Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances

In this study, we construct a coordinate-space chiral potential, including Δ-isobar intermediate states in its two-pion-exchange component up to order Q3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q2 and Q4, respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constant multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a Χ2 /datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, RL and RS respectively, ranging from (RL,RS)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.