KAHIBARO
Table of Contents
Beyond Light Mesons
Heavy mesons are mesons that contain at least one heavy quark, usually a charm quark $c$ or a bottom quark $b$. Since mesons are made of a quark and an antiquark, a heavy meson can be written in forms such as $c\bar{u}$, $c\bar{d}$, $b\bar{u}$, or $b\bar{d}$. There are also mesons made from a heavy quark and its own antiquark, such as $c\bar{c}$ and $b\bar{b}$.
The word heavy refers to the large mass of the quark inside the meson. Because charm and bottom quarks are much heavier than up, down, and strange quarks, mesons containing them are much more massive than pions and kaons. Their larger mass strongly affects their decay patterns, lifetimes, and the kinds of states they can form.
A heavy meson is still a meson, so it always consists of one quark and one antiquark. The difference is that at least one of them is a heavy quark, typically $c$ or $b$.
Main Families of Heavy Mesons
Heavy mesons are commonly grouped into three important families.
The first family is the charmed mesons, usually called $D$ mesons. These contain one charm quark or one charm antiquark together with a lighter partner. Examples are $D^+$, $D^0$, and $D_s^+$.
The second family is the bottom mesons, usually called $B$ mesons. These contain one bottom quark or one bottom antiquark together with a lighter quark. Examples are $B^+$, $B^0$, and $B_s^0$.
The third family is heavy quarkonium, where the quark and antiquark are both heavy and of the same flavor. The most important examples are charmonium, $c\bar{c}$, and bottomonium, $b\bar{b}$.
| Family | Typical quark content | Example |
|---|---|---|
| Charmed mesons | $c\bar{q}$ or $\bar{c}q$ | $D^0 = c\bar{u}$ |
| Charmed strange mesons | $c\bar{s}$ or $\bar{c}s$ | $D_s^+ = c\bar{s}$ |
| Bottom mesons | $b\bar{q}$ or $\bar{b}q$ | $B^- = b\bar{u}$ |
| Bottom strange mesons | $b\bar{s}$ or $\bar{b}s$ | $B_s^0 = b\bar{s}$ |
| Charmonium | $c\bar{c}$ | $J/\psi$ |
| Bottomonium | $b\bar{b}$ | $\Upsilon$ |
Here $q$ means a light quark such as $u$ or $d$.
Charmed Mesons
Charmed mesons contain a charm quark or charm antiquark. Since the charm quark has charge $+\frac{2}{3}e$, the total charge of the meson depends on the partner antiquark or quark.
For example,
$$
D^0 = c\bar{u}
$$
because the charm quark has charge $+\frac{2}{3}e$ and the anti-up quark has charge $-\frac{2}{3}e$, so the total charge is zero.
Another example is
$$
D^+ = c\bar{d}
$$
since the anti-down quark has charge $+\frac{1}{3}e$, giving
$$
+\frac{2}{3}e + \frac{1}{3}e = +1e.
$$
The strange charmed meson is
$$
D_s^+ = c\bar{s}.
$$
These particles are unstable. They usually decay through the weak interaction, because changing charm into lighter quarks involves weak processes. As a result, their lifetimes are short, but often long enough to be measured clearly in particle detectors.
Bottom Mesons
Bottom mesons contain a bottom quark or bottom antiquark. Since the bottom quark has charge $-\frac{1}{3}e$, their charges again depend on the second constituent.
For example,
$$
B^- = b\bar{u}
$$
because
$$
-\frac{1}{3}e + \left(-\frac{2}{3}e\right) = -1e.
$$
A neutral bottom meson is
$$
B^0 = b\bar{d},
$$
with total charge
$$
-\frac{1}{3}e + \frac{1}{3}e = 0.
$$
There is also the strange bottom meson
$$
B_s^0 = b\bar{s}.
$$
Bottom mesons are especially important in modern particle physics because their decays help scientists study weak interactions and matter antimatter asymmetry. Their large mass gives many possible decay channels.
Typical heavy mesons decay mainly through the weak interaction, because the heavy quark changes into lighter quarks. This is why heavy mesons are unstable.
Heavy Quarkonium
A special kind of heavy meson is formed when a heavy quark is bound to its own antiquark. These states are called quarkonium.
For charm,
$$
c\bar{c}
$$
forms charmonium.
For bottom,
$$
b\bar{b}
$$
forms bottomonium.
These systems are important because they resemble a simple two body bound state. They are often compared, in a loose way, to the hydrogen atom, where two particles form discrete energy levels. Heavy quarkonium has ground states and excited states. Different excited states can decay by emitting photons, lighter hadrons, or lepton pairs.
Famous examples include the $J/\psi$ meson, which is a charmonium state, and the $\Upsilon$ meson, which is a bottomonium state.
Excited States and Spectroscopy
Heavy mesons can exist in several internal states. Even with the same quark content, the meson may have different total spin, orbital angular momentum, and total energy. This leads to many distinct particles with different masses.
For example, a heavy quark and antiquark can be in a lower energy state or in an excited state. The excited state can later decay into a lower state. Because of this, experiments observe whole families of related mesons.
This study of energy levels and mass differences is called meson spectroscopy. Heavy mesons are especially useful for spectroscopy because the heavy quarks make the bound states relatively well defined.
Charges of Some Heavy Mesons
The electric charge of a heavy meson is found by adding the charges of its quark and antiquark constituents.
To find the meson charge, add the constituent charges:
$$
Q_{\text{meson}} = Q_{\text{quark}} + Q_{\text{antiquark}}.
$$
Quark charges are
$$
Q_u = Q_c = Q_t = +\frac{2}{3}e,
\qquad
Q_d = Q_s = Q_b = -\frac{1}{3}e.
$$
Antiquarks have the opposite charges.
| Meson | Quark content | Charge |
|---|---|---|
| $D^0$ | $c\bar{u}$ | $0$ |
| $D^+$ | $c\bar{d}$ | $+1$ |
| $D_s^+$ | $c\bar{s}$ | $+1$ |
| $B^-$ | $b\bar{u}$ | $-1$ |
| $B^0$ | $b\bar{d}$ | $0$ |
| $B_s^0$ | $b\bar{s}$ | $0$ |
Why Heavy Mesons Matter
Heavy mesons are important because they let physicists test how quarks bind together and how heavy quarks decay. Since charm and bottom quarks are much heavier than ordinary quarks in matter, heavy mesons provide a clean way to study strong and weak interactions together.
They are also central in experiments that measure rare decays, lifetimes, and mixing effects. In particular, neutral heavy mesons such as $B^0$ and $B_s^0$ can show rich behavior that helps test the Standard Model.
A Simple Constituent Picture
A useful beginner picture is to imagine the meson as two constituents bound together by the strong interaction, one quark and one antiquark. In heavy mesons, one or both of these constituents are heavy.
In this drawing, $Q$ represents a heavy quark such as $c$ or $b$, and $\bar{q}$ represents a lighter antiquark. For quarkonium, both sides would be heavy, such as $c$ and $\bar{c}$.
Final View
Heavy mesons are mesons containing charm or bottom quarks. The most important types are $D$ mesons, $B$ mesons, charmonium, and bottomonium. Their large masses, short lifetimes, and rich excited state structure make them a major tool for studying the behavior of quarks and the forces acting on them.