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We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10.1007/JHEP06(2021)043, 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar ϕ 4 theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes. [ABSTRACT FROM AUTHOR]

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 spectrum of a bound state of three identical particles with a mass m in a finite cubic box is studied. It is shown that in the unitary limit, the energy shift of a shallow bound state is given by ΔE = c(k2/m)(xL)-3/2∣A∣2 exp(-2xL/√3), where k is the bound-state momentum, L is the box size, ∣∣A2 denotes the three-body analog of the asymptotic normalization coefficient of the bound state wave function, and c is a numerical constant. The formula is valid for kL ⪢ 1. [ABSTRACT FROM AUTHOR]

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]