Question

Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations:

(a) uus, (b) $\mathbf{c}\overline{\mathbf{s}}$ (c) $\overline{\mathbf{d}}\overline{\mathbf{d}}\overline{\mathbf{u}}$(d)$\overline{\mathbf{c}}\mathbf{b}$.

Short answer

a) The electric charge, baryon number, strangeness quantum number, and charm quantum number for $uus$are +1, +1, $-1$and 0 respectively.

b) The electric charge, baryon number, strangeness quantum number, and charm quantum number for $c\overline{s}$are +1, 0, +1 and +1 respectively.

c) The electric charge, baryon number, strangeness quantum number, and charm quantum number for $\overline{d}\overline{d}\overline{u}$are +1, $-1$, 0 and 0 respectively.

d) The electric charge, baryon number, strangeness quantum number, and charm quantum number for $\overline{c}b$are$-1$, 0, 0 and$-1$ respectively.

Step-by-step solution

Define Quark

Hadrons are composites of constituents with spin$\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}}$ fermions called quarks.

Given information

The table shows the properties of the original quarks:

Determine Q, B, S & C

a)

For the quarks: uus

$$\begin{gathered} Q=\frac{2}{3}+\frac{2}{3}+\left(-\frac{1}{3}\right) \\ =+1 \\ B=\frac{1}{3}+\frac{1}{3}+\frac{1}{3} \\ =+1 \\ S=0+0-1 \\ =-1 \\ C=0+0+0 \\ =0 \end{gathered}$$

Hence, the electric charge, baryon number, strangeness quantum number, and charm quantum number for uus are +1, +1, $-1$and 0 respectively.

b)

For the quarks:$c\overline{s}$

$$\begin{gathered} Q=\frac{2}{3}+\frac{1}{3} \\ =+1 \\ B=\frac{1}{3}-\frac{1}{3} \\ =0 \\ S=0+1 \\ =+1 \\ C=1+0 \\ =+1 \end{gathered}$$

Hence, the electric charge, baryon number, strangeness quantum number, and charm quantum number for $c\overline{s}$are +1, 0, +1 and +1 respectively.

Determine  Q, B, S & C.

c)

For the quarks:$\overline{d}\overline{d}\overline{u}$

$$\begin{gathered} Q=\frac{1}{3}+\frac{1}{3}+\left(-\frac{2}{3}\right) \\ =0 \\ B=\left(-\frac{1}{3}\right)+\left[-\frac{1}{3}\right]+\left[-\frac{1}{3}\right] \\ =-1 \\ S=0+0+0 \\ =0 \\ C=0+0+0 \\ =0 \end{gathered}$$

Hence, the electric charge, baryon number, strangeness quantum number, and charm quantum number for$\overline{d}\overline{d}\overline{u}$ are +1,$-1$, 0 and 0 respectively.

d)

For the quarks:$\overline{c}b$

$$\begin{gathered} Q=-\frac{2}{3}+\frac{1}{3} \\ =-1 \\ B=\left(-\frac{1}{3}\right)+\frac{1}{3} \\ =0 \\ S=0+0 \\ =0 \\ C=-1+0 \\ =-1 \end{gathered}$$

Hence, the electric charge, baryon number, strangeness quantum number, and charm quantum number for $\overline{c}b$are$-1$, 0, 0 and$-1$ respectively.