  Searches for invisible Higgs decays at the Large Hadron Collider constrain
dark matter Higgs-portal models, where dark matter interacts with the Standard
Model fields via the Higgs boson. While these searches complement dark matter
direct-detection experiments, a comparison of the two limits depends on the
coupling of the Higgs boson to the nucleons forming the direct-detection
nuclear target, typically parameterized in a single quantity $f_N$. We evaluate
$f_N$ using recent phenomenological and lattice-QCD calculations, and include
for the first time the coupling of the Higgs boson to two nucleons via
pion-exchange currents. We observe a partial cancellation for Higgs-portal
models that makes the two-nucleon contribution anomalously small. Our results,
summarized as $f_N=0.308(18)$, show that the uncertainty of the Higgs-nucleon
coupling has been vastly overestimated in the past. The improved limits
highlight that state-of-the-art nuclear physics input is key to fully
exploiting experimental searches.
