Color Conservation in QCD
Color conservation is a cornerstone of quantum chromodynamics (QCD), the theory describing the strong force between quarks and gluons. The rule is simple but strict:
In every strong interaction, the total color charge (the SU(3) gauge charge) is conserved.
In practice, this means a quark can change its color (say, from red to green), but the change is always balanced by a gluon that carries away the corresponding color - anticolor combination.
Example
A red quark emits a red - antigreen gluon.
The quark turns green, while the gluon carries off the “red - antigreen” piece.
$$ \text{Red quark} \longrightarrow \text{Green quark} + \text{Gluon (red - antigreen)} $$
The bookkeeping works out as follows:
- Before: red
- After: green + (red - antigreen). Since green and antigreen cancel, what’s left overall is red.
The net color charge is conserved.
Note. When I write red - antigreen, I mean a color - anticolor state, not a subtraction. In technical literature, you’ll also see it written as “red ⊗ antigreen.”
Color in QCD
In QCD, “color” has nothing to do with visible light. It is a quantum charge, similar in spirit to electric charge in quantum electrodynamics (QED), but richer in structure.
Quarks come in three “colors”:
- red
- green
- blue
Gluons, the carriers of the strong force, always carry a color - anticolor combination (e.g., red - antigreen).
Unlike photons, which are neutral, gluons themselves carry color charge.
Note. Electromagnetic and weak interactions don’t affect color. Photons don’t couple to color, so QED automatically conserves it. The weak bosons $W^\pm$ and $Z^0$ also ignore color. At those vertices, the quark’s color stays untouched.
Gluon - gluon couplings
One of the hallmarks of QCD is that gluons can interact with one another - something photons never do.
Even in these non-abelian interactions, color conservation holds: individual gluons may change, but the total color charge is unchanged.
For instance, two gluons collide. One carries red - antiblue, the other blue - antigreen. The outcome might be a red - antigreen gluon, among other allowed states. In all cases, the overall color charge is preserved.
Confinement and color neutrality
Free quarks and gluons are never observed in nature: they are permanently confined inside composite particles. This property is known as confinement.
The particles we actually detect - protons, neutrons, and the like - are always color-neutral, meaning their colors sum to zero.
For example, three quarks with red, green, and blue combine into a colorless baryon (like a proton or neutron). Likewise, a quark and an antiquark of opposite color form a colorless meson.
Because all observable particles are color-neutral, color itself is never directly measurable, and the conservation of color never shows up as an isolated effect in experiments.
Still, even though it cannot be directly observed, color conservation is essential. It guarantees the internal consistency of QCD and, more broadly, of the entire Standard Model.
Worked examples
Here are a few concrete illustrations of color conservation:
Example 1 (quark emits a gluon)
A red quark emits a red - antigreen gluon:
$$ q_{\text{red}} \;\;\longrightarrow\;\; q_{\text{green}} + g_{\text{red⊗antigreen}} $$
The quark switches color (red → green).
The gluon carries the matching color - anticolor pair.
Overall balance: red before, red after.
Example 2 (quark - quark gluon exchange)
A red quark and a green quark exchange a gluon.
The red quark becomes blue, while the green one turns red.
$$ q_{\text{red}} + q_{\text{green}} \;\;\longrightarrow\;\; q_{\text{blue}} + q_{\text{red}} + g_{\text{(intermediate)}} $$
The intermediate gluon carries the color shift.
The net color balance remains unchanged.
Example 3 (gluon - gluon interaction)
Two gluons collide: one red - antiblue, the other blue - antigreen.
The interaction may yield a red - antigreen gluon (among other outcomes).
The overall color - anticolor sum is conserved.
Example 4 (baryon formation)
Three quarks of different colors - red, green, and blue - bind together:
$$ q_{\text{red}} + q_{\text{green}} + q_{\text{blue}} \;\;\longrightarrow\;\; \text{colorless proton} $$
The three colors cancel perfectly.
The result is a color-neutral particle, which can exist freely in nature.
Example 5 (meson formation)
A red quark and an antired antiquark pair up:
$$ q_{\text{red}} + \bar{q}_{\text{antired}} \;\;\longrightarrow\;\; \text{colorless meson} $$
The color and anticolor annihilate each other.
The outcome is a color-neutral meson.
And so on.
