We calculate the transverse momentum and invariant mass dependence of elliptic flow of thermal dileptons for Au+Au collisions at the Relativistic Heavy Ion Collider. The system is described using hydrodynamics, with the assumption of formation of a thermalized quark-gluon plasma at some early time, followed by cooling through expansion, hadronization and decoupling. Dileptons are emitted throughout the expansion history: by annihilation of quarks and anti-quarks inthe early quark-gluon plasma stage and through a set of hadronic reactions during the late hadronic stage. The resulting differential elliptic flow exhibits a rich structure, with different dilepton mass windows providing access to different stages of the expansion history. Elliptic flow measurements for dileptons,combined with those of hadrons and direct photons, are a powerful tool for mapping the time-evolution of heavy-ion collisions.
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