Fate of 1D Spin-Charge Separation Away from Fermi Points

We consider the dynamic response functions of interacting one dimensional spin-$1/2$ fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum