Subleading Collinear Limits of Yang--Mills Amplitudes from Recursions

Abstract

We study the subleading adjacent-collinear limit of tree-level color-ordered Yang--Mills amplitudes. In general dimensions, a Lorentz null rotation transports the polarizations of collinear legs along the collinear path while preserving transversality and gauge equivalence. The finite coefficient then separates into a pole-free hard contribution, computed by a channel-deleted Berends--Giele recursion, and an explicit contribution from the adjacent factorization channel. In four dimensions, we construct the same coefficient directly from a collinear-aware Britto-Cachazo-Feng-Witten recursion whose terminal data are closed MHV and $\overline{\rm MHV}$ formulas. Both constructions apply at arbitrary momentum fraction and extend to collinear gluons with distinct polarizations; at the symmetric split, the auxiliary-vector dependence cancels for equal polarizations and for the polarization-symmetrized mixed limit. Open--closed disk relations then give a direct construction of one-graviton Einstein--Yang--Mills amplitudes and their higher-derivative string corrections from the recursively generated coefficients. A self-contained \textsc{Mathematica} implementation accompanies the paper.