Momentum dependent nucleon-nucleon contact interaction from a relativistic Lagrangian

A complete set of parity- and time-reversal conserving relativistic nucleon-nucleon contact operators is identified up to the order O(p4) of the expansion in soft momenta p. A basis is also provided for the corresponding non-relativistic operators contributing in the general reference frame. We show that the non-relativistic expansions of the relativistic operators involve twenty-six independent combinations, two starting at O(p0), seven at order O(p2) and seventeen at order O(p4) . This gives supporting evidence to the existence of two free low-energy constants which parametrize an interaction depending on the total nucleon pair momentum P, and were recently found to be instrumental for the resolution of the long standing Ay problem in low-energy p-d scattering. Furthermore, all remaining P-dependent interactions at the same order are uniquely determined as relativistic corrections.