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We consider the $\Lambda N\to NN$ weak transition, responsible for a largefraction of the non-mesonic weak decay of hypernuclei. We follow on thepreviously derived effective field theory and compute the next-to-leadingone-loop corrections. Explicit expressions for all diagrams are provided, whichresult in contributions to all relevant partial waves.

One-loop contributions in the EFT for the $\Lambda N \to NN$ transition