Abstract
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.
Highlights
Deep-inelastic scattering provides one of the most direct methods to measure the strong coupling constant from precision data on the scaling violations of the nucleon structure functions [1, 2].The present accuracy of these data allows to measure the mass of the charm, cf. [3], and bottom quarks due to the heavy flavor contributions
In the following we discuss the corrections to the Adler sum rule [23], which have to vanish, and calculate the corrections to the polarized Bjorken sum rule [25], the unpolarized Bjorken sum rule [24], and the Gross-Llewellyn Smith sum rule [26], which are obtained as the first moments of the massive Wilson coefficients calculated in the previous sections
For the charged current non-singlet combinations of structure functions the Cabibbo suppressed Wilson coefficient Hi,q contributes, which we have considered in the asymptotic region starting at O(a2s) as an approximation
Summary
Deep-inelastic scattering provides one of the most direct methods to measure the strong coupling constant from precision data on the scaling violations of the nucleon structure functions [1, 2]. The heavy flavor contribution to inclusive deep-inelastic structure functions are described by five Wilson coefficients in the case of pure photon exchange [8,9,10]. Four out of five Wilson coefficients contributing to the unpolarized deep inelastic structure functions have been calculated to 3-loop order for general values of Mellin N [12, 14, 15] in the asymptotic region Q2 m2. In the flavor non-singlet case the asymptotic 3-loop contributions to the combinations of the polarized structure functions g1N(S2) [16] and the unpolarized charged current structure function xF3νp + xF3νp have been computed [17]. We calculate the complete 2-loop non-singlet heavy flavor corrections to the deep inelastic charged current structure functions F1ν,p2,3 and the neutral current structure functions.
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