We present a model-independent study aimed at characterizing the nature of possible resonances in the jet-photon or jet-$Z$ final state at hadron colliders. Such resonances are expected in many models of compositeness and would be a clear indication of new physics. At leading order, in the narrow width approximation, the matrix elements are parameterized by just a few constants describing the coupling of the various helicities to the resonance. We present the full structure of such amplitudes up to spin two and use them to simulate relevant kinematic distributions that could serve to constrain the coupling structure. This also generalizes the signal generation strategy that is currently pursued by ATLAS and CMS to the most general case in the considered channels. While the determination of the P/CP properties of the interaction seems to be out of reach within this framework, there is a wealth of information to be gained about the spin of the resonance and the relative couplings of the helicities.
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