Draw a quark-level Feynman diagram for the decay of a neutral kaon into two charged pions, \(K^{0} \rightarrow \pi^{+}+\pi^{-}\).

In this decay process, we have three particles involved: a neutral kaon \(K^{0}\), a positive pion \(\pi^{+}\), and a negative pion \(\pi^{-}\). The quark compositions for these particles are as follows: - Neutral Kaon (\(K^{0}\)): \(d\bar{s}\) - Positive Pion (\(\pi^{+}\)): \(u\bar{d}\) - Negative Pion (\(\pi^{-}\)): \(d\bar{u}\)

In this decay process, the interaction involved is the weak interaction, as the quarks change their flavor from down-type to up-type and vice versa. We will represent this with a \(W\) boson, which is responsible for enabling the weak interaction in this case.

To draw the quark-level Feynman diagram for \(K^{0} \rightarrow \pi^{+}+\pi^{-}\), we need to represent the weak decay process at the quark level where a down quark (\(d\)) from the neutral kaon \(K^0\) changes into an up quark (\(u\)), while the strange antiquark (\(\bar{s}\)) from the same kaon changes into a down antiquark (\(\bar{d}\)). This is mediated by a \(W\) boson exchange. The final result will be the formation of positive and negative pions. The Feynman diagram will look like this: ``` W- d _______)_______ u K^0 π^+ ∧ | d\|/¯¯¯ W¯ ¯¯¯¯¯¯¯¯ s π^- ``` - The initial state is the neutral kaon \(K^{0}\), which is composed of a down quark (\(d\)) and a strange antiquark (\(\bar{s}\)). - The down quark (\(d\)) emits a \(W^{-}\) boson and becomes an up quark (\(u\)). The \(W^{-}\) boson travels downward and is absorbed by the strange antiquark (\(\bar{s}\)), turning it into a down antiquark (\(\bar{d}\)). - The final state consists of a positive pion (\(\pi^{+}\)), formed by an up quark (\(u\)) and a down antiquark (\(\bar{d}\)), and a negative pion (\(\pi^{-}\)), formed by a down quark (\(d\)) and an up antiquark (\(\bar{u}\)).