Threshold energy

In particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle. In most cases, since momentum is also conserved, the threshold energy is significantly greater than the rest energy of the desired particle - and thus there will still be considerable kinetic energy in the final particles.

Consider the collision of a mobile proton with a stationary proton so that a ${\displaystyle {\pi }^{0}}$ meson is produced: ${\displaystyle p^{+}+p^{+}\to p^{+}+p^{+}+\pi ^{0}}$

Transforming into the ZMF (Zero Momentum Frame or Center of Mass Frame) and assuming the outgoing particles have no KE (kinetic energy) when viewed in the ZMF, the conservation of energy equation is:

${\displaystyle E=2\gamma m_{p}c^{2}=2m_{p}c^{2}+m_{\pi }c^{2}}$

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