  We study baryon-baryon scattering by applying time-ordered perturbation
theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral
perturbation theory. We derive the corresponding diagrammatic rules paying
special attention to complications caused by momentum-dependent interactions
and propagators of particles with non-zero spin. We define the effective
potential as a sum of two-baryon irreducible contributions of time-ordered
diagrams and derive a system of integral equations for the scattering
amplitude, which provides a coupled-channel generalization of the Kadyshevsky
equation. The obtained leading-order baryon-baryon potentials are
perturbatively renormalizable, and the corresponding integral equations have
unique solutions in all partial waves. We discuss the issue of additional
finite subtractions required to improve the ultraviolet convergence of (finite)
loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$
partial wave. Assuming that corrections beyond leading order can be treated
perturbatively, we obtain a fully renormalizable formalism which can be
employed to study baryon-baryon scattering.
