Large-N_c Quark Distributions in the Delta and Chiral Logarithms in Quark Distributions of the Nucleon

Abstract

In a world with two quark flavors and a large number of colors (N_c), the polarized and unpolarized quark distributions in the delta are completely determined by those in the nucleon up to {\cal O}(1/N_c). In particular, we find q_{\Delta}(x) =[(1\pm 2T_z)u_N(x)+ (1\mp 2T_z)d_N(x)]/2 and \Delta q_\Delta(x) =[(5\pm 2T_z)\Delta u_N(x) + (5\mp 2T_z)\Delta d_N(x)]/10, where q = u, d and $T_z$ the charge state of a delta. The result can be used to estimate the leading chiral-logarithmic corrections to the quark distributions in the nucleon.