Higher moments of nucleon spin structure functions in heavy baryon chiral perturbation theory and in a resonance model

The third moment $d_2$ of the twist-3 part of the nucleon spin structure function $g_2$ is generalized to arbitrary momentum transfer $Q^2$ and is evaluated in heavy baryon chiral perturbation theory (HBChPT) up to order ${\mathcal{O}}(p^4)$ and in a unitary isobar model (MAID). We show how to link $d_2$ as well as higher moments of the nucleon spin structure functions $g_1$ and $g_2$ to nucleon spin polarizabilities. We compare our results with the most recent experimental data, and find a good description of these available data within the unitary isobar model. We proceed to extract the twist-4 matrix element $f_2$ which appears in the $1/Q^2$ suppressed term in the twist expansion of the spin structure function $g_1$ for proton and neutron.