The Chiral odd distribution function h-1: IR renormalon contribution and alpha-s correction

The chiral-odd distribution function $h_1$ is discussed in the framework of the renormalon approach. Using a bag-model calculation for $h_1$, we calculate its intrinsic uncertainty due to renormalon poles. The result is given as a function of Bjorken-$x$ as well as for the first moments separately. We also extract the perturbative corrections to the first moments of $h_1$.