The Efficient Contour of the Inverse Mellin Transformation for the Non-Singlet Structure Functions

Abstract

We estimate the accuracy of the reconstruction of the structure function xF₃(x,Q²) and the non-singlet combination for the fragmentation function \(D_{u_v }^{\pi ^ + } \) (z, Q²) used in description of the deep inelastic scattering by the Mellin inverse transformation method with the parabolic shape of contour running from the saddle point proposed by Kosower. We demonstrate the applicability of this contour calculated at some fixed value of momentum transfer squared Q²₀ for the evaluation of the non-singlet structure functions at any experimental Q² values.