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Chapter 11: Problem 71

Each of the following reactions is missing a single particle. Identify the missing particle for each reaction. (a) \(\mathrm{p}+\overline{\mathrm{p}} \rightarrow \mathrm{n}+?\) (b) \(\mathrm{p}+\mathrm{p} \rightarrow \mathrm{p}+\Lambda^{0}+?\) (c) \(\pi^{?}+p \rightarrow \Sigma^{-}+?\) (d) \(\mathrm{K}^{-}+\mathrm{n} \rightarrow \Lambda^{0}+?\) (e) \(\tau^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}+?\) (f) \(\bar{v}_{\mathrm{e}}+\mathrm{p} \rightarrow \mathrm{n}+?\)

Short Answer

Expert verified
The missing particles for the given reactions are: (a) \(\bar{\mathrm{n}}\) (b) \(\pi^{+}\) (c) \(\pi^{+}\) and \(\pi^{-}\) (d) \(\pi^{-}\) (e) \(v_e\) (f) \(\mathrm{e}^{+}\)

Step by step solution

01

(a) Identifying the missing particle in p + p̅ → n + ?

To identify the missing particle, we must apply conservation laws. In this case, we must conserve charge and baryon number. Charge Conservation: The initial charge is 1 + (-1) = 0, and the final charge is 0 + Q, where Q is the charge of the missing particle. Thus, Q = 0. Baryon Number Conservation: The initial baryon number is 1 + (-1) = 0, and the final baryon number is 1 + 0 + B, where B is the baryon number of the missing particle. Thus, B = -1. Therefore, the missing particle is an anti-neutron (\(\bar{\mathrm{n}}\)).
02

(b) Identifying the missing particle in p + p → p + Λ^0 + ?

Again, apply the conservation laws to identify the missing particle. Charge Conservation: The initial charge is 1 + 1 = 2, and the final charge is 1 + 0 + Q. Thus, Q = 1. Baryon Number Conservation: The initial baryon number is 1+1 = 2, and the final baryon number is 1 + 1 + B. Thus, B = 0. The missing particle is a positive pion (\(\pi^{+}\)).
03

(c) Identifying the missing particle in π^? + p → Σ^- + ?

Apply conservation laws to find the missing charge (Q) and baryon number (B) of the unknown pion and missing particle. Charge Conservation: Q_pion + 1 = -1 + Q_missing, where Q_pion is the charge of the unknown pion and Q_missing is the charge of the missing particle. Baryon Number Conservation: B_pion + 1 = 1 + B_missing, where B_pion is the baryon number of the unknown pion (0) and B_missing is the baryon number of the missing particle. From the charge equation, we get: Q_pion = Q_missing - 2. From the baryon equation, we get: B_missing = 0. The unknown pion is a positive pion (\(\pi^{+}\)) and the missing particle is a negative pion (\(\pi^{-}\)).
04

(d) Identifying the missing particle in K^- + n → Λ^0 + ?

Apply conservation laws to find the missing particle. Charge Conservation: The initial charge is -1 + 0 = -1, and the final charge is 0 + Q. Thus, Q = -1. Baryon Number Conservation: The initial baryon number is 0 + 1 = 1, and the final baryon number is 1 + B. Thus, B = 0. The missing particle is a negative pion (\(\pi^{-}\)).
05

(e) Identifying the missing particle in τ^+ → e^+ + v_e + ?

Apply conservation laws to find the missing particle. Charge Conservation: The initial charge is -1, and the final charge is 1 + 0 + Q. Thus, Q = -2. Lepton Number Conservation: The initial lepton number is 1, and the final lepton number is 0 + 1 + L, where L is the lepton number of the missing particle. Thus, L = 0. There is an inconsistency with charge conservation, as no particle carrying -2 charge is present in the problem. The correct reaction should be \(\tau^{-} \rightarrow \mathrm{e}^{-} + \bar{v}_{e} + ?\). In this case, the missing particle is an electron neutrino (\(v_e\)).
06

(f) Identifying the missing particle in v̅_e + p → n + ?

Apply conservation laws to find the missing particle. Charge Conservation: The initial charge is 0 + 1 = 1, and the final charge is 0 + Q. Thus, Q = 1. Baryon Number Conservation: The initial baryon number is 0 + 1 = 1, and the final baryon number is 1 + B. Thus, B = 0. Lepton Number Conservation: The initial lepton number is -1 + 0 = -1, and the final lepton number is 0 + L. Thus, L = -1. The missing particle is a positron (\(\mathrm{e}^{+}\)).

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Most popular questions from this chapter

(a) The following decay is mediated by the electroweak force: \(\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{+}+v_{\mathrm{e}}\). Draw the Feynman diagram for the decay. (b) The following scattering is mediated by the electroweak force: \(v_{e}+\mathrm{e}^{-} \rightarrow v_{e}+\mathrm{e}^{-}\) Draw the Feynman diagram for the scattering.

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