Constraining the strange-quark vacuum condensate using SU(3) flavor symmetry-breaking

While the light quark vacuum condensate $langle ar{q} q angle$ is well-understood and known to good precision, the strange quark vacuum condensate $langle ar{s} s angle$ is not as well determined. Using the renormalization-group invariant strange quark mass ratio $r_m = m_s/m_q$, as well as properties of pions and kaons, we develop a simple constraint on a dimensionless PCAC deviation parameter $r_p$ and the quark condensate ratio $r_c = langle ar{s}s angle/langle ar{u}u angle$ to ensure self-consistency between the two parameters, and to tighten the bounds on $r_p$. We compare predictions in the literature against this constraint.