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We use an S-wave toy model for the two-nucleon system to show that theimplicit renormalization of a contact theory matches the explicitrenormalization through a flow equation which integrates out the high momentumcomponents. By fitting the low-momentum interaction with a new contact theory,we show that the running of the contact strengths in both original and fittedcontact theories match over a wide cutoff range.

Implicit vs Explicit renormalization of the $NN$ force