Does the Higgs boson decay to invisible particles?

In plain words

The Higgs could be a bridge to hidden particles, decaying into things detectors cannot see. Current data allow up to about one decay in ten to be invisible.

Precise statement

Measure $\operatorname{BR}(h \to \mathrm{invisible})$ beyond the SM $h \to ZZ* \to 4\,\nu$ value of $\sim 1.2 \times 10^{-3}$. LHC limits are about $0.1\ \text{to}\ 0.15$ at 95 percent CL (ATLAS and CMS, 2023); an answer is a detection or a bound near $10^{-3}$.

What would settle it

HL-LHC vector-boson-fusion searches and a Higgs factory measuring Z h with $h \to \mathrm{invisible}$ to $\sim 0.3\%$.

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