The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$

J. Ablinger; A. Behring; J. Blümlein; A. De Freitas; A. von Manteuffel; C. Schneider

doi:10.1016/j.nuclphysb.2017.06.004

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arXiv · 1705.01508

The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$

J. Ablinger·A. Behring·J. Blümlein·A. De Freitas·A. von Manteuffel·C. Schneider

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Abstract

We calculate the unpolarized twist-2 three-loop splitting functions $P_{qg}^{(2)}(x)$ and $P_{gg}^{(2,\rm N_F)}(x)$ and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate $P_{gg}^{(2,\rm N_F)}(x)$ directly, $P_{qg}^{(2)}(x)$ is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.

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BibTeX RIS

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider. 2017-05-03. The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$. https://doi.org/10.1016/j.nuclphysb.2017.06.004

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