# Mass reconstruction

What is it? I always hear it and never know what exactly it means to "reconstruct" mass.

Using energy and momentum conservation, compute the 4-vector of the particle, and it's Lorentz square is the square of the mass.

Say for instance you detect the decay products of the particle, add up all 4-vectors, the square of the mass is the difference between (1) the square of the total energy of the decay products and (2) the square of the total momentum carried by the decay products.

You could also do it if by any chance you can assume the particle is the only one missing in a certain balance, and computing the missing 4-vector.

sorry, I'm going to have to verify in layman's terms.. this is way above my current education in physics. (sophmore year undergrad)

So what you're doing is analyzing the decay products, summing up their total energies to trace back the energy , and thus the masses, of their parent particles?

jtbell
Mentor
summing up their total energies to trace back the energy

And the momentum.

For any particle:

$$(mc^2)^2 = E^2 - ({\vec p }c)^2$$

If the particle then decays into a collection of other particles, the total energy and the total momentum are both conserved, so

$$(mc^2)^2 = (\Sigma E_i)^2 - (\Sigma {\vec p_i} c)^2$$

In these equations, m is the "invariant mass", also known as "rest mass"; not the "relativistic mass" which you find in many introductory treatments of relativity.

Last edited: