Comparison of two possible nuclear effective field theory expansions around the one- and two-pion exchange potentials

In the effective field theory formalism nuclear forces are organized as a low-energy expansion. Usually the lowest order in this expansion corresponds to the nonperturbative iteration of the one-pion exchange potential and a few contact-range operators as to ensure renormalization group invariance. Here I consider an alternative expansion in which two-pion exchange becomes the lowest-order finite-range interaction and as such is expected to be iterated. A comparison of this new expansion with the standard one shows a better convergence pattern for a few selected partial waves (1S0, 3P0, and 3S1 - 3D1) in two-nucleon scattering, in particular for the 1S0 channel (though both expansions converge well). I briefly comment on the possible theoretical grounds for the expansion around two-pion exchange from the point of view of effective field theory.