  The infinite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic
regime has two degenerate vacua and kink topological excitations (which are
also called spinons) interpolating between these vacua as elementary
excitations. Application of an arbitrary weak staggered longitudinal magnetic
field h induces a long-range attractive potential between two adjacent spinons
leading to their confinement into 'meson' bound states. Exploiting the
integrability of the XXZ model in the deconfined phase h = 0, we perform
perturbative calculations of the energy spectra of the two-spinon bound states
in the weak confinement regime at h \to +0, using the strength of the staggered
magnetic field h as a small parameter. Both transverse and longitudinal
dynamical structure factors of the local spin operators are calculated as well
in the two-spinon approximation in the weak confinement regime to the leading
order in h.
