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Chapter 33: Q10CQ (page 1210)
What lifetime do you expect for an antineutron isolated from normal matter?
The lifetime of an antineutron isolated from normal matter is small and stable without any change.
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(a) Find the charge, baryon number, strangeness, charm, and bottomness of the \({\rm{J/\psi }}\) particle from its quark composition.
(b) Do the same for the \(\Upsilon \) particle.
Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such "meson factories" have been used for many years to study the interaction of pions with nuclei and, hence, the strong nuclear force. One reaction that occurs is\({{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}} \to {{\rm{\Delta }}^{{\rm{ + + }}}} \to {{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}}\), where the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)is a very short-lived particle. The graph in Figure \({\rm{33}}{\rm{.26}}\)shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the\({{\rm{\Delta }}^{{\rm{ + + }}}}\).
(a) Find this lifetime.
(b) Verify from the quark composition of the particles that this reaction annihilates and then re-creates a d quark and a \({\rm{\bar d}}\)antiquark by writing the reaction and decay in terms of quarks.
(c) Draw a Feynman diagram of the production and decay of the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)showing the individual quarks involved.
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.
Beta decay is caused by the weak force, as are all reactions in which strangeness changes. Does this imply that the weak force can change quark flavor? Explain.
What length track does a \[{{\rm{\pi }}^{\rm{ + }}}\]traveling at 0.100c leave in a bubble chamber if it is created there and lives for \[{\rm{2}}{\rm{.60 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}{\rm{\;s}}\]? (Those moving faster or living longer may escape the detector before decaying.)
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