Strange Particles
Strange particles are a class of hadrons first identified between the late 1940s and early 1960s, dubbed “strange” because they behaved in a way that defied expectations:
- They are produced in strong interactions, occurring almost instantaneously in high-energy collisions (such as cosmic-ray impacts or particle-beam experiments).
- They decay comparatively slowly, via the weak interaction.
This combination was puzzling, since particles born in strong interactions typically undergo equally rapid decays mediated by the strong force.
The Discovery
The first “strange” particle was observed in 1947 by George Rochester and Clifford Butler while studying cosmic-ray tracks in a cloud chamber.
They identified a neutral particle - now known as the neutral kaon ($K^0$) - with about twice the mass of a pion and an anomalously long lifetime for a particle produced through the strong interaction.
This particle decayed into two charged pions via the weak interaction:
$K^{0} \rightarrow \pi^{+} + \pi^{-}$
Soon after, charged kaons ($K^+$) were also detected, likewise exhibiting relatively long lifetimes and decaying through weak processes, for example:
$K^{+} \rightarrow \pi^{+} + \pi^{+} + \pi^{-}$
Kaons, being bound states of a quark and an antiquark - in this case including a strange quark - and having integer spin, were placed in the meson family alongside pions.
During the 1950s, a host of other strange-quark - containing particles were discovered:
- Baryons: the $\Lambda$ baryon (heavier than the proton), along with the $\Sigma$ and $\Xi$ families - all massive baryons.
- Mesons: the $\eta$ and $\phi$ mesons, both with strange-quark content.
In just a few years, the relatively tidy particle landscape of the 1940s - when the inventory seemed complete after neutrinos and muons - exploded into a bewildering zoo, with dozens of new states clamoring for classification.
Note. This “particle zoo” prompted, in the early 1960s, the Eightfold Way classification scheme (SU(3) symmetry) developed by Gell-Mann and Ne'eman, and later the quark model, paving the way for the modern framework of particle physics.
It was also at this time that physicists introduced a new quantum number - strangeness - to account for the surprising longevity of certain strongly produced particles, such as kaons and the $\Lambda$ baryon.
Key observations were:
- The strong interaction conserves strangeness; strange particles are therefore always produced in pairs (a strange quark and a strange antiquark).
- The weak interaction can change strangeness, but on a much longer timescale - giving strange particles lifetimes characteristic of weak decays (about $10^{-10}$ s), orders of magnitude longer than strong decays (about $10^{-23}$ s).
The Strangeness Quantum Number $S$
The strangeness quantum number $S$ counts the net number of strange quarks $s$ and strange antiquarks $\bar{s}$ in a hadron:
- Each strange quark $s$ contributes $S = -1$.
- Each strange antiquark $\bar{s}$ contributes $S = +1$.
This formalism, introduced in the early 1950s by Murray Gell-Mann and Kazuhiko Nishijima, codified the peculiar behavior of strange particles (kaons, hyperons, and others) and clarified two experimental facts:
- Strange particles are readily produced in strong interactions, but always in strange - antistrange pairs.
- They have lifetimes typical of weak decays, far longer than for comparable strongly decaying states.
Thus, strangeness is conserved in both strong and electromagnetic interactions, but violated in weak processes, which can alter $S$.
Sign convention. By Gell-Mann’s original definition, each strange quark carries $S = -1$ and each strange antiquark $S = +1$. While the opposite choice might have been more intuitive, this convention is now firmly established.
