A
bstract
We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions
F
2
(
x, Q
2
)
, F
L
(
x, Q
2
)
, xF
3
(
x, Q
2
) in the
MS
¯
scheme ...and the polarized Wilson coefficients of the structure function
g
1
(
x, Q
2
) in the Larin scheme up to three-loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial-vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three-loop Wilson coefficients are calculated for the first time. As a by-product we also obtain the quarkonic three-loop anomalous dimensions from the
O
(1
/ε
) terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable
x
are provided.
We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an ...alphabet where its structure is implied by the coefficient matrix of the differential equations. These systems appear in a large variety of higher order calculations in perturbative Quantum Field Theories. We apply this method to calculate the master integrals of the three-loop massive form factors for different currents, as an illustration, and present the results for the vector form factors in detail. Here the solution space emerging is given by the cyclotomic harmonic polylogarithms and their associated special constants. No special basis representation of the master integrals is needed. The algorithm can be applied as well to more general cases factorizing at first order, which are based on more general alphabets, iterated integrals and associated constants.
We consider determinations of the strange sea in the nucleon based on QCD analyses of data collected at the LHC with focus on the recent high-statistics ATLAS measurement of the W±- and Z-boson ...production. We study the effect of different functional forms for parameterization of the parton distribution functions and the combination of various data sets in the analysis. We compare to earlier strange sea determinations and discuss ways to improve them in the future.
We compute the non-singlet nh terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This ...method has the advantage, that the master integrals have to be dealt with only in their moment representation, allowing to also consider quantities which obey differential equations, which are not first order factorizable (elliptic and higher), already at this level. To obtain all the associated recursions, up to 8000 moments had to be calculated. A new technique has been applied to solve the associated differential equation systems. Here the decoupling is performed such, that only minimal depth ε–expansions had to be performed for non–first-order factorizing systems, minimizing the calculation of initial values. The pole terms in the dimensional parameter ε can be completely predicted using renormalization group methods, as confirmed by the present results. A series of contributions at O(ε0) have first order factorizable representations. For a smaller number of color–zeta projections this is not the case. All first order factorizing terms can be represented by harmonic polylogarithms. We also obtain analytic results for the non–first-order factorizing terms by Taylor series in a variable x, for which we have calculated at least 2000 expansion coefficients, in an approximation. Based on this representation the form factors can be given in the Euclidean region and in the region q2≈0. Numerical results are presented.
We review the present status of the determination of parton distribution functions (PDFs) in the light of the precision requirements for the LHC in Run 2 and other future hadron colliders. We provide ...brief reviews of all currently available PDF sets and use them to compute cross sections for a number of benchmark processes, including Higgs boson production in gluon–gluon fusion at the LHC. We show that the differences in the predictions obtained with the various PDFs are due to particular theory assumptions made in the fits of those PDFs. We discuss PDF uncertainties in the kinematic region covered by the LHC and on averaging procedures for PDFs, such as advocated by the PDF4LHC15 sets, and provide recommendations for the usage of PDF sets for theory predictions at the LHC.
We present the scheme-invariant unpolarized and polarized flavor non–singlet evolution equation to N3LO for the structure functions F2(x,Q2) and g1(x,Q2) including the charm- and bottom quark effects ...in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non–singlet structure functions at a starting scale Q02. In this way the evolution does only depend on the strong coupling constant αs(MZ) or the QCD scale ΛQCD and the charm and bottom quark masses mc and mb and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep–inelastic scattering experiments. The yet unknown parts of the 4–loop anomalous dimensions introduce only a marginal error in this analysis.
We calculate the unpolarized twist-2 three-loop splitting functions Pqg(2)(x) and Pgg(2,NF)(x) and the associated anomalous dimensions using massive three-loop operator matrix elements. While we ...calculate Pgg(2,NF)(x) directly, Pqg(2)(x) is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.
We calculate the polarized massive two–loop pure singlet Wilson coefficient contributing to the structure functions g1(x,Q2) analytically in the whole kinematic region. The Wilson coefficient ...contains Kummer–elliptic integrals. We derive the representation in the asymptotic region Q2≫m2, retaining power corrections, and in the threshold region. The massless Wilson coefficient is recalculated. The corresponding twist–2 corrections to the structure function g2(x,Q2) are obtained by the Wandzura–Wilczek relation. Numerical results are presented.
An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer–Poincaré letters is presented. These quantities emerge in analytic single and ...multiscale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities.
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