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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 predicts a large multiplet of (pseudo-)Goldstone bosons and their low energy interactions below the ultraviolet (UV) completion scale $Λ\sim 4πf \sim O(10)$ 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 coupled channel analysis tends to push the unitarity violation scale $Λ_U$ significantly below the conventional UV scale $Λ\sim 4πf$ as estimated by naive dimensional analysis (NDA). Specifically, $Λ_U \sim (3-4)f$, lying in the multi-TeV range for $f\sim 1$ TeV. We interpret this as an encouraging sign that the upcoming LHC may explore aspects of Little Higgs UV completions, and we discuss some potential signatures. The meanings of the two estimated UV scales $Λ_U$ (from unitarity violation) and $Λ$ (from NDA) together with their implications for an effective field theory analysis of the Little Higgs models are also discussed.