Four-Loop Gluon Anomalous Dimension of General Lorentz Spin: Transcendental Part
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910174742052864 |
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| author | Kniehl, B. A. Moch, S. -O. Velizhanin, V. N. Vogt, A. |
| author_facet | Kniehl, B. A. Moch, S. -O. Velizhanin, V. N. Vogt, A. |
| contents | We consider the anomalous dimension $γ_{gg}^{(3)}(N)$ of the twist-two gluon operator of arbitrary Lorentz spin $N$ in the quark flavor singlet sector of a general gauge theory at four loops and construct its contribution proportional to $ζ(3)$ in analytic form by applying the Lenstra-Lenstra-Lovász algorithm to the available low-$N$ moments. We exploit generalized Gribov-Liptov reciprocity, establish new self-tuning relations for the anomalous dimension matrix of the singlet sector, and inject information from $\mathcal{N}=1,4$ supersymmetric Yang-Mills theories. We also present the contribution to the rational part of $γ_{gg}^{(3)}(N)$ with color factor $C_F^2n_f^2$. Exact contributions to the four-loop splitting function $P_{gg}^{(3)}(x)$ hence resulting via inverse Mellin transformation help us to reduce theoretical uncertainties in scaling violations of parton distribution functions in QCD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Four-Loop Gluon Anomalous Dimension of General Lorentz Spin: Transcendental Part Kniehl, B. A. Moch, S. -O. Velizhanin, V. N. Vogt, A. High Energy Physics - Phenomenology We consider the anomalous dimension $γ_{gg}^{(3)}(N)$ of the twist-two gluon operator of arbitrary Lorentz spin $N$ in the quark flavor singlet sector of a general gauge theory at four loops and construct its contribution proportional to $ζ(3)$ in analytic form by applying the Lenstra-Lenstra-Lovász algorithm to the available low-$N$ moments. We exploit generalized Gribov-Liptov reciprocity, establish new self-tuning relations for the anomalous dimension matrix of the singlet sector, and inject information from $\mathcal{N}=1,4$ supersymmetric Yang-Mills theories. We also present the contribution to the rational part of $γ_{gg}^{(3)}(N)$ with color factor $C_F^2n_f^2$. Exact contributions to the four-loop splitting function $P_{gg}^{(3)}(x)$ hence resulting via inverse Mellin transformation help us to reduce theoretical uncertainties in scaling violations of parton distribution functions in QCD. |
| title | Four-Loop Gluon Anomalous Dimension of General Lorentz Spin: Transcendental Part |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.25833 |