KAHIBARO
Table of Contents
A New Kind of Quantum Number
In particle physics, many reactions seem to follow hidden bookkeeping rules. Electric charge is one example, and baryon number and lepton number are others. Strangeness is another such quantum number. It was introduced to describe a puzzling fact, some particles were produced easily in high energy collisions, but then decayed more slowly than expected.
These particles were called strange particles because their behavior looked unusual. They were created in processes that happened quickly, but they decayed in processes that happened more slowly. To track this pattern, physicists assigned them a new quantum number called strangeness, usually written as $S$.
Why Strangeness Was Introduced
Before quarks were known, experiments found particles such as kaons and hyperons. These particles were often produced in pairs in strong interactions, which happen very fast. But their decays took much longer, which suggested that their decays were not caused by the strong interaction.
The idea of strangeness solved this mystery. In strong interactions, strangeness is conserved. In weak interactions, strangeness can change. This explains why strange particles can be produced readily in strong collisions, but decay more slowly through the weak interaction.
Strangeness is conserved in strong and electromagnetic interactions, but it is not generally conserved in weak interactions.
Strangeness and Quarks
In the quark model, strangeness is tied to the strange quark, written as $s$.
A strange quark has strangeness
$$
S = -1
$$
An anti strange quark, written as $\bar{s}$, has strangeness
$$
S = +1
$$
Up and down quarks have zero strangeness, and so do their antiparticles unless they contain strange content.
For a hadron, the total strangeness is the sum of the strangeness values of its quark constituents.
Rule for hadrons:
$$
S = -(\text{number of } s \text{ quarks}) + (\text{number of } \bar{s} \text{ quarks})
$$
Examples of Strangeness
Let us look at some common particles.
| Particle | Quark content | Strangeness $S$ |
|---|---|---|
| Proton $p$ | $uud$ | $0$ |
| Neutron $n$ | $udd$ | $0$ |
| Kaon $K^+$ | $u\bar{s}$ | $+1$ |
| Kaon $K^0$ | $d\bar{s}$ | $+1$ |
| Kaon $K^-$ | $\bar{u}s$ | $-1$ |
| Anti kaon $\bar{K}^0$ | $\bar{d}s$ | $-1$ |
| Lambda $\Lambda^0$ | $uds$ | $-1$ |
| Sigma $\Sigma^+$ | $uus$ | $-1$ |
| Xi $\Xi^0$ | $uss$ | $-2$ |
| Omega $\Omega^-$ | $sss$ | $-3$ |
This table shows that particles with one strange quark usually have $S=-1$, while particles with one anti strange quark have $S=+1$.
Conservation in Particle Reactions
Strangeness conservation is especially useful when checking whether a reaction can occur by the strong interaction.
Consider the reaction
$$
\pi^- + p \rightarrow \Lambda^0 + K^0
$$
The pion $\pi^-$ has $S=0$, and the proton has $S=0$, so the initial total strangeness is
$$
S_{\text{initial}} = 0
$$
On the final side, $\Lambda^0$ has $S=-1$ and $K^0$ has $S=+1$, so
$$
S_{\text{final}} = -1 + 1 = 0
$$
The total strangeness is conserved, so this reaction is allowed as a strong interaction.
Now consider the decay
$$
\Lambda^0 \rightarrow p + \pi^-
$$
The initial strangeness is
$$
S_{\text{initial}} = -1
$$
The final particles, proton and pion, each have $S=0$, so
$$
S_{\text{final}} = 0
$$
Strangeness changes by $+1$, so this decay cannot proceed via the strong interaction. It occurs through the weak interaction.
To test strangeness conservation in a reaction, add the strangeness of all initial particles and compare with the sum for all final particles.
Associated Production
A major clue in the discovery of strangeness was that strange particles were often produced together. This is called associated production.
For example,
$$
\pi^- + p \rightarrow K^0 + \Lambda^0
$$
The kaon has $S=+1$ and the lambda has $S=-1$. Their total is zero, matching the initial state. Strong interactions can therefore create a strange quark and an anti strange quark together.
This fits naturally with the quark picture. A strong interaction can create an $s\bar{s}$ pair. One of these may go into one hadron, and the other into another hadron.
Strangeness in Weak Decay
Strange particles usually decay by the weak interaction. In weak processes, strangeness can change, often by one unit.
For example, in
$$
K^+ \rightarrow \pi^+ + \pi^0
$$
the kaon has $S=+1$, while the pions have $S=0$. So strangeness changes by $-1$.
Likewise, in
$$
\Lambda^0 \rightarrow p + \pi^-
$$
the strangeness changes from $-1$ to $0$, so
$$
\Delta S = +1
$$
This is why such decays are slower than strong decays.
Typical weak decays of strange particles have
$$
\Delta S = \pm 1
$$
while strong and electromagnetic processes have
$$
\Delta S = 0
$$
Relation to the Strange Quark
The name strangeness becomes very natural in the quark model. A strange hadron is simply a hadron containing one or more strange quarks or anti strange quarks.
If a particle contains more strange quarks, the magnitude of its strangeness becomes larger. For example,
$$
\Xi^0 = uss \quad \Rightarrow \quad S=-2
$$
and
$$
\Omega^- = sss \quad \Rightarrow \quad S=-3
$$
So strangeness counts strange quark content with a sign convention.
Historical Importance
Strangeness played an important role in organizing the growing list of hadrons before the full quark model was established. It helped physicists classify particles into families and understand which reactions were allowed.
Later, when the strange quark was introduced, strangeness gained a simple microscopic meaning. It became one of the flavor quantum numbers used to describe hadrons.
What Strangeness Tells Us
Strangeness is useful because it helps answer three questions. First, does a particle contain strange quark content. Second, can a reaction happen through the strong interaction. Third, if strangeness changes, must the weak interaction be involved.
This makes strangeness a powerful conservation tool in particle physics.
Key facts about strangeness:
$$
S(s) = -1, \qquad S(\bar{s}) = +1
$$
$$
S_{\text{total}} = \sum S_i
$$
Strong and electromagnetic interactions conserve strangeness:
$$
\Delta S = 0
$$
Weak interactions may change strangeness, commonly by one unit:
$$
\Delta S = \pm 1
$$
Simple Reaction Check
Suppose we test
$$
K^- + p \rightarrow \Sigma^0 + \pi^0
$$
The initial strangeness is
$$
S_{\text{initial}} = (-1) + 0 = -1
$$
The final strangeness is
$$
S_{\text{final}} = (-1) + 0 = -1
$$
So strangeness is conserved. This reaction can proceed through the strong interaction.
Now test
$$
K^+ \rightarrow \mu^+ + \nu_\mu
$$
The initial strangeness is $+1$, and the final particles have $S=0$, so strangeness changes. Therefore the decay is weak.
Final Perspective
Strangeness is a flavor quantum number associated with the presence of strange quarks. It was invented to explain the unusual production and decay patterns of certain hadrons. Today it is understood as a simple counting rule for strange quarks and anti strange quarks, and as a conservation law that holds in strong and electromagnetic processes but can be violated in weak ones.