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Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions

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arxiv 2505.09381 v1 pith:UF4YLUNJ submitted 2025-05-14 hep-ph

B.A. Kniehl , S. Moch , V.N. Velizhanin (U. Hamburg) , A. Vogt (Liverpool U. , Dept. Math.) This is my paper · ORCID
classification hep-ph
keywords functionscontributionssplittinglimitlogarithmsquarksmall-space
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We have determined the fourth-order $n_f$ contributions to the two splitting functions governing the evolution of all flavor differences of quark distributions of hadrons in perturbative quantum chromodynamics with $n_f$ light flavors. The analytic forms of these functions are presented in both Mellin $N$-space and momentum-fraction $x$-space for a general gauge group. In the small-$x$ limit double logarithms occur, but the small-$x$ rise of both splitting functions is confined to extremely small $x$-values, $x \lesssim 10^{-6}$. The large-$x$ limit includes the $n_f$-part of the four-loop quark virtual anomalous dimension. Using this result we obtain also the $n_f$ contributions to the corresponding gluonic quantity and the complete threshold-enhanced logarithms from soft-gluon emission for a large class of inclusive observables, including Higgs boson production in gluon-gluon fusion.

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Cited by 6 Pith papers

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