A quark model analysis of the charge symmetry breaking in nuclear force

In order to investigate the charge symmetry breaking (CSB) in the short range part of the nuclear force, we calculate the difference of the masses of the neutron and the proton, $\Delta {\rm M}$, the difference of the scattering lengths of the p-p and n-n scatterings, $\Delta a$, and the difference of the analyzing power of the proton and the neutron in the n-p scattering, $\Delta A(\theta)$, by a quark model. In the present model the sources of CSB are the mass difference of the up and down quarks and the electromagnetic interaction. We investigate how much each of them contributes to $\Delta {\rm M}$, $\Delta a$ and $\Delta A(\theta)$. It is found that the contribution of CSB of the short range part in the nuclear force is large enough to explain the observed $\Delta A(\theta)$, while $\Delta a$ is rather underestimated.