A meson has rest mass (Particle Data Group, 2024) and kinetic energy in the…

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

K^+

meson has rest mass

m_K = 493.7\,\mathrm{MeV}/c^2

(Particle Data Group, 2024) and kinetic energy

T = 200\,\mathrm{MeV}

in the laboratory frame. ((a)) Convert

m_K

to kilograms, using

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

and

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

. ((b)) Use the energy-momentum relation to find the kaon's total energy

E

, its momentum magnitude

|\mathbf p|c

, its speed parameter

\beta

and its Lorentz factor

\gamma

. ((c)) Form the invariant product

p\cdot p

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

\mathrm{MeV^2}/c^2

, and check it against

m_K^2c^2

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