Dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds of the leading-order dominant excitations. We derive the exact momentum and spin-density dependences of the exponents controlling the singularities for both the longitudinal and transversal dynamical structure factors for the whole momentum range, in the thermodynamic limit. In that limit we argue that the higher-order excitations change neither the exponents nor the sharpness of the singularities. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal.