Decays of the littlest Higgs Z(H) and the onset of strong dynamics

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) -> Z(L)HH. This partial width is found to be larger than the comparable two-body decay Z(H) -> Z(L)H for values of the SU(2) mixing angle cosine theta < 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.