Nuclear Effects In The F_3 Structure Function For Finite And Asymptotic Q^2

We study nuclear effects in the structure function F_3 which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of Q^{-2} series caused by nuclear effects ("nuclear twist" series). Basing on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F_3. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q^{-2} correction. Special attention is payed to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on Q^2- and x-dependence of nuclear structure functions is found.