Chiral-Odd Twist-3 Distribution Function $e(x)$
  We clarify the nonperturbative origin of the $\delta$-function singularity at $x = 0$ in the chiral-odd twist-3 distribution function $e(x)$ of the nucleon. We also compare a theoretical prediction for $e(x)$ based on the chiral quark soliton model with the empirical information extracted from the CLAS semi-inclusive DIS measurement. 
M. Wakamatsu and Y. Ohnishi