three-point correlation functions where A ( ± ) I 0 ( t ) is either the box-source axial current A ( ± ) B 0 ( t ) or the wall-source axial current A ( ± ) W 0 ( t ). The operator O$_{i}$ can be either the sum of the squared vector plus squared axial vector current or the squared scalar plus squared pseudoscalar current, respectively, 2 Although the SS + P P operator does not contribute to B$_{q}$ − B$_{q}$ mixing in continuum QCD, its counterpart in HQET is introduced through the QCD → HQET matching as shown in Eq. (27). Because of the different spatial wavefunctions used for the APE- and HYP-smeared data, we extract the B$_{q}$ − B$_{q}$ matrix element in different ways for the two data sets. With the APE-smeared box source data, we can compute the matrix element directly from the ratio of correlators [57] 2 We neglect the odd-parity parts of O lat L and O lat S , Eqs. (44) and (45), when computing the lattice three- point correlation functions because only the parity-conserving components contribute to the desired matrix element. 22 M$_{O}$$_{i}$ = lim t$_{f}$ ≫ t ≫ $_{t$_{0}$}$2 C B $_{O$_{i}$}$( t$_{f}$, t, t$_{0}$ ) e m ∗ B $_{q}$( t$_{f}$ − t$_{0}$ ) / 2 √ C $^{BB}$( t, t$_{f}$ ) C $^{BB}$( t, t$_{0}$ ) . (72) O lat SS + PP = 2 h $^{(+)}$q h ( − $^{)}$q ) + 2 ( h $^{(+)}$γ$_{5}$ q ) ( h ( − $^{)}$γ$_{5}$ q ) . (71) O lat V V + AA = 2 ( h $^{(+)}$γ $^{µ}$q ) ( h ( − $^{)}$γ$_{µ}$ q ) + 2 ( h $^{(+)}$γ $^{µ}$γ$_{5}$ q ) ( h ( − $^{)}$γ $^{µ}$γ$_{5}$ q ) , (70) ( − ( − C I $_{O$_{i}$}$( t$_{f}$, t, t$_{0}$ ) = a 3 ∑ ⃗x ∈ $_{V}$〈 0 | A (+) I 0 ( t$_{f}$ ) $^{†}$O lat i ( ⃗ x, t ) A ( − ) I 0 ( t$_{0}$ ) $^{†}$| 0 〉 , (69) Φ ren $_{B$_{s}$}$/ Φ ren B$_{l}$ am$_{l}$/am$_{h}$ APE HYP 0.01/0.04 1.07(8) 1.10(4) 0.02/0.04 1.06(5) 1.02(3) 0.03/0.04 0.97(4) 0.99(2) TABLE V: The renormalized decay amplitude ratio Φ ren $_{B$_{s}$}$/ Φ ren B$_{l}$ for both the APE- and HYP-smeared data sets. Errors shown are statistical only.