What Causes the Mass Differences in Quark Doublets?

[mathman]

Quarks come in three pairs (u,d), (c,s), (t,b). For the lowest energy pair, the masses are approximately the same. However for the others, c is much heavier than s, and t is very much heavier than b. Is there some explanation from the theory, or is just a given to be explained by a more complete model?

 

[mormonator_rm]

It has to do with assymetry between the paired heavy-quark flavors. Charm quarks have much greater mass than strange quarks, probably because charmness contributes more mass than strangeness. Top quarks are much, much more massive than bottom quarks, probably because topness is a much stronger contributor to mass than bottomness is. Even with the up and down quarks there is some assymetry because isospin is not an exact symmetry of nature either. If isospin was an exact symmetry of nature, then the up and down quarks would become degenrerate in mass, and hence we would see such effects as the dissappearence of electric charge, the total degeneracy of nucleon masses, and the total degeneracy of pion masses, and all other isovector groups for that matter.

 

[mathman]

charmness contributes more mass than strangeness

topness is a much stronger contributor to mass than bottomness is.

Much as I hate to say it, your explanation sounds like the masses differences are a result of their being different.

 

[selfAdjoint]

AFAIK, the standard model gives no detailed account of the Higgs sector, where presumably the masses are determined.

I believe some of the supersymmetric models propose to explain the "mass spectrum". Maybe someone more knowledgeable than I can post on that.

 

[mormonator_rm]

mass degeneracy differences

What I am saying is that the reason there is a mass difference within the quark doublets is because flavour symmetry is broken. Isospin up and down are inverse, but no longer completely symmetrical. Charmness and strangeness could be considered inverse to each other, but they are no longer symmetrical. Topness and bottomness may be considered inverse, but they are no longer symmetrical. If there was total symmetry, then you would find the heavier flavors following a pattern where C = -S and T = -B. The up and down quarks would be degenerate in mass, the charm and strange quarks would be degenerate in mass, and the top and bottom quarks would be degenerate in mass.

Now, if there were no other influences, all indications are that flavor would be an exact symmetry of nature, and hence this degeneracy should exist at a limit such that all other forces become null. But we do not live in such a universe.

The up and down quarks are already a fairly good model due to the fact that they are already sufficiently degenerate that we can approximately express both quarks in terms of one flavor only. So we do not have to distinguish between "upness" and "downness" because they are very close to symmetry such that U = -D (approximately). Rather than use the flavor names, we just characterize it by one property, isospin.

Here's the first important question: What is the symmetry breaking mechanism? So far, we have some satisfactory theories; the foremost is already used as if it were a confirmed postulate, and there is alreay a great deal of work built up on it. Basically the idea is that electric charge, also known as electromagnetic symmetry, is the mechanism that breaks flavour symmetry. If you were to allow the Weinberg angle (which characterizes the splitting of weak and electromagnetic forces in the electro-weak regime) to approach a right angle, then the isospin symmetry becomes complete and electric charge dissappears. Hypercharge would be the only remaining component to be acted upon. The nucleons would become degenerate in mass and charge, and the pions would also do the same, as would all of the isospin groups. Also, the quarks would probably not mix; all of the non-diagonal terms in the Cabbibo-Kobayashi-Maskawa matrix would drop to zero, leaving the diagonals at unity. In this model there would be total degeneracy within the heavier flavour doublets, as well (so corresponding kaons and D-mesons would become degenerate, too).

Now, the second question is a bit trickier; I don't know if there is an effective answer yet, unless somebody has theorized that the Higgs field affects the flavour doublets differently based on overall mass (or something like that): Why is the degeneracy different in each doublet? I don't have any clues as yet, so I think that's the question to discuss and get some possible answers to.