The exact packing measure of Brownian double points

Let $Dsubset {mathbb{R}}^3$ be the set of double points of a three-dimensional Brownian motion. We show that, if ξ = ξ₃(2,2) is the intersection exponent of two packets of two independent Brownian motions, then almost surely, the ?-packing measure of D is zero if $$ int_{0^+} r^{-1-xi} phi(r)^{xi} , dr < infty,$$ and infinity otherwise. As an important step in the proof we show up-to-constants estimates for the tail at zero of Brownian intersection local times in dimensions two and three.