The Width Difference of $B_d$ Mesons

We estimate $\text{dg}\mathrm{/}{\mathrm{\Gamma }}_d$, including $1\mathrm{/}{m}_b$ contributions and part of the next-to-leading order QCD corrections. We find that adding the latter corrections decreases the value of $\text{dg}\mathrm{/}{\mathrm{\Gamma }}_d$ computed at the leading order by a factor of almost 2. We also show that under certain conditions an upper bound on the value of $\text{dg}\mathrm{/}{\mathrm{\Gamma }}_d$ in the presence of new physics can be derived. With the high statistics and accurate time resolution of the upcoming LHC experiment, the measurement of $\text{dg}$ seems to be possible. This measurement would be important for an accurate measurement of $\sin (2\beta )$ at the LHC. In addition, we point out the possibility that the measurement of the width difference leads to a clear signal for new physics.