As we have seen, the ${\mathbf{\pi }}^{\mathbf{-}\mathbf{1}}$meson has the quark structure $\mathit{d}\overline{\mathbf{u}}$.

Which of the following conservation laws would be violated if a${\mathbf{\pi }}^{\mathbf{-}\mathbf{1}}$

were formed, instead, from a d quark and a u quark: (a) energy, (b)

angular momentum, (c) charge, (d) lepton number, (e) linear momentum,

(f) baryon number?

The quark structure of ${\pi }^{-}$meson is $d\overline{\mathrm{u}}$

Quarks and Mesons

Mesons are hadronic subatomic particles in particle physics that are made up of an equal number of quarks and antiquarks, typically one of each, and are joined by strong interactions.

Instead of a $\overline{\mathrm{u}}$quark, we are considering a u quark. So, we just need to consider the properties of $\overline{\mathrm{u}}$and u which are different.

According to the energy conservation

The energy of $\overline{\mathrm{u}}$ quark = Energy of a u quark

Energy can be given as

$E=m{c}^2$

Where E is energy, m is mass, c is the velocity of light.

The rest mass of u quark

$$\begin{gathered} m_u=10\mathrm{MeV}/{\mathrm{c}}^2 \\ {\mathrm{m}}_{\overline{\mathrm{u}}}=10\mathrm{MeV}/{\mathrm{c}}^2 \end{gathered}$$

Because the rest mass of the particle and its antiparticle is the same therefore energy corresponding to them will be the same so the energy conservation law will not be violated.

According to the angular momentum conservation

The spin of $\overline{\mathrm{u}}$ quark = The spin of a u quark

Because the spin of a particle and its antiparticle is the same therefore spin angular momentum corresponding to them will be the same so the angular momentum conservation law will not be violated.

According to the charge conservation

The charge of $\overline{\mathrm{u}}$ quark = The charge of a u quark

Because the charge of a particle and its antiparticle are opposite, so the charge conservation law will be violated

According to the lepton number conservation

lepton number of $\overline{\mathrm{u}}$ quark = Lepton number of a u quark

Since all the quarks have lepton number zero.

Because the lepton number of a particle and its antiparticle are the same, so the lepton number conservation law will not be violated.

According to the linear momentum conservation

Linear momentum of $\overline{\mathrm{u}}$ quark = linear momentum of a u quark

Because the direction of both the particle and its antiparticle is upward, therefore, linear momentum corresponding to them will be the same so the linear momentum conservation law will not be violated

According to the Baryon number conservation

Baryon number of $\overline{\mathrm{u}}$ quark = Baryon number of a u quark

Baryon number of a u quark is $+\frac{1}{3}$

Baryon number of $\overline{\mathrm{u}}$ quark is$-\frac{1}{3}$

Because the baryon number of a particle and its antiparticle are different, so the baryon number conservation law will be violated.