We present an unquenched lattice calculation for the $B^0\mathrm{\text{−}}{\overline{B}}^0$ transition amplitude. The calculation, carried out at an inverse lattice spacing $1/a=2.22(4)\mathrm{G}\mathrm{e}\mathrm{V}$, incorporates two flavors of dynamical quarks described by the $O(a)$-improved Wilson fermion action and heavy quarks described by nonrelativistic QCD. Particular attention is paid to the uncertainty that arises from the chiral extrapolation, especially the effect of pion loops, for light quarks, which we find could be sizable for the leptonic decay constant, whereas it is small for the $B$ parameters. We obtain $f_{B_d}=191(10){(}_{-22}^{+12})\mathrm{M}\mathrm{e}\mathrm{V}$, $f_{B_s}/f_{B_d}=1.13(3){(}_{-2}^{+13})$, $B_{B_d}(m_b)=0.836(27){(}_{-62}^{+56})$, $B_{B_s}/B_{B_d}=1.017(16){(}_{-17}^{+56})$, and $\xi =1.14(3){(}_{-2}^{+13})$, where the first error is statistical, and the second is systematic, including uncertainties due to chiral extrapolation, finite lattice spacing, heavy quark expansion, and perturbative operator matching.

• Received 3 July 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.212001