Chiral Odd Structure Functions from a Chiral Soliton

We calculate the chiral odd quark distributions and the corresponding structure functions $h_T(x,Q^2)$ and $h_L(x,Q^2)$ within the Nambu-Jona-Lasinio chiral soliton model for the nucleon. The $Q^2$ evolution of the twist-2 contributions is performed according to the standard GLAP formalism while the twist-three piece, ${\bar{h}}_L(x)$, is evolved according to the large $N_C$ scheme. We carry out a comparison between the chiral odd structure functions of the proton and the neutron. At the low model scale ($Q_0^2$) we find that the leading twist effective quark distributions,$f_1^{(q)}(x,Q_0^2)$, $g_1^{(q)}(x,Q_0^2)$ and $h_T^{(q)}(x,Q_0^2)$ satisfy Soffer’s inequality for both quark flavors $q=u,d$.