Threshold energy - Aetherwisp

The threshold energy of a particle process is the minimum energy required for the process to occur. It is "minimal" in the sense that the process consumes all of this energy just to happen: the daughter particles will therefore have zero kinetic energy as there is none left to transfer.

Mathematically, for a process $a+T\to p_{1}+\ldots+p_{N}$ where $a$ is the projectile, $T$ is a stationary target and $p_{1},\ldots,p_{N}$ are the $N$ products, we define the threshold kinetic energy of the projectile as

K_{a}=\frac{1}{2m_{T}}\left[ \left( \sum_{i=1}^{N} m_{i} \right)^{2}- (m_{a}+m_{T})^{2} \right]

The threshold energy proper is

E_\text{tr}=K_{a}+m_{a}

though the kinetic energy is generally the one that matters since that's the one we control. This definition uses natural units.

It is primarily of interest in particle scattering, where the energy can be controlled in experimental settings like particle accelerators, but it is a valid quantity in particle decay as well.

> Essentially a collision between two [[proton|protons]] that led to three protons and an antiproton. The threshold energy for this process is > $$K_{p}=\frac{(4m_{p})^{2}-(2m_{p})^{2}}{2m_{p}}=6.53\text{ GeV}