Relativity constraints on the two-nucleon contact interaction

We construct the most general, relativistically invariant, contact Lagrangian at order Q² in the power counting, with Q denoting the low momentum scale. A complete, but nonminimal, set of (contact) interaction terms is identified, which upon nonrelativistic reduction generate two leading independent operator combinations of order Q⁰ and seven subleading ones of order Q²---a result derived previously in the heavy-baryon formulation of effective field theories (EFTs). We show that Poincar\'e covariance of the theory requires that additional terms with fixed coefficients be included, to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number $A>2$, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.