Example
A positively charged kaon $K^+$ contains an up quark ($u$) and a strange antiquark ($\bar{s}$), giving it $S = +1$.
$$ K^+ = u\bar{s} \quad\Rightarrow\quad S = +1$$
A negatively charged kaon $K^-$ contains an up antiquark ($\bar{u}$) and a strange quark ($s$), yielding $S = -1$.
$$K^- = \bar{u}s \quad\Rightarrow\quad S = -1$$
The $\Lambda$ baryon consists of an up quark ($u$), a down quark ($d$), and a strange quark ($s$), so $S = -1$.
$$ \Lambda = uds \quad\Rightarrow\quad S = -1$$
A proton is made of two up quarks ($u$) and one down quark ($d$), with no strange quark content, so $S = 0$.
$$ p =\; uud \quad \Rightarrow \quad\; S = 0$$
This table lists a representative set of hadrons and their corresponding strangeness quantum number $S$.
| Particle | Quark Content | S | Notes |
|---|---|---|---|
| Proton (p) | u u d | 0 | Stable light baryon |
| Neutron (n) | u d d | 0 | Light baryon; undergoes β decay |
| Pion π+ | u d̄ | 0 | Light pseudoscalar meson |
| Pion π− | ū d | 0 | Light pseudoscalar meson |
| Kaon K+ | u s̄ | +1 | Charged strange meson |
| Kaon K0 | d s̄ | +1 | Neutral strange meson |
| Kaon K− | ū s | −1 | Antiparticle of K+ |
| Anti-kaon K̄0 | d̄ s | −1 | Antiparticle of K0 |
| Λ0 | u d s | −1 | Strange baryon (Lambda) |
| Σ+ | u u s | −1 | Strange baryon (Sigma) |
| Σ0 | u d s | −1 | Strange baryon (Sigma) |
| Σ− | d d s | −1 | Strange baryon (Sigma) |
| Ξ0 | u s s | −2 | Doubly strange baryon (Xi) |
| Ξ− | d s s | −2 | Doubly strange baryon (Xi) |
| Ω− | s s s | −3 | Triply strange baryon (Omega) |
Conservation of Strangeness
The strangeness quantum number $S$ is conserved in all strong and electromagnetic interactions, but not in weak interactions.
- Strong interactions: $S$ is strictly conserved; the net strangeness cannot change.
- Weak interactions: $S$ can change; this is the mechanism by which strange particles decay.
Because the strong force preserves $S$, strange particles must be produced in pairs - a strange quark accompanied by a strange antiquark - so that the total strangeness remains unchanged.
As a result, no isolated strange particle is ever produced in a purely strong interaction.
Example 1: Strange-particle production via the strong interaction
A collision between a pion and a proton can produce a neutral kaon and a $\Lambda$ baryon:
$$ \pi^- + p^+ \rightarrow K^0 + \Lambda $$
The initial total strangeness ($S_{\text{tot}} = 0$) matches the final total ($+1 - 1 = 0$), demonstrating strangeness conservation.
$$ \pi^- (S=0) + p^+ (S=0) \rightarrow K^0 (S = +1) + \Lambda (S = -1)\; $$
Example 2: Weak decay of a strange particle
The $\Lambda$ baryon can decay into a proton and a pion:
$$ \Lambda \rightarrow p^+ + \pi^- $$
Here, the total strangeness changes from $-1$ to $0$, indicating that the process proceeds via the weak interaction, which allows $S$ to change.
$$ \Lambda (S = -1) \rightarrow p^+ (S = 0) + \pi^- (S = 0)\; $$
Why Are Strange Particles Produced in Pairs?
Strange particles (\(S \neq 0\)) are created in pairs during strong interactions due to the conservation of strangeness.
$$ S_{\text{initial}} = S_{\text{final}} $$
When the initial system has a total strangeness of \(S = 0\) - as is typically the case in collisions between protons, neutrons, pions, and similar particles - the final state must also have \(S = 0\).
This requirement ensures that strange particles produced in strong processes always appear in particle - antiparticle (or positive - negative strangeness) pairs.
Example
Consider a strong collision between a pion and a proton:
$$ \pi^- + p \ \longrightarrow \ K^0 \ (S = +1) \ + \ \Lambda \ (S = -1) $$
Here, the total strangeness changes from \(0\) to \(+1 + (-1) = 0\), preserving the conservation law.
Note: In weak interactions, strangeness is not conserved. A strange quark can transform into an up or down quark via the emission or absorption of a \(W\) boson. As a result, strange particles in weak decays can vanish without being balanced by a partner particle.
And so on.
