## Exact solutions go published!

30/11/2010

My paper presenting exact solutions to classical scalar field theories, with a corresponding quantum formulation, has been accepted for publication in the Journal of Nonlinear Mathematical Physics.  The replacement on arxiv will appear tomorrow, the link is here. I would like to thank the Editor, Norbert Euler, and an anonymous referee that pointed out to me the existence of a zero mode in the quantum fluctuations.

## The nature of eta’

30/11/2010

$\eta'$ is a very peculiar particle. It mixes with $\eta$ that has a lower mass. Recently, in their report on KLOE-2 physics, this group reported here that $\eta'$ has a significant glue component besides quarks. This means that understanding its most important decay $\eta'\rightarrow\eta\pi^+\pi^-$ is not a trivial matter. As my readers may know, I have done a computation in my contribution to proceedings to QCD 10 conference where the decay process is seen to happen through an intermediate step with the $\sigma$ resonance followed by the decay of this into two pions. The agreement we get is so good to give a correct estimation of the decay constant of the $\eta$. This implies that the $\sigma$ is a true glue state. Of course our computation is rough enough to exclude mixing with other hadronic states that should exist.

Today, on arxiv, an interesting paper appeared authored by Rafel Escribano, Pere Masjuan, Juan José Sanz-Cillero (see here). These authors give an initial overview of the experimental status of the decay we have considered above. Then, using both the technique of Chiral Perturbation Theory (ChPT) and that of Resonant Chiral Perturbation Theory (RChPT), they try to fit experimental data. I have the luck to hear a talk of Juan José in Montpellier last year about this same matter and I was aware of his struggle to reach an agreement between a successful technique, as ChPT is, and experimental data for this particular process. The leading order of the theory is well below the experimental value and so, already in that first talk, Juan José showed the need for higher order corrections. But he proved that this cannot be enough and said at that time that some other states should be accounted for to reach a satisfactory agreement. This paper goes in this direction showing that if one accounts for the presence of the $\sigma$ and a0(980), the latter being dominant, the agreement is reached. These authors were also able to show a consistent relation between ChPT and RChPT that are in some way complimentary.

This paper is relevant as gives a strong support to the idea that I put forward about $\eta'$ decay. But these authors go further implying a higher level of understanding accounting for the presence of other hadronic states in a technical affordable way. I expect further improvement by them and it will be interesting to see how these could be obtained.