Boomerang webs up to three-loop order

Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider particular class boomerang webs, consisting multiple exchanges, but where at least one has both endpoints on same Wilson line. First, use replica trick prove that involving self-energy insertions along line do not web, i.e. exponentiated colour factor vanishes. Consequently effectively involve only integrals gluons straddle or more connect other lines. Next classify calculate all semi-infinite non-lightlike lines up three-loop order, including a detailed discussion how regulate renormalize them. Furthermore, show they can be written using basis specific harmonic polylogarithms, been conjectured sufficient for expressing exchange webs. However, differ from gluon-exchange by featuring lower non-uniform transcendental weight. We cross-check our results showing certain determined so-called collinear reduction previously calculated Our necessary ingredient anomalous dimension three loops.