<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1370</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> Controversy from Dispersive Meson-Meson Scattering Data Analyses
J. R. Peláez, A. Rodas, Jacobo Ruiz de Elvira
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 $(1245\ifmmode\pm\else\textpm\fi{}40)\ensuremath{-}i(30{0}_{\ensuremath{-}70}^{+30})\text{ }\text{ }\mathrm{MeV}$ in $\ensuremath{\pi}\ensuremath{\pi}$ scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at $(138{0}_{\ensuremath{-}60}^{+70})\ensuremath{-}i(22{0}_{\ensuremath{-}70}^{+80})\text{ }\text{ }\mathrm{MeV}$ also appears in the $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}K\overline{K}$ 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 $\ensuremath{\pi}\ensuremath{\pi}$ and $K\overline{K}$ channels that should be attributed to data.