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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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Why does the \({\eta ^0}\) meson have such a short lifetime compared to most other mesons?
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.
Suppose you are designing a proton decay experiment and you can detect \({\rm{50}}\) percent of the proton decays in a tank of water.
(a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of \({\rm{1}}{{\rm{0}}^{{\rm{31}}}}{\rm{ y}}\)?
(b) How many cubic meters of water is this?
(c) If the actual lifetime is \({\rm{1}}{{\rm{0}}^{{\rm{33}}}}{\rm{ y}}\), how long would you have to wait on an average to see a single proton decay?
The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is\[{\rm{1}}{{\rm{0}}^{{\rm{14}}}}{\rm{ GeV/}}{{\rm{c}}^{\rm{2}}}\]. (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity γ would have to be.)
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.
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