Invariant Mass

The invariant mass of a system of decay particles is related to the rest mass of the original particle by the following equation:

:

\mbox{W}^2\mbox{c}^4=(\Sigma \mbox{E})^2-(\Sigma \mbox{pc})^2

Where:

:

W

is the invariant mass of the system of particles
:

\Sigma E

is the sum of the energies of the particles
:

\Sigma pc

is the vector sum of the Momenta of the particles (includes both magnitude and direction of the momenta) times the speed of light,

c

A simple way of deriving this relation is by using the momentum four-vector (in Natural Units ):
:

p_i^\mu=\left(E_i,\mathbf{p}_i
ight)

P^\mu=\left(\Sigma E_i,\Sigma \mathbf{p}_i
ight)

P^\mu P_\mu=\eta_{\mu
u}P^\mu P^
u=(\Sigma E_i)^2-(\Sigma \mathbf{p}_i)^2=W^2

, since the norm of any four-vector is invariant.

SEE ALSO

	CATEGORIES ABOUT INVARIANT MASS

	relativity

	mass

	fundamental physics concepts

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