Target Mass Corrections to the Spin-dependent Structure Functions

At the energies at which most data in polarized deep-inelastic scattering have been taken the ratio M/Q, where M is the mass of the nucleon, is not negligible. The target mass corrections should be taken into account to analyze the Q dependence of structure functions at low Q and to extract information of dynamical higher twist effects at moderate energies. We calculated the target mass corrections for spin dependent structure functions (SF) both for neutral and charged current interactions using the operator product expansion in lowest order in QCD. In this paper we present only the twist-2 contribution to the structure functions. We considered the light-cone expansion of the forward Compton amplitude in momentum space. Using the corresponding dispersion relations [2] the moments of structure functions can be expressed by the xmatrix elements of twist-2 operators. The target mass effects are calculated using the method proposed by Georgi and Politzer [3]. Following this way we expressed the moments of the SF as series of (M/Q) and functions of reduced operator matrix elements. After performing the inverse Mellin transform we get the following expressions for the SF: