a ( m$_{l}$ + m$_{res}$ ) √ M B s / M B l · ξ APE: √ m$_{B}$$_{s}$/m$_{B}$$_{d}$ · ξ = 1 . 142(72) , χ $^{2}$/ dof = 0 . 3 HYP: √ m$_{B}$$_{s}$/m$_{B}$$_{d}$ · ξ = 1 . 144(54) , χ $^{2}$/ dof = 2 . 0 FIG. 6: Chiral extrapolation of √ M$_{B}$$_{s}$/M$_{B}$$_{l}$ = √ m$_{B}$$_{s}$/m$_{B}$$_{l}$ ( f$_{B}$$_{s}$ √ B$_{B}$$_{s}$/f$_{B}$$_{l}$ √ B$_{B}$$_{l}$ ) . The blue (tri- angle) points denote the APE data, while the red (square) points denote the HYP-smeared data. The color of the shaded (hatched) error band corresponds to those of the APE (HYP) data points. The dashed vertical line denotes the physical average u - d quark mass and the black dot denotes the physical strange quark mass, at which the SU (3)-breaking ratio must be one. The SU (2) HM χ PT coefficients obtained from the fit are R$_{M}$ = 1 . 18(8) and D$_{l}$ = 2 . 6(1 . 1) in the case of APE smearing and R$_{M}$ = 1 . 18(6) and D$_{l}$ = 2 . 6(8) in the case of HYP smearing. Errors shown are statistical only. link smearing APE HYP Φ$_{B}$$_{s}$ / Φ$_{B}$$_{d}$ 1.165(88) 1.153(47) √ m$_{B}$$_{s}$/m$_{B}$$_{d}$ · ξ 1.142(72) 1.144(54) In this section we estimate the systematic uncertainties in the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ . For clarity, we present each source of error in a separate subsection. The TABLE VII: Results for Φ$_{B}$$_{s}$ / Φ$_{B}$$_{d}$ and √ m$_{B}$$_{s}$/m$_{B}$$_{d}$ · ξ at the physical point. Only statistical errors are shown. VI. ESTIMATION OF SYSTEMATIC ERRORS 30