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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 propose a method to determine the isoscalar scattering length on the lattice. Our method represents the generalization of Lüscher''s approach in the presence of inelastic channels (complex scattering length). In addition, the proposed approach allows one to find the position of the S-matrix pole corresponding the resonance. [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]

The extraction of the B → K ⁎ transition form factors from lattice data is studied, applying non-relativistic effective field theory in a finite volume. The possible mixing of πK and ηK states is taken into account. The two-channel analogue of the Lellouch–Lüscher formula is reproduced. Due to the resonance nature of the K ⁎ , an equation is derived, which allows to determine the form factors at the pole position in a process-independent manner. The infinitely-narrow width approximation of the results is discussed. [ABSTRACT FROM AUTHOR]

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the ΔNγ* transition form factors from lattice data. A counterpart of the Lüscher approach for the matrix elements of unstable states is formulated. In particular, we thoroughly discuss various kinematic settings, which are used in the calculation of the above matrix element on the lattice. The emerging Lüscher-Lellouch factor and the analytic continuation of the matrix elements into the complex plane are also considered in detail. A full group-theoretical analysis of the problem is made, including the partial-wave mixing and projecting out the invariant form factors from data. [ABSTRACT FROM AUTHOR]