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Using the framework of nonrelativistic effective field theory, the finite-volume ground-state energy shift is calculated up to and including O(L-6) for the system of three pions in the channel with the total isospin I=1. The relativistic corrections are included perturbatively, up to the same order in the inverse of the box size L. The obtained explicit expression, together with the known result for the system with maximal isospin I=3, can be used for the extraction of two independent effective three-body couplings from the measured ground-state spectrum of three pions. [ABSTRACT FROM AUTHOR]

The paper presents an extension and a refinement of our previous work on the extraction of the doubly virtual forward Compton scattering amplitude on the lattice by using the background field technique [1]. The zero frequency limit for the periodic background field is discussed, in which the well-known result is reproduced. Further, an upper limit for the magnitude of the external field is established for which the perturbative treatment is still possible. Finally, the framework is set for the evaluation of the finite-volume corrections allowing for the analysis of upcoming lattice results. [ABSTRACT FROM AUTHOR]

The energy shift of a nucleon in a static periodic magnetic field is evaluated at second order in the external field strength in perturbation theory. It is shown that the measurement of this energy shift on the lattice allows one to determine the unknown subtraction function in the forward doubly virtual Compton scattering amplitude. The limits of applicability of the obtained formula for the energy shift are discussed. [ABSTRACT FROM AUTHOR]

The recoil retardation effect in the K-d scattering length is studied. Using the nonrelativistic effective field theory approach, 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 nonperturbative due to the large values of the KN 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. [ABSTRACT FROM AUTHOR]

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order L-6. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order L-3. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Lüscher equation. [ABSTRACT FROM AUTHOR]