Question

Sketch the Feynman diagram if the proposed decay is possible.

${\mu }^{+}\to e^{+}+v_e$

Short answer

The decay is not possible as the lepton number is not conserved.

Step-by-step solution

Given data

The proposed reaction is ${\mu }^{+}\to e^{+}+v_e$

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:

$$\begin{gathered} {\mu }^{+}\to e^{+}+v_e \\ (+e)\to (+e)+\left(0\right) \\ (+e)\to (+e) \end{gathered}$$

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.

$\begin{array}{rcl}{\mu }^{+}& \to & e^{+}+v_e\\ 106\text{MeV}/{\text{c}}^2& \to & 0.511\text{MeV}/{\text{c}}^2\\ & & \end{array}$

The mass after the decay is $0.511\text{MeV}/{\text{c}}^2$ less than that of the initial mass $106\text{MeV}/{\text{c}}^2$.

Find conservation of lepton number

Conservation of lepton number:

$$\begin{gathered} {\mu }^{+}\to e^{+}+v_e \\ (-1)\to (-1)+(-1) \\ (-1)\to (-2) \end{gathered}$$

The lepton number is not conserved.

Therefore, the proposed decay is not possible