## QCD and gluon propagator

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.

### 4 Responses to QCD and gluon propagator

1. ervin says:

Dear Marco,

Are you familiar with the works of Pedro Costa, M.C. Ruiva and C.A. de Sousa? (see for example Phys. Rev. D 77, 096001 (2008) and included references). It seems to me that your results need to be be linked in a way or another to the thermodynamics and critical behavior of the NJL model, as developed by these authors.

Yours,

Ervin Goldfain

2. mfrasca says:

They do thermodynamics with a phenomenological NJL model. It does not apply to my case but the reverse can be true: one can do thermodynamics using NJL model derived from QCD.

Marco

3. ervin says:

Marco,

But if your approach to infrared QCD and Costa’s phenomenological NJL model both lead to promising results, is not sensible to assume that they are linked in some fundamental way?

Ervin

4. mfrasca says:

NJL model was born as a phenomenological model in the ’60 and since then nobody has been able to derive it satisfactorily from QCD. There have been some researcher as Terry Goldman that showed as knowing the gluon propagator can give back a proper NJL model and I all have is just the gluon propagator.

The model in that paper is just the one normally used in current literature and so one or another it does not matter for a thermodynamical study.

Marco

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