In practice, we use Coulomb gauge-fixed wall sources for the b -quark to calculate the local-wall ( LW ) and wall-wall ( W W ) correlation functions with the local ( L ) and wall-source ( W ) axial currents given by From the ratio of C LW to C WW we obtain the combined decay amplitude where we determine the unphysical B -meson rest mass m ∗ B$_{q}$ via A derivation of Eq. (63) is presented in Appendix C. Finally we compute the renormalized decay amplitude using the perturbative matching factors given in Tables II and III. The contribution propor- tional to c MF A improves the heavy-light axial current operator through O ( α$_{s}$pa ), where the sinh arises from the symmetric derivative in the O ( pa ) operator. The overall multiplicative factor Z$_{Φ}$ is needed to obtain the combined decay amplitude in the continuum. The computation of the statistical errors throughout this paper follows the prescrip- tion for numerically computing the autocorrelation function as proposed in reference [61]. The autocorrelation function quantifies the degree of correlation between two measurements made at different trajectories, and depends upon the observable of interest. By summing the autocorrelation function over the separation between measurements, one obtains the integrated autocorrelation time. We obtain a better estimate of the true statistical error by inflating the variance of the measured Monte Carlo data using the integrated autocorrela- tion time. In many instances we must compute the errors in a quantity which itself depends 18 Φ ren B$_{q}$ = Z$_{Φ}$ [ 1 + c MF A sinh ( am ∗ B$_{q}$ ) ] Φ lat $_{B$_{q}$}$, (65) am ∗ B$_{q}$ = lim t ≫ $_{t$_{0}$}$log ( C $^{LW}$( t, t$_{0}$ ) C $^{LW}$( t + a, t$_{0}$ ) ) . (64) Φ lat B$_{q}$ = lim t ≫ t$_{0}$ √ 2 L 3 |C $^{LW}$( t, t$_{0}$ ) | √ C $^{WW}$( t, t$_{0}$ )e − m ∗ B $_{q}$( t − t$_{0}$ $_{)}$, (63) A W 0 ( t ) = a 6 ∑ ⃗y ∈ V ∑ ⃗z ∈ V ( h $^{(+)}$( ⃗ y, t ) γ$_{0}$γ$_{5}$q ( ⃗ z, t ) + h ( − $^{)}$( ⃗ y, t ) γ$_{0}$γ$_{5}$q ( ⃗ z, t ) ) . (62) A L $_{0}$( ⃗ x, t ) = h $^{(+)}$( ⃗ x, t ) γ$_{0}$γ$_{5}$q ( ⃗ x, t ) + h ( − $^{)}$( ⃗ x, t ) γ$_{0}$γ$_{5}$q ( ⃗ x, t ) , (61) C $^{LW}$( t, t$_{0}$ ) = a 3 ∑ ⃗x ∈ $_{V}$〈 0 | A L $_{0}$( ⃗ x, t ) A W 0 ( t$_{0}$ ) $^{†}$| 0 〉 , (59) C $^{WW}$( t, t$_{0}$ ) = 〈 0 | A W 0 ( t ) A W 0 ( t$_{0}$ ) $^{†}$| 0 〉 , (60)