KAHIBARO
Table of Contents
Strange mesons
Kaons are mesons that contain one strange quark or one strange antiquark, together with one up or down quark or antiquark. They are important because they were among the first particles to show that new quantum numbers were needed in particle physics, especially strangeness. Since this chapter is about kaons specifically, the focus is on what they are made of, how they are classified, and their most characteristic physical features.
A meson is a quark-antiquark particle, so every kaon has exactly two constituents, one quark and one antiquark. What makes a kaon different from a pion is the presence of strangeness through the strange quark, $s$, or strange antiquark, $\bar{s}$.
Quark content of kaons
The four basic kaons are built from combinations of up, down, and strange flavors. Their electric charges follow directly from the quark charges, where
$$
Q_u = +\frac{2}{3}, \qquad Q_d = -\frac{1}{3}, \qquad Q_s = -\frac{1}{3}
$$
and antiquarks have opposite charges.
The most common kaons are shown in the table below.
| Particle | Quark content | Charge |
|---|---|---|
| $K^+$ | $u\bar{s}$ | $+1$ |
| $K^0$ | $d\bar{s}$ | $0$ |
| $K^-$ | $\bar{u}s$ | $-1$ |
| $\bar{K}^0$ | $\bar{d}s$ | $0$ |
For example, the charge of the positive kaon is
$$
Q(K^+) = Q_u + Q_{\bar{s}} = \frac{2}{3} + \frac{1}{3} = +1
$$
and the neutral kaon has
$$
Q(K^0) = Q_d + Q_{\bar{s}} = -\frac{1}{3} + \frac{1}{3} = 0
$$
A kaon is a meson containing exactly one strange constituent, either $s$ or $\bar{s}$, together with a light up or down partner.
Strangeness of kaons
Kaons are closely tied to the quantum number called strangeness. By convention, the strange quark has strangeness
$$
S(s) = -1
$$
so the strange antiquark has
$$
S(\bar{s}) = +1
$$
This means
$$
S(K^+) = S(K^0) = +1
$$
because both contain $\bar{s}$, while
$$
S(K^-) = S(\bar{K}^0) = -1
$$
because both contain $s$.
This property made kaons historically very interesting. In some reactions they are produced strongly, where strangeness is conserved, but they decay weakly, where strangeness can change. That combination explains why they can be produced relatively easily yet live longer than many strongly interacting particles.
For kaons, strangeness is determined by the strange constituent. If the kaon contains $\bar{s}$, then $S=+1$. If it contains $s$, then $S=-1$.
Kaons as members of the pseudoscalar meson family
The lightest kaons belong to the pseudoscalar meson family. These have spin $0$. They are similar in that sense to pions, but they are heavier because the strange quark is heavier than the up and down quarks.
So, compared with pions, kaons usually have larger mass and different decay behavior. Their greater mass affects which decays are possible and how much kinetic energy can appear in the decay products.
A simple quark picture is shown below.
Charged and neutral kaons
Charged kaons, $K^+$ and $K^-$, are particle-antiparticle partners. Neutral kaons are a little more subtle. The particles $K^0$ and $\bar{K}^0$ are distinct in quark content, even though both are electrically neutral.
This is an important point. Neutral does not mean identical. The state $K^0 = d\bar{s}$ is different from $\bar{K}^0 = \bar{d}s$. Because they are different states, they can be created in different reactions and can transform into one another through weak interactions.
Do not confuse $K^0$ with $\bar{K}^0$. Both are neutral, but they have different quark content:
$$
K^0 = d\bar{s}, \qquad \bar{K}^0 = \bar{d}s
$$
Kaon masses and lifetimes
Kaons are heavier than pions but much lighter than many hadrons containing charm or bottom quarks. Their masses are roughly around $494 \text{ MeV}/c^2$ for charged kaons and about $498 \text{ MeV}/c^2$ for neutral kaons.
| Kaon | Approximate mass |
|---|---|
| $K^\pm$ | $494 \text{ MeV}/c^2$ |
| $K^0, \bar{K}^0$ | $498 \text{ MeV}/c^2$ |
Their lifetimes are long compared with particles that decay via the strong interaction. This is because kaons decay mainly through the weak interaction. The weak interaction is much slower than the strong interaction.
Charged kaons typically live for about
$$
\tau \sim 10^{-8}\,\text{s}
$$
Neutral kaons are more complicated because the physical neutral-kaon states observed in experiments are mixtures of $K^0$ and $\bar{K}^0$, and these mixtures can have very different lifetimes.
Typical decays
Kaons decay into lighter particles, often including pions, muons, electrons, and neutrinos. Some common examples are
$$
K^+ \to \mu^+ + \nu_\mu
$$
and
$$
K^+ \to \pi^+ + \pi^0
$$
Neutral kaons can also decay into pions. Their decay patterns played a major role in the study of weak interactions and symmetry properties.
The exact decay probabilities are part of kaon phenomenology, but at a basic level, the key idea is that kaons are unstable strange mesons that decay weakly into lighter particles.
Why kaons matter
Kaons are historically and physically important for several reasons. They provided early evidence that hadrons could carry a new conserved quantity in strong interactions, strangeness. They also revealed unusual behavior in the neutral sector, where particle and antiparticle states can mix. This made kaons central to the development of modern particle physics.
In the quark model, kaons are also a clear and simple example of how hadrons are built from quark flavors. They show how the addition of a strange quark changes mass, quantum numbers, and decay properties compared with the lighter mesons.
Key facts about kaons:
$$
K^+ = u\bar{s}, \quad K^0 = d\bar{s}, \quad K^- = \bar{u}s, \quad \bar{K}^0 = \bar{d}s
$$
They are mesons, they contain strangeness, and they decay mainly through the weak interaction.
Summary picture
Kaons sit between the very light non-strange mesons and the much heavier mesons containing charm or bottom. They are strange mesons made from one light quark and one strange quark or antiquark. Their charge comes from the constituent quark charges, and their defining feature is their nonzero strangeness.