The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function F2(x,Q2) and the corresponding transition matrix element AQq(3),PS in the ...variable flavor number scheme are computed. In Mellin-N space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function F2(x,Q2) are presented.
We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from nf = 3 light flavors in the fixed-flavor-number (FFN) scheme ...and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in Q2 / m2h, the ratio of the virtuality of the exchanged gauge boson Q 2 to the heavy-quark mass squared m2h. Little impact of resummation effects is found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small Q2
The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For ...the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈0,∞ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈0,1 at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.
We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in ...perturbative QCD. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for all first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.
We present an improved determination of the up- and down-quark distributions in the proton using recent data on charged lepton asymmetries from W± gauge-boson production at the LHC and Tevatron. The ...analysis is performed in the framework of a global fit of parton distribution functions. The fit results are consistent with a nonzero isospin asymmetry of the sea, x(d¯−u¯), at small values of Bjorken x∼10−4 indicating a delayed onset of the Regge asymptotics of a vanishing (d¯−u¯)-asymmetry at small x. We compare with up- and down-quark distributions available in the literature and provide accurate predictions for the production of single top-quarks at the LHC, a process which can serve as a standard candle for the light quark flavor content of the proton.
In the asymptotic limit Q2 ≫ m2, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only ...govern the structure of infrared divergences but also control the high energy logarithms. This enables us to obtain the complete logarithmic three-loop and partial four-loop contributions to the heavy quark form factors in perturbative quantum chromodynamics.
We calculate all contributions ∝TF to the polarized three–loop anomalous dimensions in the M–scheme using massive operator matrix elements and compare to results in the literature. This includes the ...complete anomalous dimensions γqq(2),PS and γqg(2). We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γqg(2). Due to the necessity of deeper expansions of the master integrals in the dimensional parameter ε=D−4, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions ∝TF to the three–loop QCD β–function.
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