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Chapter 33: Q32CQ (page 1211)
Gluons and the photon are massless. Does this imply that the W+. W- and Z0 are the ultimate carriers of the weak force?
The fact that gluons and photons have no mass does not imply that \({W^ + },{W^ - }\)and \({Z^0}\) are the ultimate carriers of the weak force.
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Is the decay \({{\rm{\mu }}^{\rm{ - }}} \to {{\rm{e}}^{\rm{ - }}}{\rm{ + }}{{\rm{\nu }}_{\rm{e}}}{\rm{ + }}{{\rm{\nu }}_{\rm{\mu }}}\)possible considering the appropriate conservation laws? State why or why not.
(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)?
One of the decay modes of the omega minus is \({\Omega ^ - } \to {\Xi ^0} + {\pi ^ - }\).
(a) What is the change in strangeness?
(b) Verify that baryon number and charge are conserved, while lepton numbers are unaffected.
(c) Write the equation in terms of the constituent quarks, indicating that the weak force is responsible.
The decay mode of the positive tau is\({{\bf{\tau }}^ + } \to {\rm{ }}{{\bf{\mu }}^ + }{\rm{ }} + {\rm{ }}{{\bf{\nu }}_{\bf{\mu }}}{\rm{ }} + {\rm{ }}{{\bf{\bar \nu }}_{\bf{\tau }}}\).
(a) What energy is released?
(b) Verify that charge and lepton family numbers are conserved.
(c) The \({\tau ^ + }\)is the antiparticle of the \({\tau ^ - }\). Verify that all the decay products of the \({\tau ^ + }\)are the antiparticles of those in the decay of the \({\tau ^ - }\) given in the text.
The reaction \({{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}} \to {{\rm{\Delta }}^{{\rm{ + + }}}}\) (described in the preceding problem) takes place via the strong force.
(a) What is the baryon number of the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)particle?
(b) Draw a Feynman diagram of the reaction showing the individual quarks involved.
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