  We show that the pre-factors of all terms of the one-dimensional Hubbard
model correlation-function asymptotic expansions have an universal form, as the
corresponding critical exponents. In addition to calculating such pre-factors,
our study clarifies the relation of the low-energy Tomonaga-Luttinger liquid
behavior to the scattering mechanisms which control the spectral properties of
the model at all energy scales. Our results are of general nature for many
integrable interacting models and provide a broader understanding of the
unusual properties of quasi-1D nanostructures, organic conductors, and optical
lattices of fermionic atoms.
