Determination of SU(2) chiral perturbation theory low energy constants from a precise description of pion-pion scattering threshold parameters
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2013
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Amer Physical Soc
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Abstract
We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D, and F waves are consistent with previous determinations but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.
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©2013 American Physical Society.
J. R. P. thanks the late F. J. Ynduráin for many discussions about the possibility to carry out this project after completing [13]. J. Nebreda acknowledges funding by the German Academic Exchange Service (DAAD) and the Fundación Ramón Areces. G. R. acknowledges partial support by the EU Integrated Infrastructure Initiative HadronPhysics3 Project under Grant No. 283286 and by DFG (CRC 16, ‘‘Subnuclear Structure of Matter’’ and CRC 110, ‘‘Symmetries and the Emergence of Structure in QCD’’). We also thank B. Kubis and U.-G. Meißner for their reading of the manuscript and their valuable suggestions and corrections, Z. H. Guo and H. Q. Zheng for clarifying the use of their axiomatic bounds, and B. Ananthanarayan for kindly helping us with the existing sum rules for c parameters. This work is partly supported by DGICYT Contracts No. FPA2011-27853-C02-02 and No. FPA2010-17806, and the EU Integrated Infrastructure Initiative Hadron Physics Project under Contract No. RII3-CT-2004-506078.