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Magazine Chapter 2: Problem 5
Draw Feynman diagrams (in terms of transitions at the quark level if hadrons are involved) for the following weak decays: $$ \begin{aligned} &\pi^{+} \rightarrow \mu^{+}+v_{\mu} \\ &\Lambda \rightarrow p+e^{-}+v_{e} \\ &K^{0} \rightarrow \pi^{+}+\pi^{-} \\ &\pi^{+} \rightarrow \pi^{0}+e^{+}+v_{e} \end{aligned} $$ Draw Feynman diagrams for the following strong decays: $$ \begin{aligned} \omega^{0} & \rightarrow \pi^{+}+\pi^{-}+\pi^{0} \\ \rho^{0} & \rightarrow \pi^{+}+\pi^{-} \\ \Delta^{++} & \rightarrow p+\pi^{+} \end{aligned} $$
Short Answer
Expert verified
Draw quark transitions for weak decays using W bosons, and gluon exchanges for strong decays.
Step by step solution
01
Understand the process
To solve this exercise, we need to draw Feynman diagrams representing weak and strong decays at the quark level. For weak decays involving hadrons, we look for the underlying quark transitions mediated by the weak nuclear force, often involving W bosons. For strong decays, we understand them as involving the exchange of gluons, since they are mediated by the strong nuclear force.
02
Draw Feynman Diagram for 蟺鈦 鈫 渭鈦 + 谓_渭
The decay of the charged pion 蟺鈦 occurs through weak interaction. At the quark level, 蟺鈦 consists of an up (u) quark and an anti-down (d虅) quark. The up quark (u) transforms into a down quark (d) via exchange of a W鈦 boson, which then decays into a muon (渭鈦) and a muon neutrino (谓_渭). Draw the u and d虅 quark splitting with a W鈦 boson exiting and decaying into 渭鈦 and 谓_渭.
03
Draw Feynman Diagram for 螞 鈫 p + e^- + 谓_e
The lambda baryon (螞), made of uds quarks, transitions to a proton (p) which consists of uud quarks. The strange quark (s) decays via exchange of a W鈦 boson into a u quark, transforming 螞 into a proton. The W鈦 then emits an electron (e鈦) and an electron neutrino (谓_e). Depict the initial uds quark structure, the s to u transformation via W鈦, and its decay to e鈦 and 谓_e.
04
Draw Feynman Diagram for K鈦 鈫 蟺鈦 + 蟺鈦
K鈦 (neutral kaon) composed of a down (d) and anti-strange (s虅) quark decays via weak process with W bosons. Here, both d and s虅 change flavors: a virtual W boson is exchanged between the d and s虅, leading to a final state of u and anti-u quarks forming 蟺鈦 and 蟺鈦. Write the d and s虅 quarks, exchange a virtual W, converting them into the u, anti-u pair followed by 蟺鈦, 蟺鈦.
05
Draw Feynman Diagram for 蟺鈦 鈫 蟺鈦 + e鈦 + 谓_e
In this weak decay, the 蟺鈦 (consisting of u and d虅) turns into 蟺鈦 (uar{u} or dar{d}) along with an electron (e鈦) and a neutrino (谓_e). The u quark turns into a d quark, exchanging a W鈦 boson which decays into a positron and a neutrino. Sketch the u to d transformation and W鈦 decay in the final electron and neutrino.
06
Draw Feynman Diagram for 蠅鈦 鈫 蟺鈦 + 蟺鈦 + 蟺鈦
This strong decay involves the 蠅鈦 meson composed primarily of u and anti-u quarks interchanging gluons, creating three pions: 蟺鈦, 蟺鈦, and 蟺鈦. Draw interactions where the constituents transition to produce the three pions directly through gluon exchange.
