Parity and time-reversal violating nuclear forces with explicit $$\Delta $$-excitations

We emphasize the usefulness of treating delta resonances as explicit degrees of freedom in applications of chiral effective field theory (EFT) to parity-violating and time-reversal-violating (PVTV) nuclear interactions. Compared with the delta-less framework, the explicit inclusion of the delta isobar allows one to resum certain types of contributions to the PVTV two-pion exchange two- and three-nucleon potentials without at the same time introducing any unknown parameters up to next-to-next-to-leading order in the EFT expansion. We provide the corresponding expressions for the delta contributions in momentum and coordinate spaces and compare the convergence of the EFT expansion in both formulations.