  The potential in coordinate space for the $\Lambda N\to NN$ weak transition,
which drives the weak decay of most hypernuclei, is derived within the
effective field theory formalism up to next-to-leading order. This coordinate
space potential allows us to discuss how the different contributions to the
potential add up at the different scales. Explicit expressions are given for
each two-pion-exchange diagram contributing to the interaction. The potential
is also reorganized into spin and isospin operators, and the coefficient for
each operator is given in analytical form and represented in coordinate space.
The relevance of explicitly including the mass differences among the baryons
appearing in the two-pion-exchange diagrams is also discussed in detail.
