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Chapter 33: Q29CQ (page 1211)
The quarks in a particle are confined, meaning individual quarks cannot be directly observed. Are gluons confined as well? Explain
A hadron does contain gluons. A meson is exchanged instead of a gluon in hadron-hadron interactions because gluon exchange would violate quark confinement.
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One decay mode for the eta-zero meson is\({{\rm{\eta }}^{\rm{0}}} \to {\rm{\gamma + \gamma }}\).
(a) Find the energy released.
(b) What is the uncertainty in the energy due to the short lifetime?
(c) Write the decay in terms of the constituent quarks.
(d) Verify that baryon number, lepton numbers, and charge are conserved.
The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere as seen in the figure given below. Suppose a cosmic ray particle having an energy of \({\rm{1}}{{\rm{0}}^{{\rm{10}}}}{\rm{ GeV}}\)converts its energy into particles with masses averaging 200 MeV/c2
(a) How many particles are created?
(b) If the particles rain down on an \({\rm{1}}{\rm{.00 - k}}{{\rm{m}}^{\rm{2}}}\) area, how many particles are there per square meter?
Plans for an accelerator that produces a secondary beam of \({\rm{K}}\)-mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \({\rm{500 MeV}}\).
(a) What would the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/{\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) be for these particles?
(b) How long would their average lifetime be in the laboratory?
(c) How far could they travel in this time?
The primary decay mode for the negative pion \({\pi ^{\rm{ - }}} \to {{\rm{\mu }}^{\rm{ - }}}{\rm{ + }}{{\rm{\bar \upsilon }}_{\rm{\mu }}}\).
(a) What is the energy release in \({\rm{MeV}}\) in this decay?
(b) Using conservation of momentum, how much energy does each of the decay products receive, given the \({\pi ^{\rm{ - }}}\) is at rest when it decays? You may assume the muon antineutrino is massless and has momentum \(p = \frac{{{E_\nu }}}{c}\), just like a photon.
Discuss how we know that \[{\rm{\pi }}\]-mesons\[\left( {{{\rm{\pi }}^{\rm{ + }}}{\rm{,\pi ,}}{{\rm{\pi }}^{\rm{0}}}} \right)\]) are not fundamental particles and are not the basic carriers of the strong force.
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