Extracting the pairing gap from van Hove singularities in RF spectra of the Fermi Hubbard model

We show that van Hove singularities in rf spectra of the 3D attractive Fermi Hubbard model provide a robust route to extracting the pairing gap. Four types of singularities are classified, and their spectral positions are shown to depend solely on the pairing gap $Δ$ and chemical potential $μ$ through simple algebraic relations. Measuring two well-resolved singularities therefore determines both parameters without requiring full spectral fitting. Numerical simulations incorporating phenomenological lifetime and scattering broadenings confirm that these features remain visible in both momentum-integrated and $k_z$-integrated spectra, and become more pronounced at stronger coupling where conventional back-bending methods lose sensitivity. At half filling, particle-hole symmetry fixes $μ$, reducing the extraction to a single singularity measurement. These results establish vHS analysis as a practical spectroscopic diagnostic for pairing in quantum-simulated 3D Fermi Hubbard systems.