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Chapter 33: Q41PE (page 1213)
(a) What particle has the quark composition \({\rm{\bar u \bar u \bar d}}\)?
(b) What should its decay mode be?
(a) The particle having the quark composition\(\bar u\bar u\bar d\)is an antiproton.
(b) The decay mode of antiproton should be \({\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ - }}}\).
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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?
An antibaryon has three antiquarks with colors\[{\rm{\bar R\bar G\bar B}}\]. What is its color?
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?
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.
Consider a detector needed to observe the proposed, but extremely rare, decay of an electron. Construct a problem in which you calculate the amount of matter needed in the detector to be able to observe the decay, assuming that it has a signature that is clearly identifiable. Among the things to consider are the estimated half-life (long for rare events), and the number of decays per unit time that you wish to observe, as well as the number of electrons in the detector substance.
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