Chapter 12, Problem 24P

To determine

To distinguish a particle made up of $\overline{d}\overline{u}\overline{s}$ and $dus$. And similarly, for the particle made up of $\overline{d}\overline{s}\overline{s}$ and $dss$.

Answer to Problem 24P

There is a difference of baryon number and strangeness for the $\overline{d}\overline{u}\overline{s}$ and $dus$ combination. For $\overline{d}\overline{s}\overline{s}$ and $dss$ combination there is a difference of fractional charge, baryon number and strangeness.

Explanation of Solution

Introduction:

The baryon is a type of composite subatomic particle which consists of quarks and antiquarks.

The subatomic particles in baryon category are made up of up, down and strange quark.

Compare the particle composed of $\overline{d}\overline{u}\overline{s}$ and $dus$.

• The baryon number of both combinations is different:

Baryon number for each quark is $+\frac{1}{3}$ and for each anti quark is $-\frac{1}{3}$.

So, Baryon number for $\overline{d}\overline{u}\overline{s}$ combination is $-\frac{1}{3}-\frac{1}{3}-\frac{1}{3}=-1$

And Baryon number for $dsu$ combination is $+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=+1$

• The strangeness of both combinations is different:

Strangeness number for up, down, antiup and antidown quark is $0$ and for strange quark is $-1$ and for anti-strange quark is $+1$

So, strangeness number for $\overline{d}\overline{u}\overline{s}$ combination is $0+0+1=+1$

And strangeness number for $dsu$ combination is $0+0-1=-1$

Compare the particle composed of $\overline{d}\overline{s}\overline{s}$ and $dss$.

• The baryon number of both combinations is different:

Baryon number for each quark is $+\frac{1}{3}$ and for each anti quark is $-\frac{1}{3}$.

So, Baryon number for $\overline{d}\overline{s}\overline{s}$ combination is $-\frac{1}{3}-\frac{1}{3}-\frac{1}{3}=-1$

And Baryon number for $dss$ combination is $+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=+1$

• The strangeness of both combinations is different:

Strangeness number for up, down, anti up and anti down quark is $0$ and for strange quark is $-1$ and for anti-strange quark is $+1$

So, strangeness number for $\overline{d}\overline{s}\overline{s}$ combination is $0+1+1=+2$

And strangeness number for $dss$ combination is $0-1-1=-2$

• The fractional change of combination of quarks are different.

The fractional charge of Up quark is +2/3, while down, strange, and all have a charge of -1/3.

Total fractional charge of $\overline{d}\overline{s}\overline{s}$ = $+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=+1$

Total fractional charge of $dss$ = $-\frac{1}{3}-\frac{1}{3}-\frac{1}{3}=-1$.

Conclusion:

Thus, $\overline{d}\overline{u}\overline{s}$ and $dus$ combination there is a difference of baryon number and strangeness. And for $\overline{d}\overline{s}\overline{s}$ and $dss$ combination there is a difference of fractional charge, baryon number and strangeness.