Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present the next-to-next-to-next-to-leading order (N^3LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N^3LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in N=4 super Yang-Mills theory.
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hep-ph 5representative citing papers
Computes N³LO twist-2 matching for linearly polarized gluon TMDs with NNLL small-x resummation for fragmentation functions.
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.
citing papers explorer
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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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The N$^3$LO Twist-2 Matching of Linearly Polarized Gluon TMDs
Computes N³LO twist-2 matching for linearly polarized gluon TMDs with NNLL small-x resummation for fragmentation functions.
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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 small-x logarithmic structure.
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Progress on the soft anomalous dimension in QCD
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.
- Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part