Chapter 15, Problem 8P

(a)

To determine

Supply the missing neutrinos in ${\pi }^{-}\to {\mu }^{-}+?$

Answer to Problem 8P

The missing neutrinos in ${\pi }^{-}\to {\mu }^{-}+?$ is $\underset{\_}{{\overline{v}}_{\mu }}$ .

Explanation of Solution

Consider table 15.2 and refer equation 15.1,

The missing neutrinos in pion are Muon-neutrino.

    ${\pi }^{-}\to {\mu }^{-}+{\overline{v}}_{\mu }$        (I)

Here, ${\pi }^{-}$ is the pion, ${\mu }^{-}$ is the muon and ${\overline{v}}_{\mu }$ is the muon-neutrino.

Conclusion:

In this case, the muon-lepton is conserved.

    $L_{\mu }:0\to 1-1$

Therefore, the missing neutrinos in ${\pi }^{-}\to {\mu }^{-}+?$ is $\underset{\_}{{\overline{v}}_{\mu }}$.

(b)

To determine

Supply the missing neutrinos in $K^{+}\to {\mu }^{+}+?$

Answer to Problem 8P

The missing neutrinos in $K^{+}\to {\mu }^{+}+?$ is $\underset{\_}{v_{\mu }}$ .

Explanation of Solution

Consider table 15.2.

The missing neutrino in Kaon is Muon-neutrino.

    $K^{+}\to {\mu }^{+}+v_{\mu }$        (II)

Here, $K^{+}$ is the Kaon, ${\mu }^{+}$ is the muon and $v_{\mu }$ is the muon-neutrino.

Conclusion:

In this case, the muon-lepton is conserved.

    $L_{\mu }:0\to -1+1$

Therefore, the missing neutrinos in $K^{+}\to {\mu }^{+}+?$ is $\underset{\_}{v_{\mu }}$.

(c)

To determine

Supply the missing neutrinos in $?+\text{p}\to \text{n}+e^{+}$.

Answer to Problem 8P

The missing neutrinos in $?+\text{p}\to \text{n}+e^{+}$ is $\underset{\_}{{\overline{v}}_e}$ .

Explanation of Solution

Using table 15.2,

The missing neutrino is electron-neutrino.

    ${\overline{v}}_e+\text{p}\to \text{n}+e^{+}$        (III)

Here, ${\overline{v}}_e$ is the electron-neutrino, $p$ is the proton and $n$ is the neutron.

Conclusion:

In this case, the electron-lepton is conserved.

    $L_e:-1+0\to 0-1$

Therefore, the missing neutrinos in $?+\text{p}\to \text{n}+e^{+}$ is $\underset{\_}{{\overline{v}}_e}$.

(d)

To determine

Supply the missing neutrinos in $?+n\to p+e^{-}$.

Answer to Problem 8P

The missing neutrinos in $?+n\to p+e^{-}$ is $\underset{\_}{v_e}$ .

Explanation of Solution

Using table 15.2,

The missing neutrino is electron-neutrino.

    $?+n\to p+e^{-}$        (IV)

Here, ${\overline{v}}_e$ is the electron-neutrino, $p$ is the proton and $n$ is the neutron.

Conclusion:

In this case, the electron-lepton is conserved.

    $L_e:1+0\to 0+1$

Therefore, the missing neutrinos in $?+n\to p+e^{-}$ is $\underset{\_}{v_e}$.

(e)

To determine

Supply the missing neutrinos in $?+\text{n}\to p+{\mu }^{-}$.

Answer to Problem 8P

The missing neutrinos in $?+\text{n}\to p+{\mu }^{-}$ is $\underset{\_}{v_{\mu }}$ .

Explanation of Solution

Using table 15.2,

The missing neutrino is electron-neutrino.

    $v_{\mu }+\text{n}\to p+{\mu }^{-}$        (V)

Here, ${\overline{v}}_e$ is the electron-neutrino, $p$ is the proton and $n$ is the neutron.

Conclusion:

In this case, the muon-lepton is conserved.

    $L_{\mu }:1+0\to 0+1$

Therefore, the missing neutrinos in $?+\text{n}\to p+{\mu }^{-}$ is $\underset{\_}{v_{\mu }}$.

(f)

To determine

Supply the missing neutrinos in ${\mu }^{-}\to e^{-}+?+?$.

Answer to Problem 8P

The missing neutrinos in ${\mu }^{-}\to e^{-}+?+?$ is $\underset{\_}{{\overline{v}}_e+v_{\mu }}$ .

Explanation of Solution

Using table 15.2,

The missing neutrino is electron-neutrino.

    ${\mu }^{-}\to e^{-}+{\overline{v}}_e+v_{\mu }$        (VI)

Here, ${\overline{v}}_e$ is the electron-neutrino, $p$ is the proton and $n$ is the neutron.

Conclusion:

In this case, the muon-lepton and electron-lepton are conserved.

    $\begin{array}{l}{L}_{\mu }:1\to 0+0+1\\ L_e:0+1-1+0\end{array}$

Therefore, the missing neutrinos in ${\mu }^{-}\to e^{-}+?+?$ is $\underset{\_}{{\overline{v}}_e+v_{\mu }}$.