  We present a novel analysis of the $\pi N$ scattering amplitude in Lorentz
covariant baryon chiral perturbation theory renormalized in the
extended-on-mass-shell scheme. This amplitude, valid up to $\mathcal{O}(p^3)$
in the chiral expansion, systematically includes the effects of the
$\Delta(1232)$ in the $\delta$-counting, has the right analytic properties and
is renormalization-scale independent. This approach overcomes the limitations
that previous chiral analyses of the $\pi N$ scattering amplitude had,
providing an accurate description of the partial wave phase shifts of the
Karlsruhe-Helsinki and George-Washington groups up to energies just below the
resonance region. We also study the solution of the Matsinos group which
focuses on the parameterization of the data at low energies. Once the values of
the low-energy constants are determined by adjusting the center-of-mass energy
dependence of the amplitude to the scattering data, we obtain predictions on
different observables. In particular, we extract an accurate value for the
pion-nucleon sigma term, $ \sigma_{\pi N}$. This allows us to avoid the usual
method of extrapolation to the unphysical region of the amplitude. Our study
indicates that the inclusion of modern meson-factory and pionic-atom data
favors relatively large values of the sigma term. We report the value
$\sigma_{\pi N}=59(7)$MeV and comment on implications that this result may
have.
