Question

Sketch the Feynman diagram if the proposed decay is possible.

$K^{+}\to {\mu }^{+}+{\overline{v}}_{\mu }$

Short answer

The proposed decay is not possible.

Step-by-step solution

Given data

The proposed reaction is $K^{+}\to {\mu }^{+}+{\overline{v}}_{\mu }$

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:

$$\begin{gathered} K^{+}\to {\mu }^{+}+{\overline{v}}_{\mu } \\ (+e)\to (+e)+\left(0\right) \\ (+e)\to (+e) \end{gathered}$$

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

Therefore, the charge is conserved.

Find conservation of mass

Conservation of mass is given below:

$$\begin{gathered} K^{+}\to {\mu }^{+}+{\overline{v}}_{\mu } \\ 494\text{MeV}/{\text{c}}^2\to 106\text{MeV}/{\text{c}}^2 \end{gathered}$$

The mass after the decay is $106\text{MeV}/{\text{c}}^2$ less than that of the initial mass $494\text{MeV}/{\text{c}}^2$.

Find conservation of lepton number

Conservation of lepton number:

$$\begin{gathered} K^{+}\to {\mu }^{+}+{\overline{v}}_{\mu } \\ \left(0\right)\to (-1)+(-1) \\ \left(0\right)\to (-2) \end{gathered}$$

The lepton number is not conserved.

Therefore, this decay is not possible.