# configs. am$_{l}$/am$_{h}$ am$_{x}$ APE HYP 0.01/0.04 0.01, 0.0359 298 300 0.02/0.04 0.02, 0.0359 298 300 0.03/0.04 0.03, 0.0359 298 300 TABLE IV: Parameters used in our simulations. The columns from left to right are the light and (approximately) strange sea quark masses, the light and strange valence quark masses, and the number of configurations analyzed for both of our setups using APE or HYP link smearing in the static quark gauge links. strange quark mass am$_{s}$ = 0 . 0359 [19]. We also use two different link smearings (APE and HYP) to improve the static heavy quark action in order to help estimate discretization effects. Table IV presents the parameters chosen for our matrix element computations. In the first subsection we calculate the ratio of B -meson decay constants and in the second we calculate the ratio of Δ B = 2 mixing matrix elements. In QCD the decay constant f$_{B}$$_{q}$ for the B$_{q}$ -meson is defined by the vacuum-to-meson matrix element Because the decay constant f$_{B}$$_{q}$ behaves as 1 / √ m$_{B}$$_{q}$ in the limit of large B$_{q}$ -meson mass, we calculate the combined decay amplitude where m$_{B}$$_{q}$ is the physical mass of the B$_{q}$ -meson. We determine the quantity Φ$_{B}$$_{q}$ by com- puting two-point correlation functions of the static-light axial current A ( ± )stat µ = h ( ± $^{)}$γ$_{µ}$ γ$_{5}$q . 1 1 For the case of static b -quarks, we can relate the B -meson interpolating operator h ( − $^{)}$γ$_{5}$ q to the axial current operator in the temporal direction using the relation h ( ± $^{)}$( x ) γ$_{0}$ = ± h ( ± $^{)}$( x ), and thereby express all correlation functions entirely in terms of the axial current. 17 Φ$_{B}$$_{q}$ = f$_{B}$$_{q}$ √ m$_{B}$$_{q}$, (58) 〈 0 | bγ$_{µ}$γ$_{5}$q | B$_{q}$ ( p ) 〉 = if$_{B}$$_{q}$p$_{µ}$. (57) A. Calculation of the ratio of B -meson decay constants