KAHIBARO
Table of Contents
Meaning of charm
Charm is a particle quantum number used to describe the presence of charm quarks in a particle. It helps classify hadrons and track what happens in particle reactions and decays.
A charm quark, written as $c$, carries charm number
$$
C = +1
$$
Its antiparticle, the anti-charm quark $\bar c$, carries charm number
$$
C = -1
$$
Any quark that is not a charm quark has charm number $0$.
For a composite particle, the total charm is the sum of the charm numbers of all its constituent quarks and antiquarks.
Important rule:
$$
C = N_c - N_{\bar c}
$$
where $N_c$ is the number of charm quarks and $N_{\bar c}$ is the number of anti-charm quarks.
Why charm is useful
Charm was introduced because some particles could not be fully described using only charge, baryon number, lepton number, and strangeness. When new hadrons containing charm quarks were discovered, physicists needed a new quantum number to label them.
Charm helps us do two main things. It helps identify the quark content of hadrons, and it helps check whether a reaction is allowed under a given interaction.
Charm of common particles
The charm number depends directly on quark content. A hadron with one charm quark has $C=+1$. A hadron with one anti-charm quark has $C=-1$. A particle containing both $c$ and $\bar c$ has net charm zero.
| Particle | Quark content | Charm number |
|---|---|---|
| Proton $p$ | $uud$ | $0$ |
| Neutron $n$ | $udd$ | $0$ |
| $D^+$ meson | $c\bar d$ | $+1$ |
| $D^0$ meson | $c\bar u$ | $+1$ |
| $\bar D^0$ meson | $\bar c u$ | $-1$ |
| $D^-$ meson | $\bar c d$ | $-1$ |
| $J/\psi$ | $c\bar c$ | $0$ |
| $\Lambda_c^+$ | $udc$ | $+1$ |
The particle $J/\psi$ is a good example of an important idea. Even though it contains charm, it also contains anti-charm, so the net charm is zero.
Open charm and hidden charm
Particles are often grouped into two useful categories.
Open charm means the particle has nonzero net charm, such as $D^+$ or $\Lambda_c^+$.
Hidden charm means the particle contains a $c\bar c$ pair but has total charm zero, such as $J/\psi$.
This distinction matters because open-charm and hidden-charm particles are produced and decay in different ways.
Conservation of charm
Charm is not always conserved in every type of interaction in the same way.
In strong interactions, charm is conserved.
In electromagnetic interactions, charm is also conserved.
In weak interactions, charm can change.
Key idea:
Strong and electromagnetic processes conserve charm.
Weak processes can change charm, typically by $\Delta C = \pm 1$.
This makes charm very useful for identifying which interaction is likely responsible for a process.
Examples of conservation and nonconservation
Consider strong production of a charm and anti-charm pair:
$$
p + p \to p + p + D^0 + \bar D^0
$$
The initial total charm is $0$. The final charm is
$$
C_{\text{final}} = (+1) + (-1) = 0
$$
So charm is conserved.
Now consider a weak decay of a charmed meson:
$$
D^+ \to K^- + \pi^+ + \pi^+
$$
The initial particle has $C=+1$. The final particles have no charm, so the final charm is $0$. Charm changed, so this must proceed through the weak interaction.
Charm in quark transitions
At the quark level, weak processes can convert a charm quark into lighter quarks. For example, a charm quark may change into a strange quark or a down quark through the weak interaction.
Symbolically, one possible weak transition is
$$
c \to s + W^+
$$
The charm number changes from $+1$ to $0$. This is why charmed particles can decay into non-charmed particles.
A full treatment of weak interactions belongs elsewhere, but here the important point is that charm is not an absolutely conserved quantity in nature. Its conservation depends on the interaction.
Relation to other flavor quantum numbers
Charm belongs to a family of flavor quantum numbers used to track quark types inside hadrons. Strangeness tracks strange quarks, and charm tracks charm quarks. Each flavor quantum number is defined by counting a particular quark minus its antiquark.
This makes charm part of a broader bookkeeping system in particle physics.
Simple visual picture
A charmed meson can be pictured as a quark and an antiquark, with one of them carrying charm.
How to calculate charm quickly
To find the charm number of a hadron, inspect its quark content and count charm quarks and anti-charm quarks.
If a particle has one $c$ and no $\bar c$, then $C=+1$.
If it has one $\bar c$ and no $c$, then $C=-1$.
If it has one of each, then $C=0$.
If it has none, then $C=0$.
Quick calculation rule:
$$
C = (\text{number of } c) - (\text{number of } \bar c)
$$
Add the contributions from all constituents.
Summary
Charm is the quantum number associated with charm quarks. A charm quark has $C=+1$, an anti-charm quark has $C=-1$, and the total charm of a particle is the sum over its constituents. Charm is conserved in strong and electromagnetic interactions, but it can change in weak interactions. Because of this, charm is a powerful tool for classifying hadrons and analyzing particle reactions.