How to obtain the correct neutron-proton mass difference

Abstract

We have calculated the inelastic contribution to the p-n mass difference as well as the elastic one, by using the Cottingham formula. It is found out that, in order to get the correct sign of the p-n mass difference, the ratio of the longitudinal to transverse cross sections, R(q 2) , must be smaller than 2, and that (2 - R(q 2 ) W p-n 1( ω, q 2) → 0 as q 2 → ∞ is required to ensure a finite p-n mass difference. Numerical calculations have been carried out by assuming the appropriate forms for R( q 2) and W p-n 1 ( ω, q 2). The model in which a photon couples to a parton via a heavy vector meson is considered as an example, and we get the result that the mass of this vector meson may be about 150 times the nucleon mass in order to get the correct p-n mass difference, −1.29 MeV.