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Abstract: Based on the analysis of decays, the NA48/2 Collaboration has recently determined the S-wave ππ scattering lengths with high precision. In addition, the scattering length has been independently measured, although less precisely so. The present article discusses in detail one of the theoretical frameworks used in the data analysis. [Copyright &y& Elsevier]

Abstract: In this paper we propose a model-independent method to extract the resonance parameters on the lattice directly from the Euclidean 2-point correlation functions of the field operators at finite times. The method is tested in case of the two-point function of the Δ-resonance, calculated at one loop in Small Scale Expansion. Further, the method is applied to a -dimensional model with two coupled Ising spins and the results are compared with earlier ones obtained by using Lüscher''s approach. [Copyright &y& Elsevier]

Abstract: We study the extraction of Δ-resonance parameters from lattice data for small quark masses, corresponding to the case of an unstable Δ. To this end, we calculate the spectrum of the correlator of two Δ-fields in a finite Euclidean box up-to-and-including in the small scale expansion using infrared regularization. On the basis of our numerical study, we argue that the extraction of the parameters of the Δ-resonance (in particular, of the mass and the pion–nucleon–delta coupling constant) from the measured volume dependence of the lowest energy levels should be feasible. [Copyright &y& Elsevier]