Question

Sketch the Feynman diagram if the proposed decay is possible.

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

Short answer

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

Step-by-step solution

Given data 

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

Concept of Feynman diagram 

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

Step 3:Find whether the charge is conserved

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.

Find conservation of mass

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 $1116\text{MeV}/{\text{c}}^2$.

Find conservation of baryons number

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.

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.

Feynman diagram is shown in figure 1.

Figure 1