Local chiral potentials and the structure of light nuclei

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them 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 long-range part of these local potentials includes one- and two-pion exchange contributions without and with \(\Delta\)-isobars in the intermediate states up to order \(Q^3\) (\(Q\) denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order \(Q^4\). 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.