Energy separation of single-particle and continuum states in a S=1/2 weakly-coupled chains antiferromagnet

Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional S=1/2 antiferromagnet BaCu_2Si_2O_7, where the saturation value for the N\'eel order parameter is $m_0=0.12 \mu_{\rm B}$ per spin. At low energies the spectrum is totally dominated by resolution-limited spin wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly-interacting quantum half-integer spin chains.