Next-to-next-to-leading QCD corrections to the $$ {\mathrm{B}}^{+}-{\mathrm{B}}_{\mathrm{d}}^0 $$, D+ − D0, and $$ {\mathrm{D}}_{\mathrm{s}}^{+}-{\mathrm{D}}^0 $$ 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

with respect to the leading universal contribution to the total decay width. We calculate three-loop contributions of order

$$ {\alpha}_s^2/{m}_q^3 $$ α s 2 / m q 3

to the lifetime ratios

$$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ τ B + / τ B d 0

, τ ( D ⁺ )/ τ ( D ⁰ ), and

$$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ τ D s + / τ D 0

in the limit of exact isospin and V-spin symmetry, respectively. Furthermore, we present new

$$ {\alpha}_s/{m}_q^3 $$ α s / m q 3

corrections to the Cabibbo-suppressed terms in

$$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ τ B + / τ B d 0

. Combining our perturbative coefficients with hadronic matrix elements calculated from Heavy Quark Effective Theory sum rules, we find

$$ \tau \left({B}^{+}\right)/\tau \left({B}_d^0\right) $$ 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

$$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ τ D s + / τ D 0

= 1.289 ± 0.042. We find good agreement of our predictions with experimental data, which constitutes a successful probe of the calculations of hadronic matrix elements and permits estimates of the unknown

$$ 1/{m}_Q^4 $$ 1 / m Q 4

contributions as well as the V-spin breaking terms in

$$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ τ D s + / τ D 0

.