  Exact formulas for the singularities of the dynamical structure factor,
S^{zz}(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and
magnetic field in the critical regime are derived, expressing the exponents in
terms of the phase shifts which are known exactly from the Bethe ansatz
solution. We also study the long time asymptotics of the self-correlation
function <0|S_j^z(t)S_j^z(0)|0>. Utilizing these results to supplement very
accurate time-dependent Density Matrix Renormalization Group (DMRG) for short
to moderate times, we calculate S^{zz}(q,omega) to very high precision.
