Scrutinizing ΠΠ Scattering In Light Of Recent Lattice Phase Shifts Model

We use PKU representation to analyze the IJ=00,11,20 phase shift data ofscatterings obtained from the lattice QCD simulation.In the representation of PKU,the unitary and analytical properties of scattering amplitudes are automatically satisfied,and the amplitudes can be factorized into contributions of poles and cuts.We estimate the contribution of the left-hand cut from the SU(2)chiral perturbation theory,and use the BNR relation as the constraint of crossing symmetry about different wave amplitudes.Then,we extract the resonance state information from the lattice QCD data.We find that there exists a pair of bound state and virtual state poles below the threshold,not just one bound state,when the lattice data are obtained with respect to m_π=391 Me V.The constraint of BNR relation also helps confirm the existence of virtual state of IJ=20 partial wave.The lattice data of a 236Me V pion are analyzed and the pole positions are determined.More information about the resonance states ofσpole can be obtained by the pole positions at differentmeson masses.