time slice √ M ren$_{B}$ s /M ren$_{B}$ l am$_{l}$ = 0 . 01 APE: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 1 . 050(78) HYP: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 1 . 110(49) time slice am$_{l}$ = 0 . 02 APE: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 1 . 038(40) HYP: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 1 . 006(38) time slice √ M ren$_{B}$ s /M ren$_{B}$ l am$_{l}$ = 0 . 03 APE: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 0 . 992(27) HYP: √ M ren $_{B$_{s}$}$/M ren B$_{l}$ = 0 . 987(17) FIG. 4: Determination of √ M ren $_{B$_{s}$}$/M ren B$_{l}$ using the average of two time sources on the three sea quark ensembles. The blue (triangle) points denote the APE data, while the red (square) points denote the HYP-smeared data. The shaded (hatched) band corresponds to the plateau extracted from averaging the APE (HYP) data over four consecutive time slices. Errors shown are statistical only. quickly than SU (3) χ PT [34–37]. For the case of SU (3)-breaking ratios such as f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ , however, SU (3) HM χ PT has the advantage that the chiral extrapolation formulae manifestly preserve the fact that the ratios must be equal to one in the limit m$_{l}$ → m$_{s}$ . Within the framework of SU (2) HM χ PT, this fact must be introduced in a more ad hoc manner such as by matching the SU (2) HM χ PT expression at small quark masses onto an analytic form at large quark masses that becomes one when m$_{l}$ → m$_{s}$ . We therefore plan 25