 Soft-particle endpoint

A boundary of phase space approached as a massless outgoing particle's energy tends to zero. A zero four-vector is not a physical positive-energy one-particle state. An energy bound requiring such a particle is a supremum or infimum, even when the closed kinematic interval is conventionally described using minimum and maximum. This distinction can matter when applying three-body formulas at mixed massive-massless recoil thresholds.