, no fit in order to extract the new unknowns has been performed. The different structures which appear in the obtained transition amplitude, involving spin, isospin and orbital degrees of freedom, produce sizable contributions to all relevant partial waves. To illustrate this fact, we have presented the potential in $r$ space corresponding to the different Feynman diagrams for the $^3S_1- ^3S_1$ partial wave. Box and cross-box diagrams are found to produce substantial contributions at distances of the order of 1 fm, larger than the ones corresponding to the one-pion-exchange and one-kaon-exchange mechanisms. In view of this result, it would be interesting to see if one-loop contributions play an equivalent role in other partial wave transitions, testing possible cancellations or enhancements that would leave the results for the decay rates either unchanged or modified. A complete analysis of the higher order terms would require a larger set of independent hypernuclear decay measurements and a more accurate measure of some observables, specially those related to the parity violating asymmetry for s-shell and p-shell hypernuclei. Moreover, it would be desirable to arrange for alternative experiments focused to obtain information on the weak $\Delta S=1$ interaction. A step in this direction was taken more than ten years ago by experimental groups at RCNP in Osaka (Japan) \[15,16\], by looking at the weak strangeness production reaction $np \to \Lambda
p$. Unfortunately, the small value for the cross-section for this process precluded the compilation of new data. We think that it is important to foster new experimental avenues of approaching the weak interaction among baryons in the strange sector, and even try to recover the Osaka experiment within the research plan of the new experimental facilities devoted to the study of strange systems.

To ease the use of the obtained EFT amplitudes, we have provided with the explicit analytic expressions for all diagrams which will in future work be implemented in the calcul