The f0(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 $(1245\pm 40)-i(300_{-70}^{+30})$ 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 $\pi \pi \to K\bar{K}$ 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 $K\bar{K}$ channels that should be attributed to data.

arXiv comment13 pages, 8 figures. v2 version: improved results for the f0(1370) pole determination in the pipi to KKbar channel, minor amendments, appendices expanded

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