from the point of view of
chiral symmetry restoration at high temperature and baryon chemical potential.
We compute analytically the effective potential in the high- and
low-temperature approximations up to sixth order, including the contribution of
the ring diagrams to account for the plasma screening properties. We determine
the model parameters, namely, the couplings and mass-parameter, from conditions
valid at the first order phase transition at vanishing temperature and, using
the Hagedorn limiting temperature concept applied to finite baryon density, for
a critical baryochemical potential of order of the nucleon mass. We show that
when using the set of parameters thus determined, the second order phase
transition line (our proxy for the crossover transition) that starts at finite
temperature and zero baryon chemical potential converges to the line of first
order phase transitions that starts at zero temperature and finite baryon
chemical potential to determine the critical end point to lie in the region
$5.02<\mu_B^{\mbox{CEP}}/T_c<5.18$, $0.14<T^{\mbox{CEP}}/T_c<0.23$, where $T_c$
is the critical transition temperature at zero baryon chemical potential.
