Factorization for massive N-jet operators with multiple collinear directions

Determine the factorization properties of the massive N-jet operator in QCD with multiple collinear directions and multiple mass scales, explicitly characterizing how soft functions with non-trivial color structures factorize within soft-collinear effective theory.

Background

This work establishes that ultra-collinear modes cancel to all orders for the on-shell massive Sudakov form factor and provides two-loop results and resummation foundations for the soft and jet functions, focusing on configurations with two collinear directions.

Extending these results to amplitudes with multiple collinear directions (N-jet operators) introduces soft functions with non-trivial color structures and multiple mass scales. The authors identify the detailed investigation of factorization in this multi-direction, multi-scale setting as an open problem.

References

A related open problem concerns the case of multiple collinear directions in QCD, that is, amplitudes represented in SCET by an N-jet operator. In this case, the soft functions acquire non-trivial color structures.

— The Fate of Ultra-Collinear Modes in On-Shell Massive Sudakov Form Factors  (2604.02859 - Schnubel et al., 3 Apr 2026) in Section 6 (Summary and outlook)