time slice AP E a 3 M ren$_{B}$ q am$_{l}$ $^{= 0}$.02 a $^{3}$Mren B$_{s}$ a $^{3}$Mren B$_{l}$ time slice H Y P a 3 M ren$_{B}$ q am$_{l}$ = 0 . 02 a $^{3}$Mren B$_{s}$ a $^{3}$Mren B$_{l}$ FIG. 3: Determination of M ren B$_{s}$ and M ren B$_{l}$ on the am$_{l}$ = 0 . 02 ensemble. The left-hand plot shows the APE data, while the right-hand plot shows the HYP-smeared data. For each panel, the shaded band corresponds to the plateau extracted from averaging the data over four consecutive time slices. Errors shown are statistical only. TABLE VI: The renormalized SU (3)-breaking ratio √ M ren $_{B$_{s}$}$/M ren B$_{l}$ for both the APE and HYP- smeared data sets. Errors shown are statistical only. √ M ren $_{B$_{s}$}$/M ren B$_{l}$ am$_{l}$/am$_{h}$ APE HYP 0.01/0.04 1.050(78) 1.110(49) 0.02/0.04 1.038(40) 1.006(38) 0.03/0.04 0.992(27) 0.987(17) η ’s) are integrated out of the theory. Thus SU (2) χ PT does not require an expansion in the strange quark mass about the chiral limit, and the SU (2) χ PT expansion parameter in isospin-symmetric simulations is m$_{l}$/ Λ$_{χ}$, where m$_{l}$ is the light up-down sea quark mass and Λ$_{χ}$ is a typical hadronic scale. This improves the convergence of the chiral expansion relative to SU (3) χ PT, as long as m$_{l}$ is sufficiently light that corrections of O ( m$_{l}$/m$_{s}$ ) are small. Studies by the RBC and UKQCD Collaborations, the PACS-CS Collaboration, and the MILC Collaboration confirm this picture and show that, for light pseudoscalar meson masses and decay constants, SU (2) χ PT within its applicable region converges more 24