Question
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 $\pi^+ + p \rightarrow \Delta^{++} \rightarrow \pi^+ + p$, where the $\Delta^{++}$ is a is a very short-lived particle. The graph in Figure 33.26 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 $\Delta^{++}$. (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 $\overline{d}$ antiquark by writing the reaction and decay in terms of quarks. (c) Draw a Feynman diagram of the production and decay of the $\Delta^{++}$ showing the individual quarks involved. Figure 33.26 This graph shows the probability of an interaction between a pi plus meson and a proton as a function of energy.
1. $3.3\times 10^{-24}\textrm{ s}$
2. Please see the solution video
3. Please see the solution video.

# OpenStax College Physics for AP® Courses, Chapter 33, Problem 22 (Problems & Exercises)  In order to watch this solution you need to have a subscription.

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