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Scalar Loops in Little Higgs Models

Loops of the scalar particles present in Little Higgs models generate radiatively scalar operators that have been overlooked before in Little Higgs analyses. We compute them using a technique, recently proposed to deal with scalar fluctuations in non-linear sigma models, that greatly simplifies the calculation. In particular models some of these operators are not induced by loops of gauge bosons or fermions, are consistent with the Little Higgs symmetries that protect the Higgs boson mass, and must also be included in the Lagrangian. In general, scalar loops multiplicatively renormalize the tree-level scalar operators, O_S -> O_S [1- N Λ^2/(4πf)^2] with large N (e.g. N ~ 20 for the Littlest Higgs), suggesting a true UV cutoff Λ< 4 πf/\sqrt{N} significantly below the estimate 4πf of naive dimensional analysis. This can have important implications for the phenomenology and viability of Little Higgs models.