QCD constants from sigma resonance

In our recent paper we were able to compute a relevant property of the resonance. We have obtained its decay width as (see here):

being , the string tension that is one of the constants to be determined, and the pion decay constant. From asymptotic freedom we know that

being the number of flavors and the scale where infrared physics sets in and is another constant to be computed. We have computed the mass of the resonance from the gluon propagator obtaining

and we have all the theoretical data to compute and from experimental data. This can be accomplished using two main references (here and here) that give:

and

respectively. These produce the following values for QCD constants

and

We have not evaluated the errors being this a back of envelope computation. A striking result is that the ratio of these constants is the same in both cases giving the pure number 1.44 that I am not able to explain.

These results, besides being truly consistent, are really striking making possible a deep understanding of QCD. I would appreciate any reference about these values and on their determination, both theoretical and experimental, from other processes in QCD. These values are critical indeed for strong interactions.