Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
Large-nf Contributions to the Four-Loop Splitting Functions in QCD
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abstract
We have computed the fourth-order nf^2 contributions to all three non-singlet quark-quark splitting functions and their four nf^3 flavour-singlet counterparts for the evolution of the parton distributions of hadrons in perturbative QCD with nf effectively massless quark flavours. The analytic form of these functions is presented in both Mellin N-space and momentum-fraction x-space; the large-x and small-x limits are discussed. Our results agree with all available predictions derived from lower-order information. The large-x limit of the quark-quark cases provides the complete nf^2 part of the four-loop cusp anomalous dimension which agrees with two recent partial computations.
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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.
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 small-x logarithmic structure.
A lightcone-expansion strategy using Wilson-line correlators and the Method of Regions yields the three-loop soft anomalous dimension for QCD amplitudes with one massive colored particle and arbitrary massless ones.
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