  This paper is our progress report on the project "Ising spectroscopy",
devoted to systematic study of the mass spectrum of particles in 2D Ising Field
Theory in a magnetic field. Here we address the low-temperature regime, and
develop quantitative approach based on the idea (originally due to McCoy and
Wu) of particles being the "mesons", consisting predominantly of two quarks
confined by a long-range force. Systematic implementation of this idea leads to
a version of the Bethe-Salpeter equation, which yields infinite sequence of
meson masses. The Bethe-Salpeter spectrum becomes exact in the limit when the
magnetic field is small, and we develop the corresponding weak-coupling
expansions of the meson masses. The Bethe-Salpeter equation ignores the
contributions from the multi-quark components of the meson's states, but we
discuss how it can be improved by treating these components perturbatively, and
in particular by incorporating the radiative corrections to the quark mass and
the coupling parameter (the "string tension"). The approach fails to properly
treat the mesons above the stability threshold, where they are expected to
become resonance states, but it is shown to yield very good approximation for
the masses of all stable particles, at all real values of the IFT parameters in
the low-temperature regime. We briefly discuss how the Bethe-Salpeter
approximation can be used to address the case of complex parameters, which was
the main motivation of this work.
