Statistical learnability of nuclear masses

After more than 80 years from the seminal work of Weizsäcker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models (~MeV) are orders of magnitude larger than experimental errors (~keV). Predicting the mass of atomic nuclei with precision is extremely challenging. This is due to the nontrivial many-body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. Statistical theory of learning will be used to provide the bounds to prediction errors of a model trained with a finite data set. These bounds are validated with neural network models and compared with state of the art mass models. It will be argued that nuclear structure mass models explore a system on the limit of the precision bounds, as defined by the statistical theory of learning