Spectrum of three-body bound states in a finite volume

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 $\Delta E=c (\kappa^2/m)\,(\kappa L)^{-3/2}|A|^2\exp(-2\kappa L/\sqrt{3})$, where $\kappa$ is the bound-state momentum, $L$ is the box size, $|A|^2$ 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 $\kappa L\gg 1$.Comment: An error in the calculation of the overlap integral in Eq. (11) is corrected. Our main result given in Eq. (26) remains the same, except the numerical value of the constant c, which changes approximately by 10

Nucleon in a periodic magnetic field

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.Comment: The explicit factor $e$ is restored in the equations. The conclusions are unchange

The Dynamical Retardation Corrections to the Mass Spectrum of Heavy Quarkonia

A new version for the relativistic generalization of the wide class of static quark--antiquark confining potentials is suggested. The comparison of this approach with other ones, known in literature, is considered. With the use of Logunov--Tavkhelidze quasipotential approach the first--order retardation corrections to the heavy quarkonia mass spectrum are calculated. As expected, these corrections turn out to be small for all low--lying heavy meson states.Comment: 16 pages, LaTeX, no figure

Kaon-nucleon scattering lengths from kaonic deuterium experiments

The extraction of the S-wave kaon-nucleon scattering lengths a0 and a1 from a combined analysis of existing kaonic hydrogen and synthetic deuterium data has been carried out within the framework of a low-energy effective field theory. It turns out that with the present DEAR central values for the kaonic hydrogen ground-state energy and width, a solution for a0 and a1 exists only in a restricted domain of input values for the kaon-deuteron scattering length. Consequently, measuring this scattering length imposes stringent constraints on the theoretical description of the kaon-deuteron interactions at low energies.Comment: 9 pages, 2 postscript figure