Question Video: Determining the Color Charge of a Gluon Physics

The Feynman diagram shows two up quarks exchanging a gluon. What is the color charge of the gluon?


Video Transcript

The Feynman diagram shows two up quarks exchanging a gluon. What is the color charge of the gluon?

Before we go anywhere with answering this question, since it’s a question about color charge, let’s add some color to our diagram. We’ve now colored the up quark symbols and their corresponding lines on the diagram so that their color matches the color in the parentheses. This isn’t actually a necessary step for solving the problem, but it will help us visualize what we’re working with. Since we’re dealing with color charge in this question, let’s recall some key facts about color charge.

Color charge is a property of quarks and gluons, and it comes in three pairs of values. We abstractly call them red and antired, green and antigreen, and blue and antiblue. Just like a positive electric charge is the opposite value of a negative electric charge, an anticolor charge is the opposite value of the corresponding color charge. For example, antiblue is the opposite value of blue. Also like electric charge, color charge is a conserved quantity. That is, the total color of all the particles entering an interaction must be the same as the total color of all the particles leaving an interaction.

These few facts about color charge are actually all that we need to answer this question. There is, however, one useful fact about the color charge of gluons that will help us make sure that our answer is on the right track. When gluons participate in interactions, they always do so with two color charges, one color — red, green, or blue — and one anticolor — antired, antigreen, or antiblue. With all this in hand, let’s conserve color charge in our Feynman diagram, starting with the top vertex.

Using our notation for representing color charge, we can write that green color charge becomes blue color charge plus the unknown color charges of the gluon. Since blue appears in the final configuration but not in the initial configuration, it must be balanced by antiblue in the color of the gluon. Furthermore, since green is the only color appearing in the initial configuration, it must also appear in the final configuration.

Since the final color of the up quark is blue, not green, this green must be accounted for in the color of the gluon as well. So, a gluon with color charge green-antiblue will conserve color charge at this vertex. Let’s double-check that this gluon also conserves color charge at the second vertex where an up quark with blue color charge becomes an up quark with green color charge.

Going into the vertex, we have blue from the quark and green-antiblue from the gluon. Going out of the vertex, we only have green from the quark. Adding up the total color of the particles entering the interaction, blue from the up quark is exactly cancelled by antiblue from the gluon, which leaves a net color of green, also from the gluon. The total color leaving the interaction is just the single green charge of the up quark. Because the total color both before and after this interaction is green, we see that a green-antiblue gluon does indeed ensure that color charge is conserved at this vertex. So, by conserving color charge at each vertex, we’ve both determined and confirmed that the color charge of this gluon is green-antiblue.

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