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Chapter 33: Q28CQ (page 1211)
Identify evidence for electroweak unification.
The predictions of one massless, three massive bosons, and one massive spin=0 boson confirmed the theory.
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Verify the quantum numbers given for the proton and neutron in Table \[33.2\] by adding the quantum numbers for their quark constituents as given in Table \[33.4\].
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.
(a) How much energy would be released if the proton did decay via the conjectured reaction \({\rm{p}} \to {\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ + }}}\)?
(b) Given that the \({\pi ^{\rm{0}}}\) decays to two \(\gamma {\rm{ s}}\) and that the \({{\rm{e}}^{\rm{ + }}}\) will find an electron to annihilate, what total energy is ultimately produced in proton decay?
(c) Why is this energy greater than the proton鈥檚 total mass (converted to energy)?
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?
(a) Verify from its quark composition that the \({\rm{\Delta + }}\)particle could be an excited state of the proton.
(b) There is a spread of about \({\rm{100 MeV}}\) in the decay energy of the \({\rm{\Delta + }}\), interpreted as uncertainty due to its short lifetime. What is its approximate lifetime?
(c) Does its decay proceed via the strong or weak force?
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