Realistic electroweak completion of the stochastic scalar-doublet model

Determine whether the stochastic scalar-doublet framework can be incorporated into a realistic electroweak theory that reproduces the observed Higgs boson properties.

Background

The paper treats the complex scalar doublet as a toy model with the same internal U(1)×SU(2) quantum numbers as the Standard Model Higgs doublet, but replaces the conventional Higgs potential with a simplified mass term and a stochastic white-noise coupling.

The unresolved problem is whether the stochastic construction can be extended beyond this toy-model setting while retaining a realistic Higgs sector and reproducing observed Higgs properties.

References

The extent to which these ideas can be incorporated into a realistic electroweak theory capable of reproducing the observed Higgs boson properties remains an open question and is left for future work.

— Statistical Symmetry Breaking and Emergent Colored Noise in a Stochastic Scalar-Doublet Field Theory  (2609.03312 - Wang, 3 Sep 2026) in Section 2, Action and symmetry

The extent to which these features persist in the fully coupled scalar-doublet-gauge-field system remains an open question and is left for future investigation.

— Statistical Symmetry Breaking and Emergent Colored Noise in a Stochastic Scalar-Doublet Field Theory  (2609.03312 - Wang, 3 Sep 2026) in Section 3, Euler-Lagrangian equation and its solution