  The Little Higgs mechanism, as realized in various models, requires a set of
new massive gauge bosons, some of which mix with gauge bosons of the Standard
Model. For a range of mixing angles the coupling of gauge bosons to scalars can
become strong, ultimately resulting in a breakdown of perturbative calculation.
This phenomenon is studied in the Littlest Higgs model, where the approach to
strong dynamics is characterized by increasing tree-level decay widths of the
neutral Z_H boson to lighter gauge bosons plus multiple scalars. These
increasing widths suggest a distinctive qualitative collider signature for the
approach to the strong coupling regime of large Higgs and other scalar
multiplicities. In this work we catalog the kinematically allowed three-body
decays of the Z_H, and calculate the partial width of the process Z_H to Z_L H
H. This partial width is found to be larger than the comparable two-body decay
Z_H to Z_L H for values of the SU(2) mixing angle cosine(theta) less than 0.13,
indicating divergence of the littlest Higgs sigma field expansion at values of
cosine(theta) larger than a simple parametric calculation would suggest.
Additionally, we present analytical expressions for all two-body decays of the
Littlest Higgs Z_H gauge boson, including the effects of all final-state
masses.
