4-momentum vector of particles

The momentum
Since all particles in HEP detectors are very fast moving objects, we are using the relativistic momentum vector to describe their movement:

As you now know, an important property of this vector is its length, the invariant mass. Since all units are now measured in eV, all formulaes become very easy to use, like:

A very useful relation is:

which tells you the speed of a particle, when you know its momentum and energy

Particle Decays
Only a very small number of particles found in the HEP detectors are stable enough to be seen. We detect their decay products instead! In the decay process, the total energy and the momentum of the system has to be conserved, that means the two 4-momenta of the decay daughters sum up to the original 4-momentum of the mother. You can therefore reconstruct the original momentum and the mass of the mother from detected particles.
When 1 and 2 are the daughter momenta, the mass of the mother m is:

Page 1 of Finding Particles

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CLEO WEB PAGES
Updated: 28. November 1995
Author: Andreas H. Wolf (ahw@mps.ohio-state.edu)