English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present the three-loop result for the soft anomalous dimension governinglong-distance singularities of multi-leg gauge-theory scattering amplitudes ofmassless partons. We compute all contributing webs involving semi-infiniteWilson lines at three loops and obtain the complete three-loop correction tothe dipole formula. We find that non-dipole corrections appear already forthree coloured partons, where the correction is a constant without kinematicdependence. Kinematic dependence appears only through conformally-invariantcross ratios for four coloured partons or more, and the result can be expressedin terms of single-valued harmonic polylogarithms of weight five. While thenon-dipole three-loop term does not vanish in two-particle collinear limits,its contribution to the splitting amplitude anomalous dimension reduces to aconstant, and it only depends on the colour charges of the collinear pair,thereby preserving strict collinear factorization properties. Finally we verifythat our result is consistent with expectations from the Regge limit.

Three-loop corrections to the soft anomalous dimension in multi-leg scattering