The Constituent Quark Limit and the Skyrmion Limit of the Chiral Quark Soliton Model

Abstract

We calculate $g_A^3$ and $g_A^0$ in the Chiral Quark-Soliton Model (or equivalently in semibosonized Nambu--Jona-Lasinio model) in the limit of small and large soliton size. In small soliton limit we recover the results of the Constituent Quark Model. The agreement between the two models is achieved due to the recently calculated $1/\Nc$ contributions to $g_A^3$ and to $g_A^0$. In the case of $g_A^3$ these terms arise from the {\it time-ordering} of the collective operators. For large solitons simple scaling arguments show that the $1/\Nc$ contributions vanish with the inverse power of the soliton size.