# Why f0(600) is not seen on lattice computations?

1. Jun 19, 2008

### Lester

There is a lot of activity around the full identification of the light meson spectrum and the identification of glueballs. For these aims a lot of insight should come from lattice QCD. Presently, not all the resonances seen that appear on PDG review are obtained on lattice. What is the reason for this? Is there any paper written about this matter?

f0(600) or sigma is a resonance with a mass of about 450 MeV and a broad width decay. A large number of authors agree about a large gluonia content of this particle even if there are notable different points of view (e.g. as a tetraquark state). If this is the glueball this is also the ground state of a pure Yang-Mills theory being higher than the ground state of the full QCD (pion). Quarks lower the ground state!

Jon

2. Jun 19, 2008

### humanino

Choosing the f0 (sigma) to refer to a PDG particle is kind of unfair. They have a note on scalar mesons. Can you post a link to PDG, and indicate how many stars the f0 has ?

Generally speaking, you need to think about what you call a particle. What if the mass is comparable to the width ?
The main reason is simple. In lattice QCD you propagate many many times a configuration with given quantum numbers, and look at the mass distribution obtained. It works well as long as you expect a sharp peak.
The pion is a chiral pseudo-goldstone boson.

3. Jun 19, 2008

### Lester

Dear humanino,

http://pdg.lbl.gov/2007/listings/m014.pdf

There is a lot of literature about this resonance (initially people did not believe at it). E.g. look at

http://arxiv.org/abs/0804.4452

but also for a different view

http://arxiv.org/abs/0801.2288

About the pion I think that any particle we observe belongs to the spectrum of the theory. Pion should be considered the lower state of QCD and so is its ground state even if I can agree with your description.

Jon

4. Jun 21, 2008

### CarlB

Funny thing, the PDG only gives stars to baryons, not to mesons, leptons, quarks, or even photons. Anyway, the f_0(600) is a very well known state.

Lester, thanks for the link to the diquark /anti-diquark model of the scalar mesons. Very interesting. Of course that would explain a lack of success with lattice calculations.

A lot of the mesons are hard to identify because their quantum numbers cancel between the quark and anti-quark. An interesting pattern is that the b-bbar and c-cbar $$J^{PC} = 1^{--}$$ i.e. Upsilon and J/psi, both come in very clean, six mass eigenstates, but the corresponding lower mass mesons are quite confused. Lattice gauge calculations can get the lower couple of these resonaces but not the upper ones. It looks suspiciously like parameter fitting to me, in this case the parameter is the quark masses. And simulations of different mesons seems to require the same quark to have different masses, depending on application, LOL.

Even the vector mesons are a little confused. What they now call the omega(2290) used to be called the X(2290). I suspect it is actually a phi(2290) (i.e. an s-sbar). All three have the same quantum numbers ($$I^gJ^{PC} = 0^-1^{--}$$ so it's a matter of the quark content. I will have to drop by the library and look up the papers on the X(2290) and see what justified putting it in the omega category. For me, my interest is in the context of fitting them as Koide triplets. I typed in the Upsilon and J/psi fits over where people are discussing triality as it seems to be an application:
https://www.physicsforums.com/showpost.php?p=1770683&postcount=452

5. Jun 21, 2008

### mormonator_rm

Considering the f0(600)/sigma meson has a width that is generally larger than its mass, I find it no surprise that it doesn't emerge in lattice QCD. Not only that, but you realize that if a "particle" has a width larger than its mass, it is by definition entirely "virtual". There is some debate about the f0(600) being a kinematic effect in pion-pion scattering and such, as there is no clear signal that it actually involves anything other than pion interactions. It doesn't even have a distinct or noticeable radiative decay such that f0(1370) couldn't account for what is seen in that range (seeings f0(1370) also has a large width and very uncertain mass). So... f0(600) might not even be a "particle" at all, maybe just an effect of the pion scattering behavior.

Even if f0(600) is a "particle" in some sense, its mass would no doubt be pushed around alot by mixing features in the scalar nonet, including the glueball. It may also be classed as a meson-meson molecule like the f0(980) and a0(980) very often are, or as a tetraquark like Jaffe suggested a long time back. It may also be classed as a chiral meson or "chiralon", or partner to the pion, in the event that Ishida's work from last decade was right about it. Somehow, nobody seems to ever produce anything that remotely describes the nature we see, and it seems that every experiment produces a slightly different picture of it, almost as if it changes from experiment to experiment based on the conditions of the tests themselves. This kind of behavior does not bode well for f0(600) being anything but a garbage heap for light scalar signals that don't make any sense.

I wrote a paper some time ago about the idea of tetraquark-meson-glueball mixing that incorporated the sigma resonance, but it was never submitted or published. I never really finished it. Around that same time I read a paper that indicated they had found eight... yes, eight different low-mass scalar resonances in the range 350 to 750 MeV that had smaller widths but acted like a "sigma resonance" with large width and mass around 450 MeV when the resolution of the histogram was to poor to seperate the peaks properly. That paper was actually removed within a month after it was first posted, and has never been reposted since to my knowledge.

This is part of the reason why I don't bother with f0(600) any more. I'm just going to wait to see what more experiments are able to reveal... or not reveal... about the "resonance" before I ever consider trying to work on it ever again.

6. Jun 21, 2008

### mormonator_rm

Well known in the sense that everybody was talking about it for a long time after Tornqvist et al brought it back as a recognized resonance of sorts... if you mean it is well known experimentally, I would say not really. There have been plenty of experiments on it, but they tend to produce low statistics and varying results from one to the next. It's not a very clean set of information that we have on f0(600).

Among other things...

Well, b-bbar and c-cbar are easier to work with because you don't have so much in the way of relativistic corrections. Light quark mesons are fraught with relativistic effects and mixing behaviors that can screw up the nice spectroscopic order that we enjoy in charmonium and bottomonium. That and the strong constant gets incredibly large with light quarks, and hence quite non-perturbative. Not a pretty picture at all...