07
Draw Feynman Diagram for 蟻鈦 鈫 蟺鈦 + 蟺鈦
Consisting of an up quark and anti-up or down anti-down, the 蟻鈦 undergoes a strong decay through gluon exchange resulting in 蟺鈦 and 蟺鈦 from intermediate quark exchange forming pions. Display initial structure, gluon-mediated transformation yielding 蟺鈦 and 蟺鈦.
08
Draw Feynman Diagram for 螖鈦衡伜 鈫 p + 蟺鈦
The 螖鈦衡伜 baryon comprises three up quarks (uuu) and undergoes a strong decay. Two up quarks form a proton (uud), and the remaining u quark combines with gluon effects to generate a pion (蟺鈦). Illustrate this by showing the initial uuu structure and transformation to uud and 蟺鈦 by strong forces.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Weak Decay
Weak decay is a fascinating process where particles change into other particles via the weak nuclear force. One of the key features of weak decay is the transformation of a quark from one type, or 'flavor', to another. For example, in the decay of a charged pion (\(\pi^+\)) into a muon (\(\mu^+\)) and a muon neutrino (\(u_\mu\)), the up quark (\(u\)) changes into a down quark (\(d\)). This transformation is mediated by the exchange of a W boson, a carrier of the weak force. Here鈥檚 what typically happens during weak decay:
- A quark changes flavor, such as up to down or strange to up.
- A W boson is exchanged, often turning into a lepton-neutrino pair.
- This process alters the particle's charge and sometimes results in new particles, like leptons or neutrinos.
Strong Decay
Strong decay is a process where particles break apart through the strong nuclear force, the force that holds atomic nuclei together. Unlike weak decay, strong decay does not involve the transformation of particle types. Instead, it involves the exchange of gluons, which are responsible for holding quarks together inside protons and neutrons. For example, during the decay of rho meson (\(\rho^0\)) into two pions (\(\pi^+\) and \(\pi^-\)), gluons are exchanged between the quarks leading to this final state. In strong decay:
- Particles break apart into smaller particles, often into mesons or baryons.
- Included are gluon exchanges which facilitate the change from one particle into another.
- It is characterized by being one of the fastest known particle interactions.
Quark Transitions
Quark transitions are an essential part of particle physics, primarily seen during processes like weak decay. A quark transition involves a quark changing from one type to another, such as from an up quark to a down quark, which can happen via the weak force. In decay processes, such as the decay of the lambda particle (\(\Lambda\)) into a proton (\(p\)), the strange quark (\(s\)) transitions to an up quark (\(u\)). Important points about quark transitions include:
- They are primarily mediated by W bosons in weak interactions.
- These transitions can alter the charge and identity of particles, resulting in new particle formation.
- Understanding these transitions is vital for predicting the outcomes of particle interactions.
W Boson
The W boson is one of the carriers of the weak nuclear force, fundamental in the process of weak decays in particle physics. Specifically, W bosons are involved in changing the identity of particles. When a W boson is exchanged, it causes quarks to change types. For instance, in a decay like \(\pi^+ \rightarrow \mu^+ + u_\mu\), the W boson allows the up quark (\(u\)) to effectively "switch" to a down quark (\(d\)). Key features of W bosons include:
- They are charged particles, existing as either \(W^+\) or \(W^-\).
- Their involvement in quark transitions often results in charged lepton production, such as electrons or muons.
- Understanding W bosons is crucial to explaining how the weak force operates.
Gluon Exchange
Gluon exchange is a critical aspect of strong interactions in particle physics, facilitating the binding of quarks within protons and neutrons. Gluons are the "glue" that hold quarks together, mediating the strong nuclear force. During processes such as the decay of \(\Delta^{++}\) into a proton (\(p\)) and a pion (\(\pi^+\)), gluons are exchanged among quarks leading to the final state particles. Important insights about gluon exchange are:
- Gluons carry the force but are themselves color-neutral, meaning they don't change the "color charge" during exchanges.
- They result in a binding effect that is incredibly strong over very short distances, ensuring nucleons stay intact.
- They facilitate the conversion or rearrangement of quarks leading to the production of new particles.
