Parity-violating two-pion exchange nucleon-nucleon interaction

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 with those from diagrams with only nucleon intermediate states. The reason for this behavior, which is opposite that of 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.