This paper presents the measurement of the relative width difference ΔΓ$_{d}$ /Γ$_{d}$ of the $ {B}^0\hbox{-} {\overline{B}}^0 $ system using the data collected by the ATLAS experiment at the LHC in pp collisions at $ \sqrt{s}=7 $ TeV and $ \sqrt{s}=8 $ TeV and corresponding to an integrated luminosity of 25.2 fb$^{−1}$. The value of ΔΓ$_{d}$ /Γ$_{d}$ is obtained by comparing the decay-time distributions of B$^{0}$ → J/ψK$_{S}$ and B$^{0}$ → J/ψK$^{*0}$(892) decays. The result is ΔΓ$_{d}$ /Γ$_{d}$ = (−0.1±1.1 (stat.)± 0.9 (syst.)) × 10$^{−2}$. Currently, this is the most precise single measurement of ΔΓ$_{d}$ /Γ$_{d}$ . It agrees with the Standard Model prediction and the measurements by other
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