We calculate the combination 2a 0 (0) Ϫ5a 0 (2) ͑the Olsson sum rule͒ and the scattering lengths and effective ranges a 1 ,a 2 (I) and b 1 ,b 2 (I) dispersively ͑with the Froissart-Gribov representation͒ using, at low energy, the phase shifts for scattering obtained by Colangelo, Gasser, and Leutwyler ͑CGL͒ from the Roy equations and chiral perturbation theory, plus experiment and Regge behavior at high energy, or directly, using the CGL parameters for a's and b's. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several ͑2 to 5͒ standard deviations, and is essentially independent of the details of the intermediate energy region (0.82рEр1.42 GeV) and, in some cases, of the high energy behavior assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.
We study the large N c behavior of couplings among light meson states with different compositions in terms of quarks and gluons. We shortly review the most common compositions of mesons, which are of interest for the understanding of low-lying meson resonances, namely, the ordinary quark-antiquark states as well as the nonordinary glueball, tetraquark, and other states. We dedicate special attention to Jaffe's generalization of the tetraquark with N c − 1 qq pairs, which is the only type of state we have identified whose width does not necessarily vanish with N c , though it does decouple exponentially with N c from the ππ channel, so that it is weakly coupled to the meson-meson system.
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.
We report our progress on the data analysis of ππ scattering data in terms of Forward Dispersion Relations (FDR), as well as Roy equations (RE) and their once-subtracted counterpart, GKPY equations. The first part of the analysis consists of independent fits to the different ππ channels. The GKPY equations provide a more stringent consistency check for the parametrizations of the S0-wave data in the region from 400 to 1100 MeV, In the second part we present our preliminary analysis where the fits are constrained to satisfy all dispersion relations within errors, including the new GKPY Eqs., thus providing a very precise and model independent description of data using just analyticity, causality and crossing.
International Workshop on Effective Field Theories: from the pion to the upsilon
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