Unitarity of Little Higgs Models Signals New Physics of UV Completion

The ``Little Higgs'' opens up a new avenue for natural electroweak symmetry breaking in which the standard model Higgs particle is realized as a pseudo-Goldstone boson and thus is generically light. The symmetry breaking structure of the Little Higgs models generally predicts a large multiplet of (pseudo-)Goldstone bosons, owing their underlying dynamics to the ultraviolet (UV) completion scale $\Lambda \sim 4\pi f \sim O(10)$ TeV, where $f$ is the Goldstone decay constant. We study unitarity of the Little Higgs models by systematically analyzing the high energy scatterings of these (pseudo-)Goldstone bosons. We reveal that the collective effect of the Goldstone scatterings via the coupled channel analysis tends to push the unitarity violation scale $\Lambda_U$ significantly below the conventional UV scale $\Lambda \sim 4\pi f$ as estimated by naive dimensional analysis (NDA). Namely, $\Lambda_U \sim (3-4)f$ lies in the multi-TeV range for $f\sim 1$ TeV. We interpret this as an encouraging sign that the upcoming LHC can explore aspects of the Little Higgs UV completion, and we discuss some potential signatures. The meanings of the two estimated UV scales $\Lambda_U$ (from unitarity violation) and $\Lambda$ (from NDA) together with their implications for an effective theory analysis of the Little Higgs models are also addressed.