f(0)(1370) Controversy from dispersive meson-meson scattering data analyses

Abstract

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.