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.
Universal structure of subleading infrared poles in gauge theory amplitudes
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abstract
We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G(alpha_s), depending on both the spin and gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix elements involving the gluon field strength. We then show that G(alpha_s) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B_delta (alpha_s) of delta(1 - z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B_delta (alpha_s). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.
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Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
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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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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On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
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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.