Suppression of Higgs Mixing by Quantum Zeno Effect

The Higgs portal interaction to a singlet sector of the standard model (SM) gauge group is widely-studied. In this Letter, we show that a quantum effect is important if the Higgs field mixes with another singlet scalar field whose decay rate is larger than the mass difference between the two mass eigenstates. This effect may be interpreted as the quantum Zeno effect. In either the quantum mechanics or the quantum field theory, we show that the resulting propagating mode is not the eigenstate of the mass matrix, but it is approximately the eigenstate of the interaction. As a consequence, the decoupling of the mixing effect happens at the infinity limit of the decay width of the exotic scalar even if the na\"{i}ve mixing parameter is not small. With a finite decay width of the exotic scalar, we derive the effective mass of the propagating mode in the SM sector, its decay rate, and the couplings at the 1-loop level. It turns out that the mixed mass eigenstates can mimic the discovered 125 GeV Higgs boson. This fuzzy Higgs boson can be obtained in a simple perturbative renormalizable model. It is consistent with the 125 GeV SM Higgs boson when the mass difference is smaller than ${\cal O}(0.1)$GeV (${\cal O}(1)$GeV) for ${\cal O}(1)$ (${\cal O}(0.01)$) mixing. We argue the possible natural scenario for the tiny mass splitting and the possibility that the upper bound of the mass difference is larger for a strongly-coupled singlet sector. To probe the fuzzy Higgs boson scenario, it is difficult to directly produce the singlet sector particles. Nevertheless, the future Higgs factories may probe this scenario by precisely measuring the Higgs boson invisible decay rate and the deviation of the Higgs coupling. Applications of the mechanism are also mentioned.