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Four-loop anomalous dimension of flavor non-singlet twist-two operator of general Lorentz spin in QCD: zeta(3) term
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Four-loop anomalous dimension of flavor non-singlet twist-two operator of general Lorentz spin in QCD: zeta(3) term
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We consider the anomalous dimension of the flavor non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in QCD and construct its contribution proportional to zeta(3) in analytic form by applying advanced methods of number theory on the available knowledge of low-N moments. In conjunction with similar results on the zeta(5) and zeta(4) contributions, this completes our knowledge of the transcendental part of the considered anomalous dimension. This also provides important constraints on the as-yet elusive all-N form of the rational part. Via Mellin transformation, we thus obtain the exact functional form in x of the respective piece of the non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting function at four loops. This allows us to appreciably reduce the theoretical uncertainty in the approximation of that splitting function otherwise amenable from the first few low-N moments.
Forward citations
Cited by 4 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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Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
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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