## The width of the sigma computed

One of the most challenging open problems in QCD in the low energy limit is to compute the properties of the $\sigma$ resonance. The very nature of this particle is currently unknown and different views have been proposed (tetraquark or glueball). I have put a paper of mine on arxiv (see here) where I compute the large width of this resonance obtaining agreement with experimental derivation of this quantity. I put here this equation that is

$\Gamma_\sigma = \frac{6}{\pi}\frac{G^2_{NJL}}{4\pi\alpha_s} m_\sigma f_\pi^4\sqrt{1-\frac{4m_\pi^2}{m_\sigma^2}}$

being $G_{NJL}=3.76\frac{4\pi\alpha_s}{\sigma}$ being $\sigma$ the string tension generally taken to be 440 MeV and $f_\pi\approx 93\ MeV$ the pion decay constant. The agreement is obtained with $\alpha_s\approx 2$ giving a consistent result. This is the first time that this rate is obtained from first principles directly from QCD and gives an explanation of the reason why this resonance is so broad. The process considered is $\sigma\to\pi^+\pi^-$ that is dominant. Similarly, the other seen process, $\sigma\to\gamma\gamma$, has been interpreted as due to pion rescattering.

On the basis of these computations, this particle is the lowest glueball state. This is also consistent with a theorem proved in the paper that mixing between glueballs and quarks, in the limit of a very large coupling,  is not seen at the leading order. This implies that the spectrum of pure Yang-Mills theory is seen experimentally almost without interaction with quarks.

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