  We study the transverse dynamical susceptibility of an antiferromagnetic
spin$-1/2$ chain in presence of a longitudinal Zeeman field. In the low
magnetization regime in the gapless phase, we show that the marginally
irrelevant backscattering interaction between the spinons creates a non-zero
gap between two branches of excitations at small momentum. We further
demonstrate how this gap varies upon introducing a second neighbor
antiferromagnetic interaction, vanishing in the limit of a non-interacting
"spinon gas". In the high magnetization regime, as the Zeeman field approaches
the saturation value, we uncover the appearance of two-magnon bound states in
the transverse susceptibility. This bound state feature generalizes the one
arising from string states in the Bethe ansatz solution of the integrable case.
Our results are based on numerically accurate, unbiased matrix-product-state
techniques as well as analytic approximations.
