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We employ a relativistic transport theory to describe the fireball expansionof the matter created in ultra-relativistic heavy-ion collisions (uRHICs).Developing an approach to fix locally the shear viscosity to entropy density$\eta/s$, we study the impact of a temperature dependent $\eta/s(T)$ on thebuild-up of the elliptic flow, $v_2$, a measure of the angular anisotropy inthe particle production. Beam Energy Scan from $\sqrt{s_{NN}}= \rm 62.4 GeV$ atRHIC up to 2.76 TeV at LHC has shown that the $v_2(p_T)$ as a function of thetransverse momentum $p_T$ appears to be nearly invariant with energy. We showthat such a surprising behavior is determined by a rise and fall of $\eta/s(T)$with a minimum at $T\sim T_c$, as one would expect if the matter undergoes aphase transition or a cross-over. This provides an evidence for phasetransition occurring in the uRHIC's and a first constraint on the temperaturedependence of $\eta/s$. In particular, a constant $\eta/s$ at all temperaturesor a too strong T-dependence would cause a breaking of the scaling of$v_2(p_T)$ with the energy.

Elliptic Flow from a Beam Energy Scan: a signature of a phase transition to the Quark-Gluon Plasma