5 v 1 1 S ep 2 00 0 1 π − π interaction amplitudes with chiral constraints

The ππ interactions are one of the main sources of information on low energy physics. Their knowledge in scalar-isoscalar channel allows us to investigate scalar meson spectroscopy and to test the predictions of many theoretical models. Amplitudes of the ππ interactions should fulfill some basic conditions like unitarity and crossing symmetry. Described in 1) three-coupled channel amplitudes for ππ , KK and σσ interactions were constructed using a S-matrix unitary model without any constraints on model parameters. Several soutions were obtained by fits to experimental data in effective two pion mass region mππ from the ππ threshold to 1600 MeV. Problem of the crossing symmetry for the ππ scattering has been studied in the past using dispersion techniques 2), 3) which led to the construction of Roy’s equations. Using them with parameters as presented in 3) we calculated new real parts (treated hereafter as output) for the ππ amplitudes obtained in 1). The aim of our study was comparison of the output with real parts of given amplitudes (treated hereafter as input). Roy’s equations explicitly depend both on the energy behaviour of amplitudes and on theresold parameters aIJ (for I = 0 and 2)so such comparison was done for various ππ threshold parameters in isoscalar and isotensor waves.