Abstract
Many lattice studies of heavy quark diffusion originate from a colour-electric correlator, obtained as a leading term after an expansion in the inverse of the heavy-quark mass. In view of the fact that the charm quark is not particularly heavy, we consider subleading terms in the expansion. Working out correlators up to mathcal{O} (1/M2), we argue that the leading corrections are suppressed by mathcal{O} (T/M), and one of them can be extracted from a colour-magnetic correlator. The corresponding transport coefficient is non-perturbative already at leading order in the weak-coupling expansion, and therefore requires a nonperturbative determination.
Highlights
The physics of heavy quark diffusion and kinetic equilibration is closely related to that of Brownian motion, described by the Langevin equation
In the non-relativistic limit, this physics is described by three quantities: the diffusion coefficient, D; the momentum diffusion coefficient, κ; and the drag coefficient, η
Which of the quantities is viewed as “primary” depends on the context: for any mass, D can be expressed through a Kubo relation which in principle permits for a lattice study; in the large-mass limit, κ can be expressed through a Kubo relation which permits for a lattice study whose systematic errors should be better under control than for D; in the large-mass limit, η can be interpreted as a kinetic equilibration rate which leads to a direct physical interpretation
Summary
Consider the Lorentz force acting on a probe particle of momentum p and charge q:. p = q E + v × B (t) ≡ F(t). Given the particle’s large inertia, the time scale of the variation of velocities is larger than the time scale of the variation of the electric and magnetic field strengths This slow evolution is expected to be described by the Langevin equation, p − η p = f (t) , fi(t) = 0 , fi(t′)fj(t) = κ δij δ(t − t′). With the mass including a dispersive correction as we are within the low-energy effective description, leads to γv. The third correction is from Ek(t′)El(t) , weighted by − v2δikδjl + vivkδjl + δikvjvl v2 δik δj l according to eq (2.8) This a “trivial” effect, inhibiting acceleration towards the speed of light, and eliminated by going from M v back into the covariant momentum p. There is a dispersive effect, substituting the vacuum mass M through a thermally corrected Mkin
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
