Measurement of $\hat{q}$ in RHI collisions using di-hadron correlations

In the BDMPSZ model, the energy loss of an outgoing parton in a medium $-dE/dx$ is the transport coefficient $\hat{q}$ times $L$ the length traveled. This results in jet quenching, which is well established. However BDMPSZ also predicts an azimuthal broadening of di-jets also proportional to $\hat{q}L$ which has so far not been observed. The broadening should produce a larger $k_T$ in A$+$A than in p$+$p collisions. This presentation introduces the observation that the $k_T$ measured in p$+$p collisions for di-hadrons with $p_{Tt}$ and $p_{Ta}$ must be reduced to compensate for the energy loss of both the trigger and away parent partons when comparing to the $k_T$ measured with the same di-hadron $p_{Tt}$ and $p_{Ta}$ in A$+$A collisions. This idea is applied to a recent STAR di-hadron measurement in Au$+$Au at $\sqrt{s_{NN}}$=200 GeV, [Phys. Lett. B760 (2016) 689], with result $ =2.1\pm 0.6$ GeV$^2$. This is more precise but in agreement with a theoretical calculation of $ =14^{+42}_{-14}$ GeV$^2$ using the same data. Assuming a length $ \approx 7$ fm for central Au$+$Au collisions the present result gives $\hat{q}\approx 0.30\pm 0.09$ GeV$^2$/fm, in fair agreement with the JET collaboration result from single hadron suppression of $\hat{q}\approx 1.2\pm 0.3$ GeV$^2$/fm at an initial time $\tau_0=0.6$ fm/c in Au$+$Au collisions at $\sqrt{s_{NN}}=200$ GeV. There are several interesting details to be discussed: for a given $p_{Tt}$ the $ $ seems to decrease then vanish with increasing $p_{Ta}$; the di-jet spends a much longer time in the medium ($\approx 7$ fm/c) then $\tau_0=0.6$ fm/c which likely affects the value of $\hat{q}$ that would be observed.