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The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\) and transversity. (English) Zbl 1325.81168
Summary: We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\) in the asymptotic region \(\mathrm{Q}^{\mathrm{2}} \gg \mathrm{m}^{\mathrm{2}}\) and the associated operator matrix element \(A_{q q, Q}^{(\mathrm{3}), \mathrm{NS}}(N)\) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable \(N\). This matrix element is associated with the vector current and axial vector current for the even and the odd moments \(N\), respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to \(\mathrm{O}(\mathrm{N}_{\mathrm{F}})\) and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in \(N\) space and harmonic polylogarithms in \(x\)-space. Numerical results are presented for the non-singlet charm quark contribution to \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\).

MSC:
81V05 Strong interaction, including quantum chromodynamics
81U35 Inelastic and multichannel quantum scattering
81T18 Feynman diagrams
11G55 Polylogarithms and relations with \(K\)-theory
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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