The second order hydrodynamic transport coefficient $\kappa$ for the gluon plasma from the lattice

The quark gluon plasma produced in heavy ion collisions behaves like an almost ideal fluid described by viscous hydrodynamics with a number of transport coefficients. The second order coefficient $\kappa$ is related to a Euclidean correlator of the energy-momentum tensor at vanishing frequency and low momentum. This allows for a lattice determination without maximum entropy methods or modelling, but the required lattice sizes represent a formidable challenge. We calculate $\kappa$ in leading order lattice perturbation theory and simulations on ${120}^3\times 6,8$ lattices with $a<0.1$ fm. In the temperature range $2T_{\mathrm{c}}-10T_{\mathrm{c}}$ we find $\kappa =0.36(15)T^2$. The error covers both a suitably rescaled AdS/CFT prediction as well as, remarkably, the result of leading order perturbation theory. This suggests that appropriate noise reduction methods on the lattice and NLO perturbative calculations could provide an accurate QCD prediction in the near future.