If electro-weak symmetry is broken by a new strongly interacting sector, new physics will probably manifest itself in gauge boson scattering at the LHC. The relevant dynamics is well described in terms of an effective lagrangian. We discuss the probable size of the coefficients of the relevant operators under a combination of model-independent constraints and reasonable assumptions based on two models of the strongly interacting sector. We compare these values with LHC sensitivity and argue that they will be too small to be seen. Therefore, the presence of vector and scalar resonances required by unitarity will be the only characteristic signature. We analyze the most likely masses and widths of these resonances.PACS numbers: 11.15. Ex,12.39.Fe,12.60.Fr,12.60.Nz
I. MOTIVATIONSIf the breaking of the electro-weak symmetry is due to a new and strongly interacting sector, it is quite possible that the LHC will not discover any new fundamental particle below the scale of 2 TeV. In this scenario-in which there is no SUSY and no light (fundamental or composite) Higgs boson to be seen-it becomes particularly relevant to analyze the physics of gauge boson scattering-W W , W Z and ZZ-because it is here that the strongly interacting sector should manifest itself most directly.Gauge boson scattering in this regime looks similar in many ways to ππ scattering in QCD and similar techniques can be used. The natural language is that of the effective electro-weak lagrangian introduced in [1]. This lagrangian contains all dimension four operators for the propagation and interaction of the Goldstone bosons of the breaking of the global SU (2) × U (1) symmetry. If we knew the coefficients of these operators we could predict the physics of gauge boson scattering at the LHC. Unfortunately the crucial coefficients do not enter directly in currently measured observables. We do not know their values and constraints on them can only be inferred by their effect in small loop corrections to the EW observables. Accordingly they are rather weak. In addition, even though the LHC will explore these terms directly, its sensitivity is not as good as we would like it to be and an important range of values will remain unexplored.This lack of predictive power can be ameliorated if we assume some model of the strong dynamics responsible of the electro-weak symmetry breaking. In this case, additional relations among the coefficients can be found and used to relate them to known constraints. Our strategy is therefore to use our prejudices-that is, model-dependent relationships among the coefficients of the effective lagrangian-plus general constraints coming from causality and analyticity of the amplitudes to see what values the relevant coefficients of the effective electro-weak lagrangian can assume without violating any of the current bounds.We are aware that in many models the relations among the coefficients we utilize can be made weaker and therefore our bounds will not apply. Nevertheless we find it useful to be as conservative as possible a...