A new model of jet quenching in nuclear collisions, CUJET3.0, is constructed by generalizing the perturbative QCD based CUJET2.0 model to include two complementary non-perturbative features of the QCD confinement cross-over phase transition near $T_capprox 160$ MeV: (1) the suppression of quark and gluon degrees of freedom and (2) the emergence of chromo-magnetic monopole degrees of freedom. Such a semi-Quark-Gluon-Monopole Plasma (sQGMP) microscopic scenario is tested by comparing predictions of the leading hadron nuclear modification factors, $R^h_{AA}(p_T>10{rm GeV/c},sqrt{s})$, and their azimuthal elliptic asymmetry $v^h_2(p_T>10{rm GeV/c},sqrt{s})$ with available data on $h=pi,D,B$ jet fragments from nuclear collisions at RHIC($sqrt{s}=0.2$ ATeV) and LHC($sqrt{s}$=2.76 ATeV). The sQGMP model is shown to solve the long standing $R_{AA}$ vs $v_2$ puzzle by predicting a maximum of the jet quenching parameter field $hat{q}(E,T)/T^3$ near $T_c$. The consistency of jet quenching with observed bulk perfect fluidity is demonstrated by extrapolating the sQGMP $hat{q}$ down to thermal energy $Esim 3 T$ scales and showing that the sQGMP shear viscosity to entropy density ratio $eta/s approx T^3/hat{q}$ falls close to the unitarity bound, $1/4pi$, in the range $(1-2)T_c$. Detailed comparisons of CUJET2.0 and CUJET3.0 reveal that the remarkably different $hat{q}(T)$ could be consistent with the same $R_{AA}$ data and could only be distinguished by anisotropy observables. These findings demonstrate clearly the inadequacy of focusing on the jet path averaged quantity $<hat{q}>$ as the only relevant medium property to characterize jet quenching, and point to the crucial roles of other essential factors, such as the chromo electric and magnetic composites of the plasma, the screening masses and the running couplings at multiple scales that all strongly influence jet energy loss.
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