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The double fermionic contribution to the four-loop quark-to-gluon splitting function

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arxiv 2310.01245 v1 pith:YT5ACNYT submitted 2023-10-02 hep-ph

The double fermionic contribution to the four-loop quark-to-gluon splitting function

G. Falcioni (Zurich U. , Turin U.) , F. Herzog (U. Edinburgh , Higgs Ctr. Theor. Phys.) , S. Moch (Hamburg U. , Inst. Theor. Phys. II) , J. Vermaseren (Nikhef , Amsterdam)
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A. Vogt (Liverpool U. Dept. Math.)
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classification hep-ph
keywords resultsdoublefermionicfirstformfunctionleadingquark-to-gluon
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We have computed the first 30 even-N moments for the double fermionic (nf^2) part of the quark-to-gluon splitting function P_{gq} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. From these results we have determined the all-N form, and hence the exact x-space expression, using systems of Diophantine equations for its coefficients. The dominant and subdominant leading small-x nf^2 contributions to P_{gq}^(3)(x) are of the form 1/x ln x and ln^4 x, respectively; the leading large-x term is ln^4 (1-x). The coefficient of the first of these is new, the other two agree with results obtained before and thus provide checks of our results.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Presents the zeta(3)-proportional term of the four-loop non-singlet twist-two quark anomalous dimension for general N in closed form, extracted via analytic reconstruction from published Mellin moments.

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    Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new ...

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    hep-ph 2026-07 conditional novelty 5.0

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