The complete O(\alpha_s^2) non-singlet heavy flavor corrections to the structure functions g_{1,2}^{ep}(x,Q^2), F_{1,2,L}^{ep}(x,Q^2), F_{1,2,3}^{\nu(\bar{\nu})}(x,Q^2) and the associated sum rules

We calculate analytically the flavor non-singlet O(αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep(x,Q2) and g1,2ep(x,Q2) and charged current non-singlet structure functions F1,2,3ν(ν¯)p(x,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross–Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O(αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2≫mc,b2. We also study the target mass corrections to the above sum rules.