The spin fluctuations parallel to the external magnetic field in the ground
state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are
dominated by a two-parameter set of collective excitations. In a cyclic chain
of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z
spinons, is reconfigured as the physical vacuum for a different species of
quasi-particles, identifiable in the framework of the coordinate Bethe ansatz
by characteristic configurations of Bethe quantum numbers. The dynamically
dominant excitations are found to be scattering states of two such
quasi-particles. For N -> \infty, these collective excitations form a continuum
in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in
the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from
the Bethe wave functions for finite N. The resulting lineshape predictions for
N -> \infty complement the exact results previously derived via algebraic
analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field
limit. They are directly relevant for the interpretation of neutron scattering
data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page
