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Several authors I've consulted recently use six separate flavor quantum numbers for the six observed flavors of quarks when constructing their QCD Lagrangians That seems excessive when three "family" quantum numbers would seem to suffice. The up/down members of each family are distinguished by different charges (among other things) which would seem to prevent any (unobserved) strong-interaction induced transitions between the two family members. Thus strong interaction conservation of the three family q-numbers would be all that is needed. Only the weak interaction would be able to cause the observed charged-current, family-crossing transitions (since there are no flavor-changing neutral currents.) Is there something lacking in the three family q-number picture that the six flavor quantum number model provides?

Edit 1: Put another way the six-flavor picture sums over six separate quark fields in the Lagrangian, one for each flavor. The family or generation picture sums over only three -- an up/down field, a charm/strange field, and a top/bottom field, as a more economical picture, especially when we are working only in QCD. When we add the EW interaction each of the three splits in two. If we have no EW interaction we can't tell the difference between up and down, charm and strange, etc. so the family or generation picture seems best for QCD alone, unless we are doing something really sensitive to the mass differences of the two generation members. (In every case each field is also a color triplet in color space of course. ) Are there other factors influencing the choice of how one views this situation?

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  • $\begingroup$ Simplicity, probably. It's not always needed, but it's customary, especially since "strangeness" was historically a very important quantum number, and it's direct and straightforward to understand. $\endgroup$ – knzhou Apr 15 at 20:56
  • $\begingroup$ There are six different experimentally observed quarks with different masses and QCD only acts on the color thereof. I'm not sure what your picture is suggesting instead and why. $\endgroup$ – Cosmas Zachos Apr 15 at 22:28
  • $\begingroup$ Added an alternate statement of the question that might help. $\endgroup$ – Jim Eshelman Apr 16 at 1:07
  • $\begingroup$ Still obscure. The top is hugely different than the bottom, by dint of mass, even though strong couplings can't tell them apart. The RG treats them differently. What suggests to you they are somehow indistinguishable? $\endgroup$ – Cosmas Zachos Apr 17 at 0:34
  • $\begingroup$ By mass certainly, but with only QCD operating (imagine EW turned off for a moment) they appear otherwise indistinguishable -- all their relevant distinguishing quantum numbers are EW quantum numbers. $\endgroup$ – Jim Eshelman Apr 18 at 15:48

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