Large directed flow of open charm mesons probes the three dimensional distribution of matter in heavy ion collisions

Thermalized matter created in non-central relativistic heavy-ion collisions is expected to be tilted in the reaction plane with respect to the beam axis. The most notable consequence of this forward-backward symmetry breaking is the observation of rapidity-odd directed flow for charged particles. On the other hand, the production points for heavy quarks are forward-backward symmetric and shifted in the transverse plane with respect to the fireball. The drag of heavy quarks from the asymmetrically distributed thermalized matter generates a large directed flow for heavy flavor mesons. We predict a very large rapidity odd directed flow of $D$ mesons in non-central Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV, $several$ $times$ $larger$ than for charged particles. A possible experimental observation of a large directed flow for heavy flavor mesons would represent an almost direct probe of the 3-dimensional distribution of matter in heavy-ion collisions.