Question

Sketch the Feynman diagram if the proposed decay is possible.

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

Short answer

The proposed decay is possible.It is a weak decay.The Feynman diagram is shown in the figure as:

Step-by-step solution

Given data

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

Concept of Feynman diagram

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.

Step 3:Find whether the charge is conserved

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.

Find conservation of mass

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 $1321\text{MeV}/{\text{c}}^2$.

Find conservation of baryons number

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.

Sketch the Feynman diagram

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.