  In line with some previous works, we study in this paper the meson spectrum
in the framework of a second order quark-antiquark Bethe-Salpeter formalism
which includes confinement. An analytic one loop running coupling constant
alpha_s(Q), as proposed by Shirkov and Sovlovtsov, is used in the calculations.
As for the quark masses, the case of a purely phenomenological running mass for
the light quarks in terms of the c. m. momentum is further investigated.
Alternatively a more fundamental expression m_P(Q) is introduced for light and
strange quarks, combining renormalization group and analyticity requirements
with an approximate solution of the Dyson-Schwinger equation. The use of such
running coupling constant and masses turns out to be essential for a correct
reproduction of the the light pseudoscalar mesons.
