## Sigma resonance and its sibling

In a beautiful paper, Mennessier, Narison (the organizer of QCD 08), and Ochs extract the parameters of the decays of the sigma resonance (or f0(600) if you like). This strongly interacting particle decays in two pions or two photons. The authors fit the hadronic data and argue that the large pion-pion and small gamma-gamma widths strongly favor a large gluonic content of this particle. That is, this particle is a glueball and surely is the lowest state of SU(3) pure Yang-Mills theory as lower states are all quark composites. They give a better explanation in this paper where they conclude that the small gamma-gamma width is not compatible with the idea that this resonance is a tetraquark. Maybe, a more striking view of these authors is that, beside f0(600), another resonance having gluonic nature should be expected at about 1 GeV. We just remember recent views on the sigma that give a mass of (441 – i 272) MeV or (489 – i 264) MeV (see here and here respectively). Indeed, Particle Data Group list of particles show us that besides f0(600) there is another resonance, f0(980), whose nature is yet to be understood. But there is general agreement about the mass of this particle being 980$\pm$10 MeV and has the right quantum numbers to be a sibling of sigma.

Our view about is that these authors are on the right track. We have seen that a mass spectrum for Yang-Mills theory can be derived and is generally given by (see here)

$m_n=(2n+1)\frac{\pi}{2K(i)}\sqrt{\sigma}$

where we have called the mass of the Yang-Mills excitation $\sqrt{\sigma}=\Lambda(Ng^2/2)^{1 \over 4}$. This is also known as “string tension” and can be taken from experiments to be 410$\pm$20 MeV. From the solution of Yang-Mills in D=2+1 proposed here, we know that if excitations $m_n$ exist then also excitations with two quantum numbers $m_k+m_n$ should exist. Now one has

$m_0 = 1.198140235 \cdot 410 MeV=491 MeV$

$m_0+m_0 = 2\cdot 1.198140235 \cdot 410 MeV=982 MeV$

with the error given by the determination of the string tension. While the next excited state of this particle is

$\frac{m_1+m_0}{\sqrt{\sigma}}=4\cdot 1.198140235=4.79$

to be compared with Teper et al. that gives 4.78(9) and the error is just 0.2%!

So, all this is really striking and also supported by relevant phenomenological analysis. Time will says, but surely this is a path to be tested in the near future.