The text describes and sketches the basic Feynman diagram for the fundamental process involved in the decay of the free neutron: One of the neutron's \(d\) -quarks converts to a \(u\) -quark, emitting a virtual \(W^{-}\) boson, which decays into an electron and an electron anti-neutrino (the only decay energetically possible). Similarly describe and sketch the basic (tree-level) Feynman diagram for the fundamental process involved in each of the following decays: a) \(\mu^{-} \rightarrow e^{-}+\nu_{\mu}+\bar{\nu}_{e}\) b) \(\tau^{-} \rightarrow \pi^{-}+\nu_{\tau}\) c) \(\Delta^{++} \rightarrow p+\pi^{+}\) d) \(K^{+} \rightarrow \mu^{+}+\nu_{\mu}\) e) \(\Lambda \rightarrow p+\pi\)

Step by step solution

01

Identify the particles involved in the decay process

In this decay process, a muon (\(\mu^{-}\)) decays into an electron (\(e^{-}\)), a muon neutrino (\(\nu_{\mu}\)), and an electron antineutrino (\(\bar{\nu}_{e}\)).

02

Identify the virtual boson exchange

The boson exchange involved here is the emission of a virtual \(W^{-}\) boson.

03

Draw the Feynman diagram

The Feynman diagram for this decay consists of an incoming muon (\(\mu^{-}\)) emitting a virtual \(W^{-}\) boson and subsequently transforming into an electron (\(e^{-}\)). The virtual \(W^{-}\) boson decays into a muon neutrino (\(\nu_{\mu}\)) and an electron antineutrino (\(\bar{\nu}_{e}\)). b) \(\tau^{-} \rightarrow \pi^{-}+\nu_{\tau}\)

04

Identify the particles involved in the decay process

In this decay process, a tau lepton (\(\tau^{-}\)) decays into a pion (\(\pi^{-}\)) and a tau neutrino (\(\nu_{\tau}\)).

05

Identify the virtual boson exchange

The boson exchange involved here is the emission of a virtual \(W^{-}\) boson.

06

Draw the Feynman diagram

The Feynman diagram for this decay consists of an incoming tau lepton (\(\tau^{-}\)) emitting a virtual \(W^{-}\) boson and subsequently transforming into a tau neutrino (\(\nu_{\tau}\)). The virtual \(W^{-}\) boson decays into a quark-antiquark pair, which then forms a pion (\(\pi^{-}\)). c) \(\Delta^{++} \rightarrow p+\pi^{+}\)

07

Identify the particles involved in the decay process

In this decay process, a delta baryon (\(\Delta^{++}\)) decays into a proton and a positively charged pion (\(\pi^{+}\)).

08

Identify the virtual boson exchange

The boson exchange involved here is the exchange of a virtual \(\pi^{+}\) meson.

09

Draw the Feynman diagram

The Feynman diagram for this decay consists of an incoming \(\Delta^{++}\), represented by three quarks, going through a quark rearrangement and exchanging a virtual \(\pi^{+}\) meson (via the strong force). The final state includes a proton and a positively charged pion (\(\pi^{+}\)). d) \(K^{+} \rightarrow \mu^{+}+\nu_{\mu}\)

10

Identify the particles involved in the decay process

In this decay process, a positively charged kaon (\(K^{+}\)) decays into a positive muon (\(\mu^{+}\)) and a muon neutrino (\(\nu_{\mu}\)).

11

Identify the virtual boson exchange

The boson exchange involved here is the emission of a virtual \(W^{+}\) boson.

12

Draw the Feynman diagram

The Feynman diagram for this decay consists of an incoming \(K^{+}\), represented by a quark-antiquark pair. An up-quark changes into a strange quark with the emission of a virtual \(W^{+}\) boson, turning the kaon (\(K^+\)) into a muon (\(\mu^+\)). The virtual \(W^{+}\) boson then decays into a muon neutrino (\(\nu_{\mu}\)). e) \(\Lambda \rightarrow p+\pi\)

13

Identify the particles involved in the decay process

In this decay process, a neutral lambda baryon (\(\Lambda\)) decays into a proton (\(p\)) and a pion (\(\pi\)).

14

Identify the virtual boson exchange

The boson exchange involved here is the exchange of a virtual pion (\(\pi\)).

15

Draw the Feynman diagram

The Feynman diagram for this decay consists of an incoming \(\Lambda\), represented by a group of quarks (up, down, and strange). A quark rearrangement and the exchange of a virtual pion (\(\pi\)) lead to the formation of a proton and a pion in the final state.

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