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A perturbative calculation of the three-nucleon ground-state energy shift in a finite volume is carried out within the non-relativistic effective theory. The energy shift is evaluated up to and including $\mathcal{O}(L^{-6})$, where $L$ is the size of a cubic box. The convergence of the perturbative series at physical values of the scattering lengths is studied numerically., 16 pages, 3 figures

A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in ref.[2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed., Comment: 36 pages, 4 figures

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 $$\phi ^4$$ 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.

A dispersive analysis of $$\eta \rightarrow 3\pi $$ η→3π decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: (i) The angular averages of the amplitudes need to be performed along a complicated path in the complex plane. (ii) The averaged amplitudes develop singularities along the path of integration in the dispersive representation of the full amplitudes. It is a delicate affair to handle these singularities properly, and independent checks of the obtained solutions are demanding and time consuming. In the present article, we propose a solution method that avoids these difficulties. It is based on a simple deformation of the path of integration in the dispersive representation (not in the angular average). Numerical solutions are then obtained rather straightforwardly. We expect that the method also works for $$\omega \rightarrow 3\pi $$ ω→3π .

A dispersive analysis of $\eta\to 3\pi$ decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: i) The angular averages of the amplitudes need to be performed along a complicated path in the complex plane. ii) The averaged amplitudes develop singularities along the path of integration in the dispersive representation of the full amplitudes. It is a delicate affair to handle these singularities properly, and independent checks of the obtained solutions are demanding and time consuming. In the present article, we propose a solution method that avoids these difficulties. It is based on a simple deformation of the path of integration in the dispersive representation (not in the angular average). Numerical solutions are then obtained rather straightforwardly. We expect that the method also works for $\omega\to 3\pi$., Comment: 11 pages, 10 Figures. Version accepted for publication in EPJC. The ancillary files contain an updated set of fundamental solutions. The numerical differences to the former set are tiny, see the READMEv2 file for details

We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex $\varphi^4$ theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero., Comment: Update to match published version

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the $\Delta N\gamma^*$ transition form factors from lattice data. A counterpart of the L\"uscher 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 L\"uscher-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., Comment: 29 pages, 5 figures. Right-hand side of Eq. (4.13) is corrected by the normalization factor $V^{-1/2}$ and all related formulas namely, Eqs. (4.15), (4.16), (4,17), (4.21), (4.36), (5.1), (5.3) accordingly

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the ΔNγ⁎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.

The possibility of imposing partially twisted boundary conditions in the lattice study of the resonance states is investigated by using the effective field theory (EFT) methods. In particular, it is demonstrated that - in certain cases - it is possible to use partial twisting even in the presence of the quark annihilation diagrams., Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany, reference corrected in the replaced version

Based on the analysis of 6.031*10^7 K+- --> pi0 pi0 pi+- decays, the NA48/2 collaboration has recently determined the S-wave pi-pi scattering lengths a_0-a_2 with high precision. In addition, the scattering length a_2 has been independently measured, although less precisely so. The present article discusses in detail one of the theoretical frameworks used in the data analysis., Comment: 50 pages, 20 figures