Two-pion exchange as a leading-order contribution in chiral effective field theory

Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one-pion exchange (OPE) enters at leading order in chiral effective field theory. In the L-2S+1(J) = S-1(0) partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum Lambda(b) approximate to 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two-pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the S-1(0) partial wave. We demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs Lambda less than or similar to 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the Delta isobar degree of freedom in the potential does not change the strong contributions of TPE.