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The simple answer to your question (What implications does a quark quartet have on QCD?) is that it has no fundamental implications that I can imagine. It is an open question whether or not tetraquark ($q q \bar{q}\bar{q}$) or pentaquark ($qqqq\bar{q}$) states that live long enough to be classified as particles actually exist -- at present, our ability to ...

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With an answer selected (and bounty awarded) it is time to open a community wiki for explicit references on work along the line of getting QCD + EM, or alternatively QCD alone or QCD + "4th colour" extracting the group from the extra dimensions. An early 1975 work of founding fathers of string theory claims to have a O(6) and then a SU(4) group from the ...

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While it is certainly possible to get an $SU(3) \times U(1)$ gauge group from the metric alone, if one started with a 9d theory, there are several issues with using Graviphotons as gauge bosons in a 4d theory. Most prominently, in addition to vector bosons you will always create scalars in the adjoint from internal components of the metric, which we do not ...

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In the end, you cannot calculate the pion decay constant in chiral perturbation theory. All you can do is adjust the parameters in your n-loop calculation so that the physical value is reproduced. The standard reference for the one-loop renormalization of ChPTh is Gasser and Leutwyler, Chiral Perturbation Theory to One Loop, Annals of Physics 158, 142 ...

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