Extend convergence factors to mixed dipole configurations and massive partons

Extend the convergence-factor definitions and their emission-phase-space integrations to mixed initial–final and final–initial dipoles required for arbitrary hadron-collision processes, and incorporate mass effects in the quasi-collinear limit.

Background

The paper develops convergence factors for final-state emission with a final-state spectator and for initial-state emission with an initial-state spectator. These factors suppress spurious singularities generated when the dipole projection maps a nonsingular real-emission configuration onto a singular Born configuration, thereby allowing the partitioned subtraction integrals to be evaluated separately and reducing their dependence on generation cuts.

The authors explicitly identify the mixed initial–final and final–initial dipole configurations, together with mass corrections in the quasi-collinear limit, as remaining components needed for a complete implementation covering arbitrary hadron-collision processes. The paper does not derive the corresponding convergence factors or their integrated subtraction terms.