Speaker
Description
On-shell recursion determines constructible amplitudes from lower-point factorization data, but explicit evaluation at deformation poles can obscure their local structure. We develop an ordered reconstruction that avoids explicit pole solutions and keeps every retained contribution free of spurious poles. Each contribution supplies the current factorization deficit while remaining regular on all previously protected channels. The choice of an on-cut-equivalent numerator is not unique: different admissible choices change the deficits supplied by later contributions. Within a linear space of local rational functions containing the target amplitude and obeying the required boundary condition, we prove that every successive matching problem is consistent and that any sequence of exact admissible updates reaches the same amplitude after at most one update per channel–branch condition. We demonstrate the construction for six-gluon next-to-maximally-helicity-violating amplitudes using both all-line transverse and Britto–Cachazo–Feng–Witten deformations, without substituting deformation-pole solutions. We also apply the method to four- and five-point amplitudes with massive particles, showing how their spin-dependent factorization data can be assembled into local expressions. These examples connect the general consistency argument with explicit constructions in both massless and massive settings.