# QCD, show that a Quark and an anti-quark of the same colour attract

1. May 1, 2013

### Chain

This isn't really a homework question but it's from a past paper for revision. It is a short question so it shouldn't require lengthy mathematics. It asks you to show that a quark and an anti-quark of the same colour will attract.

The problem gives the 8 generator matrices of SU(3) and the Feynman rule for the exchange of a single gluon: $ig_sT^a \gamma ^\mu$

I'm not really sure how to find the force between them. To my understanding the Feynman rules give the probabilities of certain exchanges occurring, I don't know how this would be used to show the direction of the force between the quarks.

Thank you for your time :)

2. May 1, 2013

### fzero

One way to do this is to recall that, for electromagnetism, the Coulomb law arises by computing the Fourier transform of the momentum-space amplitude for single photon exchange. Attraction and repulsion are deduced from the sign of the interaction. By analogy, here we want the amplitude for single gluon exchange.

3. May 1, 2013

### cmcraes

Anti quarks have both opposite electrical charge and colour charge. So a positive red up quarks' antiparticle will be a negative anti-red(cyan) anti-up quark. A boson pair of quarks (a meson) consists of a quark and its corrisponding antiquark. The fact that these mesons annihilate so quickly is proof that they are attracted to eachother. Also the fact that opposite charges will attract and quarks are only found where the colour charges produce a 'white' charge. So they have to attract other wise these mesons would not exist and then decay so quickly!

4. May 2, 2013

### Chain

Ah okay, thanks for the responses guys (: