Give the quark composition of the particles in the following processes and draw the Feynman diagram

(a) $\pi ^{+}+p\rightarrow \Delta ^{++}+\pi ^{0}$

(b) $\Lambda \rightarrow \pi ^{-}+p$

(c) $n\rightarrow p+e^{-}+\overline{v}_{e}$

(d) $\Omega ^{-}\rightarrow \Xi ^{0}+e^{-}+\overline{v}_{e}$

Question

Give the quark composition of the particles in the following processes and draw the Feynman diagram

(a) [latex]\pi ^{+}+p\rightarrow \Delta ^{++}+\pi ^{0}[/latex]

(b) [latex]\Lambda \rightarrow \pi ^{-}+p[/latex]

(c) [latex]n\rightarrow p+e^{-}+\overline{v}_{e}[/latex]

(d) [latex]\Omega ^{-}\rightarrow \Xi ^{0}+e^{-}+\overline{v}_{e}[/latex]

Accepted Answer

We shall first write each reaction formula showing the quark composition of each particle and then say how the quarks have changed and draw the appropriate Feynman diagram.

[latex] \begin{matrix} ext{(a)} & \pi ^{+} + &p & ightarrow &\Delta ^{++}+ &\pi ^{0}. \ & ud^{-} & uud & &uuu & d \overline{d}\end{matrix} [/latex]

[latex] \begin{matrix} ext{(b)} & &\Lambda & ightarrow &\pi ^{-}+ &p \ & & uds & &d\overline{u} & uud\end{matrix} [/latex]

[latex] \begin{matrix} ext{(c)} & &n & ightarrow & p + &e^- + \overline{v}_e \ & & udd & & uud & e^- + \overline{v}_e\end{matrix} [/latex]

[latex] \begin{matrix} ext{(d)} & &\Omega ^- & ightarrow & \Xi ^0 + &e^- + \overline{v}_e \end{matrix} [/latex]

According to the Feynman diagram shown in Fig. 14.20, the quarks in part (a) are simply rearranged. For the (b) part, an s quark is changed into an u quark and an additional [latex]d\overline{u}[/latex] pair is created. This is shown in Fig. 14.21(A). The (B) and (C) figures of Fig. 14.21, describe the reactions given in the (c) and (d) parts of Example 14.3. For the (c) part a d quark is changed into an u quark and an additional [latex]e/ \overline{v} _{e}[/latex] pair is formed. For the (d) part an s quark is changed to a u quark and an additional [latex]e/ \overline{v} _{e}[/latex] pair is formed.

Question 14.3: Give the quark composition of the particles in the following...

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