IceCube and HAWC constraints on very-high-energy emission from the Fermi bubbles

The nature of the $\gamma$-ray emission from the \emph{Fermi} bubbles is unknown. Both hadronic and leptonic models have been formulated to explain the peculiar $\gamma$-ray signal observed by the Fermi-LAT between 0.1-500~GeV. If this emission continues above $\sim$30~TeV, hadronic models of the \emph{Fermi} bubbles would provide a significant contribution to the high-energy neutrino flux detected by the IceCube observatory. Even in models where leptonic $\gamma$-rays produce the \emph{Fermi} bubbles flux at GeV energies, a hadronic component may be observable at very high energies. The combination of IceCube and HAWC measurements have the ability to distinguish these scenarios through a comparison of the neutrino and $\gamma$-ray fluxes at a similar energy scale. We examine the most recent four-year dataset produced by the IceCube collaboration and find no evidence for neutrino emission originating from the \emph{Fermi} bubbles. In particular, we find that previously suggested excesses are consistent with the diffuse astrophysical background with a p-value of 0.22 (0.05 in an extreme scenario that all the IceCube events that overlap with the bubbles come from them). Moreover, we show that existing and upcoming HAWC observations provide independent constraints on any neutrino emission from the \emph{Fermi} bubbles, due to the close correlation between the $\gamma$-ray and neutrino fluxes in hadronic interactions. The combination of these results disfavors a significant contribution from the \emph{Fermi} bubbles to the IceCube neutrino flux.