Momentum correlations of the Hawking effect in a quantum fluid

The Hawking effect -- the amplification of fluctuations at the horizon -- has been detected in quantum fluids through real-space density correlations. However, real-space observables integrate over frequency, mixing distinct scattering channels into a single interference pattern and obscuring the spectral and entanglement structure of the emission. Here, we numerically compute momentum-space two-point correlations in a transcritical quantum fluid, using the truncated Wigner approximation applied to a realistic, driven-dissipative polariton system. We spectrally resolve the Hawking--partner as well as greybody factor channels and find that both carry comparable correlation strength, demonstrating that the well-known real-space ``moustache'' is an interference between these spectrally distinct contributions. The Hawking--partner channel is dominated by negative correlations, a direct signature of quantum-vacuum pair creation. All features reach amplitudes detectable in state-of-the-art experiments. Our results establish that the full three-mode output state must be considered for entanglement characterization, and provide a general framework applicable to any quantum fluid.