Top-antitop pairs produced in the decay of a new heavy resonance will exhibit spin correlations that contain valuable coupling information. When the tops decay, these correlations imprint themselves on the angular patterns of the final quarks and leptons. While many approaches to the measurement of top spin correlations are known, the most common ones require detailed kinematic reconstructions and are insensitive to some important spin interference effects. In particular, spin-1 resonances with mostly-vector or mostly-axial couplings to top cannot be easily discriminated from one another without appealing to mass-suppressed effects or to more model-dependent interference with continuum Standard Model production. Here, we propose to probe the structure of a resonance's couplings to tops by measuring the azimuthal angles of the tops' decay products about the production axis. These angles exhibit modulations which are typically O(0.1-1), and which by themselves allow for discrimination of spin-0 from higher spins, measurement of the CP-phase for spin-0, and measurement of the vector/axial composition for spins 1 and 2. For relativistic tops, the azimuthal decay angles can be well-approximated without detailed knowledge of the tops' velocities, and appear to be robust against imperfect energy measurements and neutrino reconstructions. We illustrate this point in the highly challenging dileptonic decay mode, which also exhibits the largest modulations. We comment on the relevance of these observables for testing axigluon-like models that explain the top quark A_FB anomaly at the Tevatron, through direct production at the LHC.Comment: 24 pages plus appendices, 6 figures. v2: added references, updated AFB model, expanded discussion of SM interference for spin-0 particl
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