## QCD and gluon propagator

08/09/2008

As I have pointed out in a preceding post, I have got a paper of mine accepted for publication (see here) where I derive a Nambu-Jona-Lasinio model from QCD. I am able to fix the following parameters

$G_{NJL}\approx 3.76 \frac{g^2}{\sigma}$

and

$\Lambda_{NJL}=\frac{\pi}{2K(i)}\sqrt{\sigma}$

being as always $\sigma=(440MeV)^2$ the string tension and g the gauge coupling. Indeed, this model is very similar to the one presented in a paper by Kurt Langfeld, Christiane Kettner, and  Hugo Reinhardt (see here and here). They solved the model through the numerical solution of the Dyson-Schwinger equations. One can verify that in this case a mean field approximation does not work. In our case, with the above parameters, one gets

$\frac{G_{NJL}\Lambda^2_{NJL}}{16\pi^2}\approx 1.117$

when $\alpha_s\approx 2.6$ and we see that we have built a consistent model. Indeed, the authors of the aforementioned paper get the following table

These results are really striking. For $\alpha_s=5.3$ our model obtain a substantial agreement with experiments. In the near future we hope to find some analytical treatment to work out these values. At this stage we can be really satisfied of this achievement.

Indeed, this comparison is somewhat rough. We have to obtain the Dyson-Schwinger equation for our model and carry out the above computations by ourselves. This is a program to work out in the future. But already at this stage, the consistency with values of $\alpha_s$ we obtain is really satisfactory.