Question

Sketch the Feynman diagram if the proposed decay is possible.

${\pi }^0\to {\mu }^{-}+{\overline{v}}_{\mu }$

Short answer

The proposed decay is not possible.

Step-by-step solution

Given data

The proposed reaction is ${\pi }^0\to {\mu }^{-}+{\overline{v}}_{\mu }$

Concept of Feynman diagram

A Feynman diagram is drawn to express the particle interaction in nature.

 Step 3:Find conservation of energy

The conservation of energy is shown below:

$$\begin{gathered} {\pi }^0\to {\mu }^{-}+{\overline{v}}_{\mu } \\ 135\text{MeV}\to 106\text{MeV} \end{gathered}$$

The energy $106\text{MeV}$ after the decay is less than the energy $135\text{MeV}$ before the decay.

 Step 4: Find conservation of lepton numbers

Conservation of Leptons is given below:

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

Thus, the leptons number before the decay is equal to the leptons number after the decay.

Therefore, the Leptons number is conserved.

Find conservation of charge

Conservation of charge is:

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

Thus, the charge before the decay and after the decay isnot equal, which implies that the charge is not conserved.

Therefore, this decay reaction is not possible.