Soft-particle endpoint
= 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.