Next-to-next-to-leading QCD corrections to the B⁺-Bd⁰, D+ − D0, and Dₛ⁺-D⁰ lifetime ratios

A bstract The total decay widths of heavy mesons can be systematically calculated in terms of an expansion in the two parameters 1/ m Q and α s ( m Q ), where Q = c , b denotes the heavy quark. The dominant contributions to meson lifetime splittings stem from terms which are suppressed by 1/mQ³ 1 / m Q 3 with respect to the leading universal contribution to the total decay width. We calculate three-loop contributions of order αₛ²/mq³ α s 2 / m q 3 to the lifetime ratios τ (B⁺)/τ (Bd⁰) τ B + / τ B d 0 , τ ( D + )/ τ ( D 0 ), and τ (Dₛ⁺)/τ (D⁰) τ D s + / τ D 0 in the limit of exact isospin and V-spin symmetry, respectively. Furthermore, we present new αₛ/mq³ α s / m q 3 corrections to the Cabibbo-suppressed terms in τ (B⁺)/τ (Bd⁰) τ B + / τ B d 0 . Combining our perturbative coefficients with hadronic matrix elements calculated from Heavy Quark Effective Theory sum rules, we find τ (B⁺)/τ (Bd⁰) τ B + / τ B d 0 = 1.072 ± 0.024. Using hadronic matrix elements from a recent lattice QCD calculation we find τ ( D + )/ τ ( D 0 ) = 2.344 ± 0.170 and τ (Dₛ⁺)/τ (D⁰) τ D s +