Ananthanarayan, B and Colangelo, G and Gasser, J and Leutwyler, H (2000) Roy equation analysis of pi pi scattering. [Preprint]

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Abstract
We analyze the Roy equations for the lowest partial waves of elastic pi pi scattering and demonstrate that the two Swave scattering lengths a_0^0 and a_0^2 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S and Pwaves is given and it is shown that the threshold parameters of the D and Fwaves are also fixed very sharply in terms of a_0^0 and a^2_0. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a_0^0,a_0^2) plane. We show that the data on the reactions e+e > pi pi and tau > pi pi nu reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K > pi pi e nu in restricting the allowed range of a_0^0, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.
Item Type:  Preprint 

Additional Information:  Phys.Rept. 353 (2001) 207279 
Keywords:  Roy equations;Dispersion relations;Partial wave analysis;Mesonmeson interactions;Pionpion scattering;Chiral symmetries 
Department/Centre:  Division of Physical & Mathematical Sciences > Centre for Theoretical Studies 
Date Deposited:  30 Jul 2004 
Last Modified:  19 Sep 2010 04:13 
URI:  http://eprints.iisc.ernet.in/id/eprint/829 
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