f0(1370) Controversy from Dispersive Meson-Meson Scattering Data Analyses

We establish the existence of the long-debated f(0)(1370) resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at (1245 +/- 40) - i(300(-70)(+30)) MeV in pi pi scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at (1380(-60)(+70)) - i(220(-70)(+80)) MeV also appears in the pi pi -> K (K) over bar over bar data analysis with partial-wave dispersion relations. Despite settling its existence, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the pi pi and K (K) over bar channels that should be attributed to data.

Automated summary

We establish the existence of the long-debated f(0)(1370) resonance in meson-meson scattering data using novel dispersive analyses. Our method relies on forward dispersion relations, which are applicable to generic inelastic resonances. We find the pole of f(0)(1370) at (1245 +/- 40) - i(300(-70)(+30)) MeV in pi pi scattering. Additionally, we observe a pole at (1380(-60)(+70)) - i(220(-70)(+80)) MeV in pi pi -> K (K) over bar over bar data analysis with partial-wave dispersion relations. However, there is still a tension between the pole parameters from the pi pi and K (K) over bar channels, likely due to data.