  We estimate the decay width difference $\Delta Gamma_d / \Gamma_d$ in the
$B_d$ system including $1/m_b$ contributions and next-to-leading order QCD
corrections, and find it to be around 0.3%. We explicitly show that the time
measurements of an untagged $B_d$ decaying to a single final state
isotropically can only be sensitive to quadratic terms in $\Delta Gamma_d /
\Gamma_d$, and hence the use of at least two different final states is desired.
We discuss such pairs of candidate decay channels for the final states and
explore the feasibility of a $\Delta Gamma_d / \Gamma_d$ measurement through
them. The measurement of this width difference is essential for an accurate
measurement of $\sin(2\beta)$ at the LHC. The nonzero width difference may also
be used to identify new physics effects and to resolve a twofold discrete
ambiguity in the $B_d$-$\bar{B}_d$ mixing phase. We also derive an upper bound
on the value of $\Delta Gamma_d / \Gamma_d$ in the presence of new physics, and
point out some differences in the phenomenology of width differences in the
$B_s$ and $B_d$ systems.
