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Buchalla, Gerhard; Catà, Oscar and Krause, Claudius (2015): A systematic approach to the SILH Lagrangian. In: Nuclear Physics B, Vol. 894: pp. 602-620 [PDF, 376kB]


We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small xi = v(2)/f(2). Here v is the electroweak scale and f is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SIM to first order in xi, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in xi has to be performed. We point out that terms of order xi(2), which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order xi/16 pi(2) that are retained, as long as xi greater than or similar to 1/16 pi(2). Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset SO(5)/SO(4) is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on SU(2)L circle times SU(2)(R)/SU(2)(V). (C) 2015 The Authors. Published by Elsevier B.V.

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