Sketch the Feynman diagram if the proposed decay is possible.

${\Xi }^{-}\to {\Lambda }^0+{\pi }^{-}$

The proposed reaction is${\Xi }^{-}\to {\Lambda }^0+{\pi }^{-}$

A Feynman diagram is used to show the interaction of particles in quantum field theory. The particles are represented by the lines in the diagram.

Conservation of charge is shown below:

$$\begin{gathered} {\Xi }^{-}\to {\Lambda }^0+{\pi }^{-} \\ (-e)\to \left(0\right)+(-e) \\ (-e)\to (-e) \end{gathered}$$

The charge before decay and after decay is equal.

Therefore, the charge is conserved.

Conservation of energy or mass is given below:

$$\begin{gathered} {\Xi }^{-}\to {\Lambda }^0+{\pi }^{-} \\ \left(1321\text{MeV}/{\text{c}}^2\right)\to \left(1116\text{MeV}/{\text{c}}^2\right)+\left(140\text{MeV}/{\text{c}}^2\right) \\ \left(1321\text{MeV}/{\text{c}}^2\right)\to \left(1256\text{MeV}/{\text{c}}^2\right) \end{gathered}$$

The mass after the decay is $1256\text{MeV}/{\text{c}}^2$ less than that of the initial mass $1321\text{MeV}/{\text{c}}^2$.

Conservation of baryons number:

$$\begin{gathered} {\Xi }^{-}\to {\Lambda }^0+{\pi }^{-} \\ \left(1\right)\to \left(1\right)+\left(0\right) \\ (+1)\to (+1) \end{gathered}$$

Thus, the baryons number before the decay is equal to the baryons number after the decay.

Therefore, the baryons' number is conserved.

From the above result, we conclude that the decay reaction is possible.

This is a weak decay because it involves W-bosons.

The Feynman diagram is shown in figure 1.

Figure 1

The proposed decay is possible.