Sketch the Feynman diagram if the proposed decay is possible.

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

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

Particle interactions can be represented as Feynman diagrams. Different types of lines are drawn in the diagrams.

Conservation of charge is shown below:

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

Thus, the charge before the decay and after the decay is equal.

Therefore, the charge is conserved.

Conservation of energy or mass is given below:

$$\begin{gathered} {\Lambda }^0\to p+{\pi }^{-} \\ \left(1116\text{MeV}/{\text{c}}^2\right)\to \left(938\text{MeV}/{\text{c}}^2\right)+\left(140\text{MeV}/{\text{c}}^2\right) \\ \left(1116\text{MeV}/{\text{c}}^2\right)\to \left(1078\text{MeV}/{\text{c}}^2\right) \end{gathered}$$

The mass after the decay is $1078\text{MeV}/{\text{c}}^2$ less than that of the initial mass $1116\text{MeV}/{\text{c}}^2$.

Conservation of baryons number:

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

Thus, the baryons' numbers before the decay are equal to the baryons' numbers after the decay.

Therefore, the baryons' numbers are conserved.

From the above result, we conclude that the decay reaction is possible.This is a weak decay because it involves W-bosons.

Feynman diagram is shown in figure 1.

Figure 1