# How to determine the mass of a quark?

As far as I know quarks are never found in isolation, so how can we determine their rest mass?

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@David: I think a good answer to the question would cover both of our interpretations. I would attempt to do so but I am sure that, before long, someone else will answer it more clearly than I could. – qftme Jul 17 '11 at 15:22
And is your problem only with quarks or with any "unusual" particles such as $W, Z$ bosons which are of course also never observed. We only observe their decay products and that is what the mass is reconstructed from. Also, there is a whole issue of running coupling which means that rest mass per se actually doesn't make sense, it's only theoretical construct and depends on the renormalization scheme (en.wikipedia.org/wiki/Minimal_subtraction_scheme). Another problem here is of course confinement. I wonder which one of these topics (if any) you are interested in. – Marek Jul 17 '11 at 20:53
Sorry, I'm a newbie in Physics world. But since you said that it's always with other stuff, can't we just weight the whole bundle of'em (quark with other stuff), then if we know the weight of other stuff, do simple math? – Saeed Neamati Jul 18 '11 at 12:25
@Saeed Neamati: One would think that the mass of proton would just be the mass of the three quarks that make it up. But the quarks are moving at high speeds so they have a lot of kinetic energy, and there is energy in the strong force that binds together the quarks. By $E=mc^2$ all this energy contributes to the mass, and it fact it makes up the 98% of the mass. So from an experimental point of view, measuring the mass of the proton doesn't tell you anything directly about the mass of the quarks: they could even be massless and still the protons would have their mass. – BebopButUnsteady Jul 18 '11 at 14:16
Poor wikipedia articles which might nevertheless point in the right directions: 1. en.wikipedia.org/wiki/Current_quark_mass 2. en.wikipedia.org/wiki/Constituent_quark_mass @pipsi: reason this question is not being answered more fully is that a complete answer would need to explain quantum field theory, renormalisation and confinement (at least, and even more from the experimental side). Perhaps there are people who are working on such an enormously long answer --- perhaps people should offer bounties to encourage... – genneth Jul 18 '11 at 16:57

## 1 Answer

For the light quarks, one can use chiral perturbation theory to relate the mass of the light hadrons to the mass of the light quarks. These two links give details and caveats of the procedures, as well as the most precise determinations:

http://pdg.lbl.gov/2011/reviews/rpp2011-rev-quark-masses.pdf

http://pdg.lbl.gov/2011/listings/rpp2011-list-light-quarks.pdf

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And the heavier quarks masses are established by resonances, I presume? – BebopButUnsteady Jul 18 '11 at 14:16
+1 for the links to the pdg. – qftme Jul 18 '11 at 16:08
@BebopButUnsteady Only for the top you can do that (and it is basically what is done). – Rafael Jul 19 '11 at 12:45