  We present a study of the one dimensional Su-Schrieffer-Heeger model
Hamiltonian by a diagrammatic perturbative method in the weak electron-phonon
coupling regime. Exact computation of both the charge carrier effective mass
and the electron spectral function shows that electrons are good quasiparticles
in the adiabatic and antiadiabatic limits but novel features emerge in the
intermediate regime, where the phonons and the electrons compare on the energy
scale. Together with a sizeable mass enhancement we observe, in the latter
regime, a spread of the spectral weight (among several transition peaks)
associated with an increased relevance of multiphonons contributions at larger
{\it e-ph} couplings. Accordingly electrons cease to be the good quasiparticles
and an onset of polaron formation is favoured.
