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We provide global parameterizations of π π → π π scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of π π → π π , both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 GeV . Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the σ / f 0 (500) , f 0 (980) and ρ (770) pole parameters. [ABSTRACT FROM AUTHOR]

We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the σ region. We also improve the matching between the parametrizations at low and intermediate energy of the S0 wave, and show that the effect of this on the sigma pole position is negligible. [ABSTRACT FROM AUTHOR]

In this work we provide a dispersive analysis of ππ→KK¯ scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from KK¯ threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region. [ABSTRACT FROM AUTHOR]

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the ππ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three ππ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for ππ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input. [ABSTRACT FROM AUTHOR]