We compute the binding energy of triton with realistic statistical errors stemming from NN scattering data uncertainties and the deuteron and obtain $E_t=-7.638(15) , {rm MeV}$. Setting the numerical precision as $Delta E_t^{rm num} lesssim 1 , {rm k
eV}$ we obtain the statistical error $Delta E_t^{rm stat}= 15(1) , {rm keV}$ which is mainly determined by the channels involving relative S-waves. This figure reflects the uncertainty of the input NN data, more than two orders of magnitude larger than the experimental precision $Delta E_t^{rm exp}= 0.1 , {rm keV}$ and provides a bottleneck in the realistic precision that can be reached. This suggests an important reduction in the numerical precision and hence in the computational effort.
We estimate the expected errors of nuclear matrix elements coming from the uncertainty on the NN interaction. We use a coarse grained (GR) interaction fitted to NN scattering data, with several prescriptions for the long-part of the interaction, incl
uding one pion exchange and chiral two-pion exchange interactions.
