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Chapter 33: Q11CQ (page 1210)
Why does the \({\eta ^0}\) meson have such a short lifetime compared to most other mesons?
As, the \({\eta ^0}\) meson consists of quark-antiquark pairs of the same flavour, its lifetime is short.
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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.
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.
Explain how conservation of baryon number is responsible for conservation of total atomic mass (total number of nucleons) in nuclear decay and reactions.
An antibaryon has three antiquarks with colors\[{\rm{\bar R\bar G\bar B}}\]. What is its color?
Verify the quantum numbers given for the \({{\rm{\Omega }}^{\rm{ + }}}\) in Table \(33.2\) by adding the quantum numbers for its quark constituents as inferred from Table \(33.4\).
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