Large Directed Flow of Open Charm Mesons Probes the Three-Dimensional Distribution of Matter in Heavy-Ion Collisions

Thermalized matter created in noncentral 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 on heavy quarks from the asymmetrically distributed thermalized matter generates substantial directed flow for heavy flavor mesons. We predict a very large rapidity-odd directed flow of D mesons in noncentral 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 three-dimensional distribution of matter in heavy-ion collisions.