4 Glauber model. The maximum initial temperature is T = 340 MeV and the initial time is τ 0 = 0 . 6 fm/c as usually done also in hydrodynamical calculations. We fol- low the dynamical evolution of quarks, anti-quarks and gluons. The last has been included, even if they are not explicitly present in the NJL model, with the aim of using a realistic density for both the total and the (anti-)quark density in the simulation of the collisions. However glu- ons do not actively participate in the evaluation of the chiral phase transition, but they simply acquire the mass of the quarks not contributing to its determination ac- cording to the the NJL model. The justification for this choice relies on the quasi-particle models that are fitted to lQCD thermodynamics [34, 35]. One finds a similar behavior of M ( T ) for both gluons and quarks approxi- mately. Of course for a more quantitative calculation a more careful treatment would be needed but it is not rel- evant to the main objective of the present seminal work, considering also that anyway the NJL model cannot be used for an accurate quantitative study. without the NJL-field but keeping constant locally the η/s . In Fig. 2 (left) it is shown the time evolution of the average elliptic flow 〈 v 2 〉 for a constant transport cross section of σ$_{tr}$ =10 mb a typical value that is able to re- produce the amount of v 2 observed in experiments [20]. Comparing the two solid lines (black and green) we can see that the NJL mean field cause a decrease of 〈 v 2 〉 of about 15%. The reduction of 〈 v 2 〉 can be expected con- sidering that the NJL field produce a scalar attractive field that at the phase transition results in a gas of mas- sive particles. In Fig.3, we show also the elliptic flow at freeze-out as a function of the transverse momentum p$_{T}$ . One can see that the role of the mean field even increases with momentum affecting also particles at a p$_{T}$ quite larger than the energy scale of the scalar con- densate 〈 ψ ¯ ψ 〉 ∼ 300 MeV . This is due to the fact that a high- p$_{T}$ particle collides mainly with the much more abundant particles in the bulk. These have an aver- age momentum comparable to the strength of the scalar field: p$_{T}$ ∼ 2 T ∼ M$_{c}$ . Therefore the effect of the scalar field extends thanks to collisions into a range quite larger than one would naively think and the interplay between collisions and mean field is fundamental. We find that the presence of an NJL-field that drives the chiral phase transition suppress the v 2 ( p$_{T}$ ) by about 20% at p$_{T}$ > 1 GeV. This would imply the need of a parton scattering cross section σ$_{tr}$ even larger than that estimated with the cascade model which was already quite larger than the pQCD estimates [25, 36]. On the other hand the mean field modifies both the local entropy density re- duced by the mass generation, and the shear viscosity that increases as shown in Fig.1 (right). Therefore even if the cross section is the same with and without the NJL field the system evolves with a different η/s . Considering that one of the main goal is to determine the η/s of the QGP we have investigated what is the action of the mean field once the η/s of the system is fixed to be the same by mean of the cross section renormalization according to Eq. (8). Therefore we have run simulations with and The results for 4 πη/s = 1 are shown by dashed lines in Fig.s 2 and 3, the (black) dashed line is the case with only the collision term (cascade) while the (green) dashed line is the case with the field. We can see that once the η/s is fixed there is essentially no difference in the calcu- lations with and without a field dynamics included. This is seen for both the average 〈 v 2 〉 and the v 2 ( p$_{T}$ ) in Fig.s 2 (left) and 3 respectively. This is a key result that shows that even in a microscopic approach that distinguishes between the mean field and the collisional dynamics the v 2 ( p$_{T}$ ) is mainly driven by the η/s of the fluid. In other words we have found that in a microscopic approach the η/s is the pertinent parameter and the language of vis- cous hydrodynamics is appropriate. Of course this does not mean that v 2 ( p$_{T}$ ) in the transport theory is the same of the viscous hydrodynamics one, but that, and even more importantly, the direct relation between v 2 ( p$_{T}$ ) and η/s is quite general and their relation is not modified by the NJL field dynamics. We have checked that this is valid also at other impact parameter ( b = 3 , 5 , 9 fm ) and for larger η/s up to π − $^{1}$. This is of course very impor- tant for the determination of η/s by mean of the data on elliptic flow and confirms the validity of the studies pursued till now even if they miss an explicit mean field FIG. 2: Left: Average elliptic flow as a function of time for Au + Au collisions in the mid-rapidity region | y | < 1 at b= 7 fm. Right: time evolution of the average transverse momen- tum for the same case as in the left panel. 0 0.5 1 1.5 2 2.5 3 p$_{T}$ [GeV] 0.05 0.1 0.15 0.2 v 2 Au+Au@200 AGeV   b=7 fm =10 mb  =10 mb + Field 4 /s=1  s=1 + Field FIG. 3: As in Fig. 2 for the elliptic flow as a function of p$_{T}$ . 1 2 3 4 5 6 7 t [fm/c] 0 0.02 0.04 0.06 0.08 v 2 Au+Au@200 AGeV   b=7 fm =10 mb =10 mb + Field 4 /s=1 4 /s=1 + Field 1 2 3 4 5 6 t [fm/c] 0.6 0.7 0.8 0.9 <p T > [GeV] =10 mb + Field =10 mb 4 /s=1 + Field 4 /s=1