  The Heisenberg-Ising spin ladder is one of the few short-range models showing
confinement of elementary excitations without the need of an external field,
neither transverse nor longitudinal. This feature makes the model suitable for
an experimental realization with ultracold atoms. In this paper, we combine
analytic and numerical techniques to precisely characterize its spectrum in the
regime of Hamiltonian parameters showing confinement. We find two kinds of
particles, which we dub intrachain and interchain mesons, that correspond to
bound states of kinks within the same chain or between different ones,
respectively. The ultimate physical reasons leading to the existence of two
families of mesons is a residual double degeneracy of the ground state: the two
types of mesons interpolate either between the same vacuum (intrachain) or
between the two different ones (interchain). While the intrachain mesons can
also be qualitatively assessed through an effective mean field description and
were previously known, the interchain ones are new and they represent general
features of spin ladders with confinement.
