Scaling patterns for azimuthal anisotropy in Pb+Pb collisions at Root_s = 2.76 TeV: Further constraints on transport coefficients

Azimuthal anisotropy measurements for charged hadrons, characterized by the second order Fourier coefficient $v_2$, are used to investigate the path length ($L$) and transverse momentum ($p_T$) dependent jet quenching patterns of the QCD medium produced in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$\,TeV. $v_2$ shows a linear decrease as $1/\sqrt{p_T}$ and a linear increase with the medium path length difference ($\Delta L$) in- and out of the $\Psi_2$ event plane. These patterns compliment a prior observation of the scaling of jet quenching ($R_{\rm AA}$) measurements. Together, they suggest that radiative parton energy loss is a dominant mechanism for jet suppression, and $v_2$ stems from the difference in the parton propagation length $\Delta L$.An estimate of the transport coefficient $\hat{q}$, gives a value comparable to that obtained in a prior study of the scaling properties of $R_{\rm AA}$. These results suggest that high-$p_T$ azimuthal anisotropy measurements provide strong constraints for delineating the mechanism(s) for parton energy loss, as well as for reliable extraction of $\hat{q}$.