Two charged-pion tracks are measured in a spectrometer

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Invariant mass: decays, thresholds and the collider frame

Problem

Two charged-pion tracks are measured in a spectrometer, each reported as a momentum magnitude and an angle from the beam axis (the

z

-axis), both tracks lying in the same vertical plane: track 1 has

p_1 = 600\,\mathrm{MeV}/c

25.0^\circ

to the beam, on one side; track 2 has

p_2 = 450\,\mathrm{MeV}/c

15.0^\circ

to the beam, on the other side. Each pion has mass

139.57\,\mathrm{MeV}/c^2

. ((a)) Write each momentum as Cartesian components

(p_x, p_z)

and hence find the invariant mass

M

of the two-pion system. ((b)) Treating

M

as the mass of a parent particle decaying into two pions, use the two-body decay formula to find the momentum

p^*

each pion would carry in the parent's rest frame, and its energy

E^*

there.

Browse the problem library