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 paper, 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 by defining the (would-be) decay process of the singlet scalar as the measurement. 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 naive 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 when the mass difference is smaller than O(0.1)GeV (O(1) GeV, O(10)GeV) for O(1) (O(0.01), O(0.001)) mixing to be consistent with the 125 GeV SM Higgs boson. 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.

Automated summary

The paper investigates the Higgs portal interaction with a singlet sector of the standard model (SM) gauge group. It shows that a quantum effect plays a crucial role when the Higgs field mixes with another singlet scalar field with a higher decay rate than the mass difference between the mass eigenstates. The research finds that the mixed mass eigenstates can mimic the 125 GeV Higgs boson, which is important for further understanding the Higgs mechanism.