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Precision vs discovery: a simple benchmark

The discovery of the Standard Model Scalar Boson (Brout-Englert-Higgs particle) opens a new field of research, namely the structure of the scalar sector. Numerous extensions exist, and imply extra particles, including additional scalars. Two main alleys are open to investigate such deviations from the minimal standard model: precision measurements could indicate a deviation from the usual expectations, or a direct discovery of new scalar partners (or other particles) would establish an alternative. In this short note, we concentrate on a very simple model, for which the respective reaches of the two approaches can be compared. This note also provides a strong incentive to pursue searches for extra "Standard Model Scalar-like" particles in the whole available energy spectrum.