Change the chapter
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.
Question Image
1. $3.3\times 10^{-24}\textrm{ s}$
2. Please see the solution video
3. Please see the solution video.
Solution Video