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We evaluate the$$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$$a_1\left(1260\right)\to \pi \sigma \left(f_0\left(500\right)\right)$decay width from the perspective that the$$a_1(1260)$$$a_1\left(1260\right)$resonance is dynamically generated from the pseudoscalar–vector interaction and the$$\sigma $$$\sigma$arises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with$$a_1(1260) \rightarrow \rho \pi $$$a_1\left(1260\right)\to \rho \pi$followed by$$\rho \rightarrow \pi \pi $$$\rho \to \pi \pi$and a fusion of two pions within the loop to produce the$$\sigma $$$\sigma$provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the$$\pi \sigma $$$\pi \sigma$channel in recent lattice QCD calculations of the$$a_1$$$a_1$.

 

A bstract We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum. 

A bstract We study the properties of three-body resonances using a lattice complex scalar φ 4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.