← Particle Physics

# Energy and Momentum in Particle Decays

Saturday, April 9, 2022

## Conservation Laws

When analyzing the decays and reactions of particles, we use conservation laws, including conservation of energy, linear momentum, total angular momentum, electric charge, lepton number, and baryon number. When creating new particles, the energy involved often comes in the form of kinetic energy of the particles used in production. Since this energy is often quite large, relativistic equations must be used for momentum and energy.

## Energy

The energy available for a decay is the difference in rest energy between the decaying particles and the produced particles:

$Q=\left(m_i-m_f\right)c^2$

The decay will only occur if the Q value is positive.

## Momentum

The energy $Q$ is shared between the particles produced in such a way to conserve linear momentum. For an initial particle at rest, the resulting particles will have equal but opposite linear momenta. For a reaction resulting in three or more particles, each particle has a spectrum of energies from zero to some maximum value (like in beta decay).