Unpolarized and polarized quark distributions in the large-Nclimit

The isosinglet unpolarized and isovector polarized twist-2 quark distributions of the nucleon at low normalization point are calculated in the large-$N_c$ limit. The nucleon is described as a soliton of the effective chiral theory. We derive the expressions for the distribution functions in the large-$N_c$ limit starting from their definition as numbers of partons carrying a momentum fraction $x$ in the infinite momentum frame. We develop a numerical method for computation of the quark and antiquark distributions as sums over the quark single-particle levels in the pion field of the soliton. The contributions of the discrete bound-state level as well as the Dirac continuum are taken into account. The quark and antiquark distributions obtained explicitly satisfy all general requirements. The results are in reasonable agreement with parametrizations of the data at a low normalization point.