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 ${}^{2S+1}{L}_J={}^1{S}_0$ 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 of about 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 ${}^1{S}_0$ 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 below about 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.

8 pages, 8 figures

References in corpus (15)

• Chiral effective field theory and nuclear forces
• Accurate nuclear radii and binding energies from a chiral interaction
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• Light nuclei with semilocal momentum-space regularized chiral interactions up to third order
• Short-range nuclear forces in singlet channels
• Power Counting of Contact-Range Currents in Effective Field Theory
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Power counting in chiral effective field theory and nuclear binding
• Hidden spin-isospin exchange symmetry
• Sigma exchange in the nuclear force and effective field theory
• Deconstructing 1S0 nucleon-nucleon scattering
• Nuclear Structure at the Crossroads
• Chiral potentials, perturbation theory, and the 1S0 channel of NN scattering

Cited by in corpus (5)

• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N${}^3$LO
• Renormalization of proton-proton fusion in chiral effective field theory
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO
• Enhancement of deltaful two-pion exchange nuclear forces