Accelerators such as the Triangle Universities Meson

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 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 \(^-d\) 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 \(\pi^{+}\) and a proton as a function of energy. The bump is interpreted as a very short lived particle called a \(\Delta^{++}\). The approximately \(100-MeV\) width of the bump is due to the short lifetime of the \(\Delta^{++}\).

Equation Transcription:

Text Transcription:

pi^+ + p rightarrow Delta^++ rightarrow pi^+ + p

Delta^++

Delta^++

d

^- d

Delta^++

pi^+

Delta^++

100-MeV

Delta^++