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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

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
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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 4 Pith papers

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  1. New results on small-x resummation for splitting functions

    hep-ph 2026-03 conditional novelty 8.0 of 10

    A closed-form all-order expression for the qg anomalous dimension, plus new all-order results for the LL gluon anomalous dimension and the finite qg/gg Green functions, derived and implemented in HELL 4.0.

  2. Anomalous dimensions at small spins

    hep-th 2025-06 accept novelty 6.0 of 10

    The quadratic mass-correction combination of twist-two anomalous dimensions stays finite at small spin in the O(N) phi^4, phi^3, and Gross-Neveu-Yukawa models at the computed loop orders, enabling explicit resummations.

  3. Candia-v2: Logarithmic expansions for DGLAP evolution in $x$-space

    hep-ph 2026-07 conditional novelty 5.0 of 10

    Candia-v2 implements (approximate) N3LO x-space DGLAP evolution — exact four-loop non-singlet splitting functions, envelope-approximated singlet inputs, three-loop heavy-quark matching — as a public C++ package with G...

  4. Alien operators for PDF evolution

    hep-ph 2025-09 unverdicted novelty 2.0 of 10

    This proceedings paper summarizes earlier results on all-spin couplings and Feynman rules for gauge-variant alien operators needed for four-loop QCD splitting functions.

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