Precise Determination of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>600</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Pole Parameters from a Dispersive Data Analysis

We use our latest dispersive analysis of $\ensuremath{\pi}\ensuremath{\pi}$ scattering data and the very recent ${K}_{\ensuremath{\ell}4}$ experimental results to obtain the mass, width, and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model-independent way by means of once- and twice-subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the ${f}_{0}(600)$ pole at $({457}_{\ensuremath{-}13}^{+14})\ensuremath{-}i({279}_{\ensuremath{-}7}^{+11})\text{ }\text{ }\mathrm{MeV}$ and that of the ${f}_{0}(980)$ at $(996\ifmmode\pm\else\textpm\fi{}7)\ensuremath{-}i({25}_{\ensuremath{-}6}^{+10})\text{ }\text{ }\mathrm{MeV}$, whereas their respective couplings to two pions are ${3.59}_{\ensuremath{-}0.13}^{+0.11}$ and $2.3\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{GeV}$.

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