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We present an analysis of the $xF_3(x,Q^2)$ structure function andGross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects andhigher twist correction. This analysis is based on the results presented in "N.M. Nath et al., Indian J Phys 90(1), 117 (2016)". The corrections due tonuclear effects predicted in several earlier analysis are incorporated to ourresults of $xF_3(x,Q^2)$ structure function and GLS sum rule for free nucleon,corrected upto next-next-to-leading order (NNLO) perturbative order andcalculate the nuclear structure function as well as sum rule for nuclei. Inaddition, by means of a simple model we have extracted the higher twistcontributions to the non-singlet structure function $xF_3(x,Q^2)$ and GLS sumrule in NNLO perturbative orders and then incorporated them to our results. OurNNLO results along with nuclear effect and higher twist corrections areobserved to be compatible with corresponding experimental data and otherphenomenological analysis.

$xF_3(x,Q^2)$ Structure Function and Gross-Llewellyn Smith Sum Rule with Nuclear Effect and Higher Twist Correction