The Complete $O(\alpha_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{ u(\bar{ u})}(x,Q^2)$ and the Associated Sum Rules

摘要

We calculate analytically the flavor non-singlet $O(\alpha_s^2)$ massiveWilson coefficients for the inclusive neutral current non-singlet structurefunctions $F_{1,2,L}^{ep}(x,Q^2)$ and $g_{1,2}^{ep}(x,Q^2)$ and charged currentnon-singlet structure functions $F_{1,2,3}^{\nu(\bar{\nu})p}(x,Q^2)$, atgeneral virtualities $Q^2$ in the deep-inelastic region. Numerical results arepresented. We illustrate the transition from low to large virtualities forthese observables, which may be contrasted to basic assumptions made in theso-called variable flavor number scheme. We also derive the correspondingresults for the Adler sum rule, the unpolarized and polarized Bjorken sum rulesand the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections atlarge scales $Q^2$ and the effects of the power corrections due to the heavyquark mass are of the size of the known $O(\alpha_s^4)$ corrections in the caseof the sum rules. The complete charm and bottom corrections are compared to theapproach using asymptotic representations in the region $Q^2 \gg m_{c,b}^2$. Wealso study the target mass corrections to the above sum rules.