  The low-energy properties of one-dimensional quantum liquids are commonly
described in terms of the Tomonaga-Luttinger liquid theory, in which the
elementary excitations are free bosons. To this approximation the theory can be
alternatively recast in terms of free fermions. In both approaches, small
perturbations give rise to finite lifetimes of excitations. We evaluate the
decay rate of fermionic excitations and show that it scales as the eighth power
of energy, in contrast to the much faster decay of bosonic excitations. Our
results can be tested experimentally by measuring the broadening of power-law
features in the density structure factor or spectral functions.
