- #1

CAF123

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Consider the process in the picture below where an ##r \bar r## state goes to an ##r \bar r## state through mediation of a gluon. The gluon may carry the colour anticolour combination ##r \bar r##. I'm just wondering...

1) Can we have a gluon with the colour assignments just ##r \bar r##? If not, why not and if so, which of the eight combinations usually given in textbooks does it correspond to?

My thoughts are: when we speak of colour singlet states, what we really mean is the state has colour configuration ##1/\sqrt{3}(r \bar r + g \bar g + b \bar b)##. So should I think of the incoming r rbar pair on the lhs of my diagram to be simultaneously including the case where we have b bar and g gbar so that we identify the intermediate gluon as the one synonomous with ##(r \bar r - b\bar b -2g \bar g)##?

1) Can we have a gluon with the colour assignments just ##r \bar r##? If not, why not and if so, which of the eight combinations usually given in textbooks does it correspond to?

My thoughts are: when we speak of colour singlet states, what we really mean is the state has colour configuration ##1/\sqrt{3}(r \bar r + g \bar g + b \bar b)##. So should I think of the incoming r rbar pair on the lhs of my diagram to be simultaneously including the case where we have b bar and g gbar so that we identify the intermediate gluon as the one synonomous with ##(r \bar r - b\bar b -2g \bar g)##?