It is well-known that scalar mesons are interpreted as pseudogoldstone bosons which is connected with spontaneous broken $SU(3) \times SU(3)$ symmetry to $SU(3) \times SU(3) / SU(3)_{chiral}$.

Is there similar explanation for vector mesons? I understand that broken symmetry corresponds to existense of particles with spin zero, but I expect that vector mesons can also be explained through something like that, because they correspond to irreducible representation of $SU(3)$ group (as well as scalar mesons).

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    $\begingroup$ Since physicists are very sloppy with this - do you mean $\otimes$ or $\times$, i.e. the tensor product or the direct product of groups? (I heavily suspect it is $\times$) $\endgroup$
    – ACuriousMind
    Mar 9, 2015 at 12:43
  • $\begingroup$ A good reference for this (maybe not the best, just the one I know about) is in the introductory chapter of Manohar and Wise's textbook on heavy quark physics. Granted, this is presented as a review for someone who's familiar with it (which I am not), and I've been hoping to find a more detailed explanation. $\endgroup$
    – jwimberley
    Mar 9, 2015 at 12:55
  • $\begingroup$ @ACuriousMind : I meaned direct product (I thought that $\otimes$ denotes direct product). $\endgroup$ Mar 9, 2015 at 13:20
  • $\begingroup$ @jwimberley : Where exactly can I find information about vector mesons in this chapter? $\endgroup$ Mar 9, 2015 at 14:39
  • $\begingroup$ @AndrewMcAddams You can't, because I was wrong! Sorry for the red herring. A later chapter does talk about the mass splitting between the spin 1 D* and B* mesons relative to the spin 0 D and B mesons, which is derived in the heavy quark limit and isn't general. I'd confused this with the introductory section 1.4, which just covers chiral symmetry breaking and the masses of spin-0 mesons. $\endgroup$
    – jwimberley
    Mar 9, 2015 at 15:10

1 Answer 1


A note on your question: the chiral SU(3)×SU(3) is dynamically broken by QCD to just the flavor ("eightfold way") SU(3). Your coset expression would be meaningful if the subscript were "vector" not "chiral", and it could serve as a summary of the 8 SSBroken axial generators of the full chiral starting group, not the surviving ones. So you might be asking for an explanation of the non-existent.

Indeed, 8 pseudoscalar mesons are the pseudogoldstone bosons corresponding to these 8 broken generators. And, indeed, glorious speculation has been proffered on vector mesons being, effectively, SSB gauge fields notably in the reference by Bando, Kugo, et al.

However, consider that any other mesons, scalars, tensors, etc., do not admit of such interpretations. If you are seeking a grand reductionist picture for all mesons in chiral symmetry breaking, it appears to be lacking---so far!


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