Chapter 1: Q71P (page 1)

Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations:\[\left( \mathbf{a} \right)\text{ }\mathbf{uus},\text{ }\left( \mathbf{b} \right)\text{ }\mathbf{c\bar{s}},\text{ }\left( \mathbf{c} \right)\text{ }\mathbf{\bar{d}\bar{d}\bar{u}},\] and \[\left( \mathbf{d} \right)\text{ }\mathbf{\bar{c}b}.\]

Short Answer

Expert verified

The electric charge, baryon number, strangeness quantum number, and charm quantum number for $uus$ are $+1,\text{ }+\text{1},\text{ }-\text{1}$ and $0$ respectively.
The electric charge, baryon number, strangeness quantum number, and charm quantum number for $c\bar{s}$ are $+1,\text{ }0,\text{ }+1$ and $+1$ respectively
The electric charge, baryon number, strangeness quantum number, and charm quantum number for $\bar{d}\bar{d}\bar{u}$ are $+1,\text{ }-1,\text{ 0}$ and $0$ respectively.
The electric charge, baryon number, strangeness quantum number, and charm quantum number for $\bar{c}b$ are $-1,\text{ }0,\text{ }0$ and $-1$ respectively.

Step by step solution

Define Quark

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

Given information

The table shows the properties of the original quarks

Symbol	$Q/e$	Baryon number$\left( B \right)$	Strangeness $\left( S \right)$	Charm
$u$	$\frac{2}{3}$	$\frac{1}{3}$	$0$	$0$
$d$	-\frac{1}{3}	$\frac{1}{3}$	$0$	$0$
$s$	-\frac{1}{3}	$\frac{1}{3}$	$-1$	$0$
$c$	$\frac{2}{3}$	$\frac{1}{3}$	$0$	$1$
$\bar{s}$	$\frac{1}{3}$	$-\frac{1}{3}$	$1$	$0$
$\bar{d}$	$\frac{1}{3}$	$-\frac{1}{3}$	$0$	$0$
$\bar{u}$	$-\frac{2}{3}$	$-\frac{1}{3}$	$0$	$0$
$\bar{c}$	$-\frac{2}{3}$	$-\frac{1}{3}$	$0$	$-1$
$b$	$-\frac{1}{3}$	$\frac{1}{3}$	$0$	$0$

Determine $Q,\text{ B, S }\!\!\And\!\!\text{ C}$

For the quarks: $uus$

$\begin{align}

& Q=\frac{2}{3}+\frac{2}{3}+\left( -\frac{1}{3} \right) \\

& =+1 \\

& B=\frac{1}{3}+\frac{1}{3}+\frac{1}{3} \\

& =+1

\end{align}$

$\begin{align}

& S=0+0-1 \\

& =-1 \\

& C=0+0+0 \\

& =0

\end{align}$

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

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

$\begin{align}

& Q=\frac{2}{3}+\frac{1}{3} \\

& =+1 \\

& B=\frac{1}{3}-\frac{1}{3} \\

& =0

\end{align}$

$\begin{align}

& S=0+1 \\

& =+1 \\

& C=1+0 \\

& =+1

\end{align}$

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

Determine $Q,\text{ B, S }\!\!\And\!\!\text{ C}$.

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

$\begin{align}

& 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

\end{align}$

$\begin{align}

& S=0+0+0 \\

& =0 \\

& C=0+0+0 \\

& =0

\end{align}$

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

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

$\begin{align}

& Q=-\frac{2}{3}+\frac{1}{3} \\

& =-1 \\

& B=\left( -\frac{1}{3} \right)+\frac{1}{3} \\

& =0

\end{align}$

$\begin{align}

& S=0+0 \\

& =0 \\

& C=-1+0 \\

& =-1

\end{align}$

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