Neutron-proton mass-splitting puzzle in Skyrme and chiral quark models

Abstract

The nonelectromagnetic part of the $n-p$ mass difference is known to vanish in the Skyrme model of pions. This result is shown to hold when the model is extended to include an isoscalar $0^{-}$ field. However the inclusion of vector mesons to describe "short-distance" effects enables the isoscalar $0^{-}$ field to contribute and this explains most of the $n-p$ splitting in a two-flavor model. To carry out the analysis we make a detailed study of chiral-symmetry breaking in the pseudoscalar-vector Lagrangian. The contribution due to the strange constituents of the nucleon is also estimated. The sum of the two contributions is shown to be sufficient to explain the experimental number. Another way to discuss "short distance" effects is the explicit inclusion of quark degrees of freedom via the "chiral quark model." We show that this can also give rise to nonzero $n-p$ splitting.