Two-Pion-Exchange contributions to the nucleon-nucleon interactions in covariant baryon chiral perturbation theory

Abstract

Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2\le L\le 6$ and mixing angles with $2\le J\le 6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic corrections play an important role in F-waves especially the ${}^3{\text{F}}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the nonrelativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.

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• Relativistic chiral description of the ${}^1{S}_0$ nucleon-nucleon scattering
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory
• $Z_{cs}(3985)$ in next-to-leading-order chiral effective field theory -- the first truncation uncertainty analysis
• Study of the hidden charm $D{\bar{D}}^{\ast }$ interactions in chiral effective field theory
• Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases
• Reexamination of antinucleon-nucleon interactions in covariant chiral effective field theory
• Peripheral nucleon-nucleon scattering at next-to-next-to-leading order in SU(3) heavy baryon chiral perturbation theory
• Charge dependent nucleon-nucleon potentials in covariant chiral effective field theory