  We calculate perturbative renormalization constants for the \Delta B=2
four-quark operators in lattice NRQCD.
  Continuum operators \bar{b}\gamma_{\mu}(1-\gamma_5)q~
  \bar{b}\gamma_{\mu}(1-\gamma_5)q and
\bar{b}(1-\gamma_5)q~\bar{b}(1-\gamma_5)q, which are necessary in evaluating
the mass and width differences in $B^0_{d(s)}-\bar{B}^0_{d(s)}$ systems, are
matched at one-loop with corresponding lattice operators constructed from the
NRQCD heavy quarks and the ${\cal O}(a)$-improved light quarks. Using these
perturbative coefficients, we also reanalyse our previous simulation results
for the matrix elements of the above operators. Our new results are free from
the systematic error of ${\cal O}(\alpha_s/(aM_b))$ in contrast to the previous
ones with matching coefficients evaluated in the static limit.
