Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory

We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable description of the phase shifts can only be obtained with a particular cutoff. Furthermore, we compare the so-obtained nonperturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic nonperturbative TPE are more moderate than those from the nonrelativistic TPE obtained in the dimensional regularization scheme. A proper convergence pattern is observed for most of the partial waves studied except for $^3F_3$, $^3F_4$, and $^3H_6$, for which the subleading TPE contributions are a bit strong. We find that for $H$ and $I$ partial waves, the OPE alone can already describe the phase shifts reasonably well.