Question
The reaction $\pi^+ p \to \Delta^{++}$ (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the $\Delta^{++}$ particle? (b) Draw a Feynman diagram of the reaction showing the individual quarks involved.
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Final Answer
1. The baryon number is +1
2. Please see the solution video.
Solution Video

OpenStax College Physics Solution, Chapter 33, Problem 23 (Problems & Exercises) (2:09)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The positive pion plus a proton creates a plus, plus delta particle and the baryon number is conserved because the positive pion has a baryon number of 0, the proton has a baryon number of 1 and this delta plus, plus has a baryon number of 1 as well so it's a total of 1 on the left and a total of 1 on the right. But you can also say that by looking at the quark compositions; the positive pion has an up and an anti-down quark whereas a proton has an up, up and a down and the plus, plus delta particle has an up, up, up quark composition. So each up quark in the delta plus, plus particle has a baryon number of positive one-third and so there are three of them so we multiply by 3 to get a total of 1. So the baryon number of the delta plus, plus is 1. OK. Then we look at the Feynman diagram which has time going upwards and space to the right and we have the proton here which is a package containing a down and up, up quark and then we have the positive pion over here which is an up and an anti-down quark. And we are told that this decay is mediated by the strong force and so when we draw an interaction between quarks, we are gonna use this helix type of line to represent this strong force interaction and all of these matter quarks have lines going from the bottom to the top where as the anti-matter quark has a line going backwards in time and we end up with the down and the anti-down quarks together annihilating I suppose you could say and you end up with three up quarks; one from the positive pion and two from the proton.