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We study the properties of three-body resonances using a lattice complex scalar φ4 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. [ABSTRACT FROM AUTHOR]

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.

We review the main results obtained in the project A.6, which dealt with hadron-hadron scattering and resonances in a finite volume. These results provide tools for the extraction of the resonance characteristics from lattice QCD simulations. In particular, in this review we focus on the evaluation of the matrix elements of the weak and electromagnetic currents between the states containing at least one resonance, as well as on the description of the three-particle states in a finite volume. We also discuss insights obtained using unitarized chiral perturbation theory in a finite volume.

We review the achievements of the project C.3, that dealt with the formulation and application of effective field theories including the Δ and Roper resonances as well as vector mesons. A particular focus was the calculation of finite volume effects and chiral extrapolations for lattice QCD.

Using the non-relativistic effective field theory approach for K−d scattering, it is demonstrated that a systematic perturbative expansion of the recoil corrections in the parameter ξ = MK/mN is possible in spite of the fact that K−d scattering at low energies is inherently non-perturbative due to the large values of the K̄N scattering lengths. The first order correction to the K−d scattering length due to single insertion of the retardation term in the multiple-scattering series is calculated. The recoil effect turns out to be reasonably small even at the physical value of MK/mN ≃ 0:5.

The notion of resonance matrix elements is discussed. The analogue of the Lellouch-Lüscher formula for the pion photo(electro)production amplitude in the Δ(1232) resonance region is given. A prescription for the pole extraction of the ΔNγ* transition form factors is provided. Theoretical prospects on the lattice calculation of B → K*(892)l+l− form factors are briefly summarized.

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to explicitly investigate the role of the three-particle force. Moreover, we discuss relaxing the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer. [ABSTRACT FROM AUTHOR]

The possibility of imposing partially twisted boundary conditions is investigated for the scalar sector of lattice QCD. According to the commonly shared belief, the presence of quark-antiquark annihilation diagrams in the intermediate state generally hinders the use of the partial twisting. Using effective field theory techniques in a finite volume, and studying the scalar sector of QCD with total isospin I = 1, we however demonstrate that partial twisting can still be performed, despite the fact that annihilation diagrams are present. The reason for this are delicate cancellations, which emerge due to the graded symmetry in partially quenched QCD with valence, sea and ghost quarks. The modified Lüscher equation in case of partial twisting is given. [ABSTRACT FROM AUTHOR]