Two-pion exchange contributions to the relativistic chiral nuclear force at N$^3$LO

TL;DR

This paper calculates two-pion exchange contributions to the nucleon-nucleon interaction at N$^3$LO using covariant baryon chiral perturbation theory, showing improved phase shift agreement and convergence over previous models.

Contribution

It provides a detailed calculation of two-pion exchange at N$^3$LO in a relativistic framework, highlighting the significance of relativistic effects in nuclear force modeling.

Findings

Better agreement with phase shift analyses for certain partial waves.

Relativistic chiral force shows improved convergence.

Relativistic corrections are important for accurate nuclear interactions.

Abstract

We present the two-pion exchange contributions to the nucleon-nucleon interaction up to next-to-next-to-next-to leading order (N$^3$LO) in covariant baryon chiral perturbation theory. Both one-loop and two-loop diagrams are calculated with the spectral functional regularization. We show that the phase shifts for partial waves with total angular momentum $3\le J\le 5$ are in better agreement with the partial wave analysis from the Nijmegen or the SAID group than their N$^2$LO counterparts. In addition, the relativistic chiral force exhibits better convergence than its non-relativistic counterpart, suggesting the importance of relativistic corrections.