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

TL;DR

This paper calculates two-pion exchange contributions to nucleon-nucleon interactions using covariant baryon chiral perturbation theory, showing relativistic effects are moderate and improve convergence compared to nonrelativistic approaches.

Contribution

It provides a relativistic calculation of TPE contributions to NN interactions up to order O(p^3), comparing results with nonrelativistic methods to assess relativistic corrections.

Findings

Relativistic TPE contributions are more moderate than nonrelativistic ones.

Relativistic corrections are significant in F-waves, especially ^3F_2.

Results suggest faster convergence of relativistic calculations across partial waves.

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 $2\leq L\leq 6$ and mixing angles with $2\leq J\leq6$ 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.