Probing the Rare Four-Bottom Higgs Decay $H\to b\bar b b\bar b$ at the HL-LHC and ILC
We propose the rare SM Higgs decay $H\to b\bar b b\bar b$ as a probe of the structure of Higgs interactions with bottom quarks and gauge bosons, and as a baseline for searches for new physics producing four-bottom final states in Higgs decays. We compute the leading contributions to this decay, including the dominant $H\to b\bar b g\to b\bar b b\bar b$ topology, the sizeable $H\to ZZ^\ast\to b\bar b b\bar b$ channel, and the loop-induced $H\to gg\to b\bar b b\bar b$ contribution. We find a branching ratio of order $1.6\times10^{-3}$ and show that destructive interference among the leading amplitudes is phenomenologically relevant. We demonstrate that this decay can be probed in associated Higgs production at both the HL-LHC and the ILC. For $pp\to WH\to Wb\bar b b\bar b$ at $\sqrt{s}=14$ TeV, we use a multivariate analysis based on boosted decision trees to exploit correlations among the four-$b$ kinematic observables. At $3000~{\rm fb}^{-1}$, the statistical significance reaches about $3.5$, while a tighter high-purity working point gives $S/B\simeq5\%$ with significance close to $3σ$. A combined high-luminosity LHC dataset could therefore make this rare decay observable. For $e^+e^-\to ZH\to Zb\bar b b\bar b$ at the ILC with $\sqrt{s}=250$ GeV, we demonstrate that the cleaner collider environment gives a high-purity signal sample. In the nominal setup, the multivariate analysis gives a significance above $5σ$ already at $300~{\rm fb}^{-1}$. At integrated luminosities of order $1-3~{\rm ab}^{-1}$, the branching ratio can be measured with several-percent precision.