A beam of protons with kinetic energy strikes a stationary proton target in a…

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

A beam of protons with kinetic energy

T_{\rm beam} = 2.500\,\mathrm{GeV}

strikes a stationary proton target in a fixed-target experiment (a thin liquid-hydrogen target, so the target proton is at rest in the laboratory). Take

m_p = 938\,\mathrm{MeV}/c^2

throughout. Two protons emerge from the interaction point and are measured in the plane containing the beam axis, one on each side of that axis, each with momentum magnitude

1.200\,\mathrm{GeV}/c

and making an angle of

29.1^\circ

with the beam direction. Nothing else is detected. Assume that, besides the two measured protons, exactly one further system of some definite invariant mass

M_X

leaves the interaction point unseen, carrying off the rest of the energy and momentum. ((a)) Find the invariant mass of the pair of detected protons. ((b)) Use conservation of four-momentum to find

M_X

. ((c)) Given the tabulated masses

m_{\pi^0} = 135.0\,\mathrm{MeV}/c^2

m_{K^0} = 497.6\,\mathrm{MeV}/c^2

and

m_\eta = 547.9\,\mathrm{MeV}/c^2

, identify the unseen particle.

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