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Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions
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Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions
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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.
Forward citations
Cited by 6 Pith papers
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The four-loop non-singlet splitting functions in QCD
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
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Closed-form expression for the ζ(3) term of the four-loop non-singlet twist-two quark anomalous dimension for arbitrary N, extracted via analytic reconstruction from Mellin moments.
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Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
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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Properties and implications of the four-loop non-singlet splitting functions in QCD
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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Candia-v2: Logarithmic expansions for DGLAP evolution in $x$-space
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...
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