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The cumulative emission resulting from hadronic cosmic-ray interactions instar-forming galaxies (SFGs) has been proposed as the dominant contribution tothe astrophysical neutrino flux at TeV to PeV energies reported by IceCube. Thesame particle interactions also inevitably create $\gamma$-ray emission thatcould be detectable as a component of the extragalactic $\gamma$-ray background(EGB), which is now measured with the Fermi-LAT in the energy range from 0.1 to820 GeV. New studies of the blazar flux distribution at $\gamma$-ray energiesabove 50 GeV place an upper bound on the residual non-blazar component of theEGB. We show that these results are in strong tension with models that considerSFGs as the dominant source of the diffuse neutrino backgrounds. Acharacteristic spectral index for parent cosmic rays in starburst galaxies of$\Gamma_{\rm SB} \simeq 2.3$ for $dN/dE \propto E^{-\Gamma_{\rm SB}}$ isconsistent with the observed scaling relation between $\gamma$-ray and IRluminosity for SFGs, the bounds from the non-blazar EGB, and the observed$\gamma$-ray spectra of individual starbursts, but underpredicts the IceCubedata by approximately an order of magnitude.

Evidence against star-forming galaxies as the dominant source of IceCube neutrinos