83 research outputs found
Spectrum of three-body bound states in a finite volume
The spectrum of a bound state of three identical particles with a mass 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 , where
is the bound-state momentum, is the box size, denotes the
three-body analog of the asymptotic normalization coefficient of the bound
state wave function and is a numerical constant. The formula is valid for
.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 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
Nucleon in a periodic magnetic field: Finite-volume aspects
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, Phys. Rev. D 95, 031502 (2017)
(arXiv:1610.05545). 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.Comment: 42 pages, 5 figures; version accepted for publication in Physical
Review
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