Analyticity constitutes a rigid constraint on hadron scattering amplitudes. This property is used to relate models in different energy regimes. Using meson photoproduction as a benchmark, we show how to test contemporary low energy models directly against high energy data. This method pinpoints deficiencies of the models and treads a path to further improvement. The implementation of this technique enables one to produce more stable and reliable partial waves for future use in hadron spectroscopy and new physics searches.Introduction.-Determination of various hadronic effects represents a major challenge in searches for New Physics through precision measurements [1][2][3][4][5]. For example, the possible identification of Beyond Standard Model signals in B meson decays is hindered by uncertainties in hadronic final state interactions. The strongly coupled nature of QCD prevents us from computing these effects directly from the underlying microscopic formulation. Nevertheless, one can use the first principles of Smatrix theory to impose stringent constraints on hadron scattering amplitudes [6][7][8]. These approaches are encountering a renewed interest even in the more formal context of strongly coupled theories [9][10][11].In this Letter, we show how to use analyticity to relate the amplitudes at high energies to the physics at low energies, where resonance effects dominate. This is not only important for reducing hadronic uncertainties in the aforementioned processes, but is of interest on its own merits for unraveling the spectrum of QCD. According to phenomenological predictions and lattice QCD simulations, the current spectrum summarized in the Particle Data Group (PDG) is far from complete [12]. For example, the recent discoveries of unexpected peaks in data indicate that the true hadron spectrum is far more complex than predicted [13][14][15][16][17][18]. As a working case, we focus here on the baryon sector in the intermediate energy range. In the PDG these N * and ∆ resonances are referred to as "poorly known" [12], despite the large amount of data available. The ambiguities encountered when identifying resonances are related to the fact that, as the center of mass energy increases, so does the number of contributing partial waves, vastly complicating the reaction models used in data analysis. The 2 − 3 GeV mass region is of particular interest for baryon spectroscopy since, besides the ordinary quark model multiplets, it is expected