Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| author | Kniehl, B. A. Moch, S. Velizhanin, V. N. Vogt, A. |
| author_facet | Kniehl, B. A. Moch, S. Velizhanin, V. N. Vogt, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions Kniehl, B. A. Moch, S. Velizhanin, V. N. Vogt, A. High Energy Physics - Phenomenology 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. |
| title | Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.09381 |