Measurement of $\hat{q}$ in Relativistic Heavy Ion Collisions using di-hadron correlations

The azimuthal width of the di-hadron correlations in p$+$p collisons, beyond the fragmentation transverse momentum, $j_T$, is dominated by $k_T$, the so-called intrinsic transverse momentum of a parton in a nucleon, which can be measured. The predicted azimuthal broadening in A$+$A collisions should produce a larger $k_T$ than in p$+$p collisions. The present work 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 Au$+$Au collisions. This idea is applied to a recent STAR di-hadron measurement, with result $\langle{\hat{q}L}\rangle=2.1\pm 0.6$ GeV$^2$. This is more precise but in agreement with a theoretical calulation of $\langle{\hat{q}L}\rangle=14^{+42}_{-14}$ GeV$^2$ using the same data. Assuming a length $\langle{L}\rangle\approx 7$ fm for central Au$+$Au collisions the present result gives $\hat{q}=0.30\pm 0.09$ GeV$^2$/fm, in fair agreement with the JET collaboration result of $\hat{q}\approx 1.2\pm 0.3$ GeV$^2$/fm at initial time $\tau_0=0.6$ fm/c in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.