A charged pion

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

Particle Physics, Ch Scales, units and the four-momentum

Problem

A charged pion, rest mass

m_\pi = 139.6\,\mathrm{MeV}/c^2

, has momentum magnitude

|\mathbf p|c = 300\,\mathrm{MeV}

in the laboratory frame. ((a)) Convert

m_\pi

to kilograms, using

1\,\mathrm{eV} = 1.602176634\times10^{-19}\,\mathrm{J}

and

c = 2.99792\times10^8\,\mathrm{m\,s^{-1}}

. ((b)) Find the pion's total energy

E

, kinetic energy

T

, speed parameter

\beta

and Lorentz factor

\gamma

. ((c)) Form the invariant product

p\cdot p

of the pion's four-momentum with itself, in

\mathrm{MeV^2}/c^2

, and check it against

m_\pi^2c^2

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