Local chiral potentials with $\Delta$-intermediate states and the structure of light nuclei

We present a fully local nucleon-nucleon potential in chiral effective field theory ($\chi$EFT) retaining pions, nucleons and $\Delta$-isobars as explicit degrees of freedom, and use it in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The calculation of the potential is carried out by including one- and two-pion-exchange contributions up to next-to-next-to-leading order (N2LO) and contact interactions up to next-to-next-to-next-to-leading order (N3LO). The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.