Asymptotic Charges and Coherent States in QCD
Riccardo Gonzo, Tristan McLoughlin, Diego Medrano, Anne Spiering
TL;DR
The paper links non-Abelian asymptotic symmetries to generalized coherent (FK) dressing in QCD, defining quantum-corrected non-linear asymptotic charges via large gauge transformations of soft evolution operators. It computes the leading one-loop IR-divergent corrections to matrix elements of the charges between dressed states and shows that, with a symmetry-preserving soft-limit ordering, the Ward identities are not corrected at this order, indicating conserved asymptotic charges. The work clarifies how soft-gluon dressing cancels the standard one-loop soft divergences and reveals ordering ambiguities analogous to subleading soft theorems, arguing for a prescription that maintains the symmetry. The results reinforce a coherent IR structure for QCD, connecting coherent-state dressing, Wilson-line pictures, and asymptotic current algebras, with potential extensions to subleading divergences and multiple insertions.
Abstract
We study the connection between asymptotic symmetries in non-Abelian gauge theories and the generalised coherent states following from the application to QCD of the Faddeev-Kulish approach to asymptotic dynamics. We compute the large gauge transformation properties of the soft evolution operators and use this to define the quantum corrected, non-linear contribution to the asymptotic charges. We then compute the one-loop, leading IR-divergent, correction to matrix elements of the charges inserted between dressed scattering states and show that the results depend on a particular order of soft limits. For one choice of ordering we find that the conservation law for the asymptotic charges is not corrected, while for a second we find a correction proportional to the one-loop soft current.