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Volume 297 - XXV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2017) - WG1 Structure Functions and Parton Densities
The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCD
J. Davies
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Pre-published on: 2017 December 29
Published on: 2018 January 16
These proceedings describe a computation of the large-$n_f$ terms contributing to the QCD splitting functions at the fourth order in the strong coupling constant $\alpha_s$. Using the FORCER package for the reduction of four-loop two-point Feynman integrals, Mellin moments of the four-loop splitting functions have been computed. These moments are used to derive analytic Mellin-space expressions, by forming and finding solutions to systems of Diophantine equations. Expressions for the terms proportional to $n_f^{\,3}$ of the flavour singlet, and to $n_f^{\,2}$ of the flavour non-singlet splitting functions have been determined.
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