We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities, and Poincaré covariance. The resulting interaction, depending on 10 unknown low-energy constants, leads to a three-nucleon potential which we give in a local form in configuration space. We also consider the leading (no-derivative) four-nucleon interaction and show that there exists only one independent operator.

• Received 23 February 2011

DOI:https://doi.org/10.1103/PhysRevC.84.014001