A striking confirmation

On arxiv today it is appeared a paper by Stephan Narison,  Gerard Mennessier and Robert Kaminski (see here). Stephan Narison is the organizer of QCD Conferences series and I attended one of this, QCD 08, last year. Narison is located in Montpellier (France) and, together with other researchers, is carrying out research aimed to an understanding of low-energy phenomenology of QCD. So, there is a strong overlapping between their work and mine. Their tools are QCD spectral sum rules and low energy theorems and the results they obtain are quite striking. Narison has written a relevant handbook of QCD (see here) that is a worthwhile tool for people aimed to work with this theory.

The paper gives further support to the idea that the resonance f0(600)/\sigma is indeed a glueball. Currently, researchers have explored another possibility, that this particle is a four quark state. Narison, Mennessier and Kaminski consider that, if this would be true, being this a state with u and d quarks, coupling with K mesons should be suppressed. This would imply that, in a computation for the rates of \sigma decays, the contribution coming in the case of K mesons in the final state should be really small. But, for a glueball state, these couplings for \pi\pi and KK decays should be almost the same.

Indeed, they get the following

|g^{os}_{\sigma\pi +\pi -}|\simeq 6 GeV, r_{\sigma\pi K}\equiv \frac{g^{os}_{\sigma K+K-}}{g^{os}_{\sigma\pi +\pi -}} \simeq 0.8

that is quite striking indeed. They do the same for f0(980) and, even if they get a similar result, they draw no conclusion about the nature of this resonance.

This, together with the small decay rate in \gamma\gamma, gives a really strong support to the conclusion that \sigma is indeed a glueball. At this stage, we would like to see an improved support from lattice computations. Surely, it is time to revise some theoretical computations of the gluon propagator.

Update: I have received the following correction to above deleted sentence by Stephan Narison. This is the right take:

One should take into account that the sigma to KK is suppressed due to phase space BUT the coupling to KK is very strong. The non-observation of sigma to KK has been the (main) motivation that it can be pi-pi or 4-quark states and nobody has payed attention to this (unobserved) decay.


8 Responses to A striking confirmation

  1. Robert Kaminski says:


    for comments. I hope other physicists will follow us analyzing structure of sigma and f_0(980) mesons.


    Robert Kaminski

    • mfrasca says:

      Dear Robert,

      Thank you very much for your comment. Your hope is my hope. The work you are carrying out about this matter gives already a solid ground to build on.


  2. rafael says:

    Hi Marco!

    Do you have an opinion about why people have not found \sigma particle on lattice computations?


    • mfrasca says:

      Hi Rafael,

      I think a good reason that I have found so far is the width of this particle. This is large and of the same magnitude of the mass. My take is that, possibly, this is the missing ground state of Yang-Mills theory that people working on lattice computations of the gluon propagator have already found. So, it is not completely true that this particle has not been seen on lattice. My question is why people doing lattice computations on the gluon propagator never checked its Fourier transformed counterpart

      G(x)=\sum_n a_ne^{-m_nx}

      and computed at least the first mass. Presently, I have fitted data by different groups with a Yukawa form obtaining this value. E.g., for Cucchieri and Mendes I get 545 MeV while the \sigma has a mass of about 440-460 MeV. Striking, isn’t it?

      Please, check the following paper by Craig McNeile, an expert about this matter,


      and mine


      Both are contributions to QCD 08 proceedings, appeared recently on Nucl. Phys. B (Supp. Proc.), and treat this matter.



  3. rafael says:


    I think sigma is a full-QCD ressonance, so, it is able to decay do other hadrons. On the other hand, Cucchieri and Mendes data are due to quenched simulations, thus, there would be a even lower ground-state (for full QCD) on a dynamical environment. Isn’t it?
    Thanks by this links, I’m giving a look!


    • mfrasca says:


      I think you should check recent literature to be updated of what people think about sigma and what experiments say. I have computed its width directly from QCD and it is obvious that a glueball can decay in two pions when there are quarks. But if you work in a quenched approximation this particle is stable and will not decay, being the lowest state. The lowest state of Yang-Mills theory is higher than full QCD as quarks lowers it. This is what I get.



  4. rafael says:

    Hi Marco,

    Yes, there is a growing literature comming from this lots of activity on hadron spectroscopy. Actually, since people learnt how to implement chiral symmetry on the lattice (by so-called Overlap fermions) studies suggests a0 and f0 as true quark-antiquark bound-states… no tetraquarks.
    Well, about \sigma I guess lattice calculations would need dynamical Overlap calculations with pion-masses down to 200 MeV and some volume around 5fm⁴. It will need half decade or more… however, the message from the lattice seems to be that negleting chyral quark dynamics prevents us to get physical ground-states of q-q_bar ressonances.


  5. mfrasca says:

    Hi Rafael,

    Interesting conclusion. Indeed my view is that tetraquarks, if they exist, could only be bound states of heavier quarks where the potential is almost Coulomb. I believe that most of these states can be seen as you describe. But we turn back to the old question: Where do glueballs lie?

    Finally, about sigma, you are just removing all the possibilities theoretical physicists put forward about its nature. Surely, it is not a q\bar q state. At best, there is some inconsistencies from lattice gluon propagator computations and those computing the spectrum of the quenched theory. I think we can agree on this as Cucchieri and Mendes get 545 MeV while Teper et al. and Morningstar et al. claim something heavier than 1 GeV.



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