  We study the long-distance asymptotic behavior of various correlation
functions for the one-dimensional (1D) attractive Hubbard model in a partially
polarized phase through the Bethe ansatz and conformal field theory approaches.
We particularly find the oscillating behavior of these correlation functions
with spatial power-law decay, of which the pair (spin) correlation function
oscillates with a frequency $\Delta k_F$ ($2\Delta k_F$). Here $\Delta
k_F=\pi(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of
spin-up and spin-down particles. Consequently, the pair correlation function in
momentum space has peaks at the mismatch $k=\Delta k_F$, which has been
observed in recent numerical work on this model. These singular peaks in
momentum space together with the spatial oscillation suggest an analog of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The
parameter $\beta$ representing the lattice effect becomes prominent in critical
exponents which determine the power-law decay of all correlation functions. We
point out that the backscattering of unpaired fermions and bound pairs within
their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.
