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

Abstract

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 2S+1 LJ = 1 S0 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 Λ b ≈ 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 1 S0 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 Λ 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the ∆ isobar degree of freedom in the potential does not change the strong contributions of TPE.

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

“…Recently Ref. [22] has consider this expansion as a possible organizing principle for the 1 S 0 singlet, leading to results which we agree with here.…”

“…Actually, this idea was already explored in the past [16,21], though usually not in the context of building a serious EFT expansion around it (except in [22]). In the Weinberg counting, scattering amplitudes are obtained from iterating the full effective potential with a finite cutoff.…”