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Chapter 33: Q21CQ (page 1211)
An antibaryon has three antiquarks with colors\[{\rm{\bar R\bar G\bar B}}\]. What is its color?
The color of an antibaryon which has three antiquarks with colors \[\overline R \,\overline G \,\overline B \] is white.
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The \[{{\rm{\pi }}^{\rm{0}}}\]is its own antiparticle and decays in the following manner: \[{\pi ^0} \to \gamma + \gamma \]. What is the energy of each \[\gamma \]ray if the \[{\pi ^0}\] is at rest when it decays?
Another component of the strong nuclear force is transmitted by the exchange of virtual \[{\rm{K - }}\]mesons. Taking \[{\rm{K - }}\]-mesons to have an average mass of \[{\rm{495}}\;{\rm{MeV/}}{{\rm{c}}^{\rm{2}}}\], what is the approximate range of this component of the strong force?
What is the wavelength of an \({\rm{50 - GeV}}\) electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.
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 3.20 - km - longSLAC produces a beam of 50 GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?
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