Are Mesons in Colour Singlet State?

[SWFvanRijk]

I read that hadrons are in colour singlet state and that gluons are not and that the colour singlet gluon is forbidden for the reason of making strong force a long range force otherwise (and that SU(3) has 8 generators and thus 8 gluons) but my question is: are mesons in a colour singlet state? If not they can't be allowed to be seen and if they are shouldn't they make the range of the force also long? (or not since they have a mass limiting their range through decaying?)

Also the most used representation of the generators have 1/sqrt(2) (r anti r - b anti b) and also one like 1/sqrt(6) (r anti r + b anti b - 2 g anti g). but arent these also 'white' ? since if measured has colour - anti colour..

 

[ohwilleke]

Your question seems to indicate that you are a bit unclear about what some key terms mean.

A hadron is a composite particle made of quarks bound to each other by gluons. Thus, mesons are a subset of hadrons consisting of two quarks (in a color and anticolor pair) bound by gluons. Baryons are another subset of hadrons consisting of three quarks (one of each color, or in the alternative one of each anticolor) bound by gluons. True tetraquarks and pentaquarks and hexaquarks, if they exist, are also hadrons. (All of this is only partially true do to "sea quarks" but is sufficient for the purposes you are discussing.)

There are also, in theory, composite particles made only of gluons sometimes called glueballs, which are a prediction of QCD that has never been observed, possibly because glueballs are bosons which should be highly prone to mixing with other kinds of bosons and hence are hard to see in isolation. (I don't know if glueballs technically qualify as hadrons or not, but they must be color neutral by including colors and anticolors and/or by having all three colors or all three anticolors).

In practice, the end result of the analysis is that quarks are "confined" by the strong force in such a manner that they must come in baryon packages, in meson packages, or in combinations of the two in terms of color (which are extremely rare although there have been a couple of credible sitings of them in the last couple of years or so), unless they are top quarks (or antitop quarks), in which case they decay faster than they can form hadrons.

I will let others address the balance of your question, but you might consider reformulating your question as it is hard to tell just what you are asking in the form in which your question is currently phrased. I think that your bottom line real question is "why isn't the strong force a long range force despite the fact that it has a carrier boson with zero rest mass?", but I don't want to try and second guess you.

Also, strictly speaking, I think your question actually belongs in the High Energy Physics, Nuclear Physics and Particle Physics forum as it is really asking a question about how the QCD part of the Standard Model works rather that deviating from it, but if a moderator thinks it should be relocated, the moderator can do that.