Spacelike collinear limits of 2-to-3 amplitudes at two loops

by Zehao Zhu (Universität Mainz)

Tuesday 13 Oct 2026, 11:00 → 12:00 Europe/Berlin

PH 3344, (5101.01.344) (TUM, Physics Department, Garching)

The gauge-theory scattering amplitudes feature strict collinear factorization in the kinematic regime where two outgoing particles are collinear. However, when an incoming and an outgoing particle become collinear, corresponding to the spacelike-collinear limit, strict collinear factorization is violated. At one loop, the factorization violating term arises from colour correlations between collinear particles and the remaining process. Starting at two loops, the splitting amplitude also depends on their kinematics. In this talk, I will discuss the spacelike collinear limit of a 2-to-3 scattering amplitude in N=4 sYM at two loops. Using the method of regions, I will show that the entire kinematic dependence in the violating term originates from a unique hidden region in the asymptotic expansion of the five-point amplitude, which is absent in the timelike-collinear limit.  In parametric space, we determine the region vector in the presence of cancellations between different Lee–Pomeransky parameters, which cannot be detected by the standard geometric method. In momentum space, the hidden region contains a Glauber loop momentum and a soft loop momentum. The Glauber mode has a virtuality dominated by its transverse components, while the soft mode has homogeneous scaling of its longitudinal and transverse components. The soft nature of the interaction explains why the early Wilson-line based computation yields the complete factorization-violating contribution.

SPCFV_TUMMPP.pdf