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

We calculate the non-perturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the non-perturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the non-perturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the non-perturbative 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 non-perturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic non-perturbative TPE are more moderate than those from the non-relativistic 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.