  We estimate \Delta Gamma_d/\Gamma_d, including 1/m_b contributions and part
of the next-to-leading order QCD corrections, and find it to be around 0.3%. We
show the methods to measure \Delta Gamma_d/\Gamma_d by using at least two
different final states on the untagged B_d decay. The nonzero width difference
can also be used to identify new physics effects and to resolve a twofold
discrete ambiguity in the B_d-\bar{B}_d mixing phase. With the high statistics
and accurate time resolution of the upcoming LHC experiment, the measurement of
\Delta Gamma_d seems to be possible. This measurement would be important for an
accurate measurement of \sin2\phi_1 at the LHC. We also derive an upper bound
on the value of \Delta Gamma_d/\Gamma_d in the presence of new physics.
