Determine the discontinuity across kinematical cuts in total-energy dispersion relations

Determine the discontinuity across a kinematical cut for the relativistic 3→3 scattering amplitude formulated with the squared total energy as the dispersion variable, thereby resolving the unknown contribution that complicates the associated N/D dispersion equation.

Background

The paper contrasts its subenergy-based dispersive representation with the earlier total-energy formulation of relativistic 3→3 scattering. In the total-energy approach, fixed kinematic variables make the two-particle subenergies multivalued functions of the total energy and generate kinematical branch points. These singularities divide the relevant function across multiple Riemann sheets and complicate the separation of dynamical and kinematical contributions.

Although the dynamical discontinuity can be determined on each kinematical sheet, the discontinuity across a kinematical cut is explicitly identified as unknown. Resolving this issue would clarify the analytic structure of the total-energy N/D formalism for three-particle scattering.