Recursion for Wilson-line form factors
Timothy Cohen (Institute for Fundamental Science, University of Oregon, Eugene, Oregon, 97403, USA, Theoretical Physics Department, CERN, Geneva, 1211, Switzerland, Theoretical Particle Physics Laboratory, EPFL, Lausanne, 1015, Switzerland, Theoretical Physics Department, CERN, Geneva, 1211, Switzerland)
; Marc Riembau (Theoretical Physics Department, CERN, Geneva, 1211, Switzerland, Theoretical Physics Department, CERN, Geneva, 1211, Switzerland)
Matrix elements of Wilson-line dressed operators play a central role in the factorization of soft and collinear modes in gauge theories. When expressed using spinor helicity variables, these so-called form factors admit a classification starting from a Maximally Helicity Violating configuration, in close analogy with gauge theory amplitudes. We show that a single-line complex momentum shift can be used to derive recursion relations that efficiently compute these helicity form factors at tree-level: a combination of lower point form factors and on-shell amplitudes serve as the input building blocks. We obtain novel compact expressions for the 1 → 2 and 1 → 3 splitting functions in QCD, which also serves to validate our methods.