In the 2009 round of proposals, the USQCD collaboration allocated about 500,000 6n hours to my project of calculating the heavy-quark momentum diffusion coefficient in the plasma of gluons. The 6n nodes correspond to a specific PC cluster at Jefferson Lab.
In the RHIC heavy ion collisions, a striking experimental observation has been that heavy quarks (in particular the charm quarks) appear to thermalize about as effectively as the light quarks. This is contrary to what a weak coupling treatment of the quark-gluon plasma would suggest, where the thermalization rate is O($\alpha_s^2 T^2/M$), and triggered a detailed lattice investigation of the heavy quark diffusion coefficient $D$. We will perform a new lattice calculation of the heavy-quark momentum diffusion coefficient $\kappa$ ($\kappa$ and $D$ are related in the heavy-mass limit by the Einstein relation $D=2T^2/\kappa$). The calculation is based on a Kubo formula derived recently, which rigorously relates $\kappa$ in the limit of infinite quark mass to the small frequency behavior of a spectral function $\rho(\omega)$. The latter is related to the Euclidean two-point function of the electric field along the world-line of the heavy quark in the heavy-quark effective theory (HQET). The attractiveness of this new method is that the large scale M of the quark mass is removed from the spectral function. We propose a lattice calculation of the heavy-quark momentum diffusion coefficient in the plasma of gluons. The calculation is based on a recently derived Kubo formula that relates this transport coefficient to the two-point function of the electric field operator in heavy-quark effective theory (HQET). The goal is to constrain the momentum diffusion coefficient at three temperatures in the RHIC and LHC range.
The idea is to calculate the force-force correlator along the worldline of a heavy quark. In the Heavy Quark Effective Theory framework this amounts to calculating the two-point function of the chromo-electric field along a Polyakov loop line. See this reference for details.
One of the issues is to obtain a sufficiently accurate signal, for which a two-level algorithm, might be helpful.
The chromo-electric field requires a renormalization factor. This factor can be calculated using the Schroedinger functional, as was done for the chromo-magnetic field in this paper.