Parity-violating two-pion exchange nucleon-nucleon interaction

TL;DR

This paper calculates the parity-violating two-pion exchange nucleon-nucleon potentials using chiral perturbation theory, revealing their relative size compared to one-pion exchange and analyzing effects involving delta-isobars, with implications for nuclear observables.

Contribution

It provides the first leading-order calculation of parity-violating two-pion exchange potentials in chiral perturbation theory, including effects of delta-isobar excitation.

Findings

Two-pion exchange potentials are about 16% of one-pion exchange at 1.4 fm.

Delta-isobar effects are smaller than nucleon-only diagrams.

Results can be integrated into parity-violating nuclear observable calculations.

Abstract

We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of $r= m_\pi^{-1} \simeq 1.4 $fm they amount to about $\pm 16%$ of the parity-violating $1\pi$-exchange potential. We evaluate also the parity-violating effects arising from $2\pi$-exchange with excitation of virtual $\Delta(1232)$-isobars. These come out to be relatively small in comparison to those from diagrams with only nucleon intermediate states. The reason for this opposite behavior to the parity-conserving case is the blocking of the dominant isoscalar central channel by CP-invariance. Furthermore, we calculate the T-matrix related to the iteration of the parity-violating $1\pi$-exchange with the parity-conserving one. The analytical results presented in this work can be easily implemented into calculations of parity-violating nuclear observables.