CP-violating phases; these would manifest themselves as apparent inconsistencies among different measurements of quantities which should be identical within the standard CKM picture. Thus a precise determination of the ratio ξ will help to constrain physics beyond the Standard Model. Furthermore, possible indications of new physics in B 0 $_{d}$-mixing at the ∼ 2.7- σ level [13] make the lattice calculation of B -meson mixing parameters timely. Recently, the HPQCD Collaboration published the first unquenched determination of ξ with an accuracy of 2.6% [14], and the Fermilab Lattice and MILC Collaborations expect to have a result with similar errors soon [15]. The HPQCD calculation employs a nonrelativistic QCD (NRQCD) action for the heavy b -quark [16], while the Fermilab/MILC calculation uses the relativistic “Fermilab” action for the b -quark [17]. Both of these computations, however, rely on the same “2+1” flavor asqtad-improved staggered ensembles generated by the MILC Collaboration [18], which include the effects of two degenerate light quarks and one heavier close-to-strange quark in the sea sector. For such a phenomenologically important quantity as ξ , it is valuable to have an inde- pendent crosscheck using different formulations of the lattice action for both the light and heavy quarks. Our calculation employs the 2+1 flavor dynamical domain-wall ensembles generated by the RBC and UKQCD Collaborations with a lattice spacing of a ≈ 0 . 11 fm ( a − 1 = 1 . 729 GeV) [19]. The use of domain-wall fermions [20–22] has the advantage over other light-quark formulations that the chiral perturbation theory expressions needed to ex- trapolate domain-wall lattice results to the physical u - and d -quark masses are closer to the continuum forms and have fewer parameters than in the Wilson or staggered cases [23, 24]. We compute the b -quarks in the static limit ( m$_{b}$ → ∞ ), which leads to correlation func- tions that are noisier than those with propagating b -quarks such as in the Fermilab [17] or NRQCD actions [16]. We therefore use the static-quark formulation of Refs. [25, 26] with either APE [27, 28] or HYP [29] smearing of the static-quark gauge links to increase the signal-to-noise ratio and reduce scaling violations (for some quantities) as compared to the Eichten-Hill action [30]. Furthermore, the approximate chiral symmetry of the domain- wall action combined with the spin symmetry of the static action simplifies the lattice-to- continuum operator matching as compared to the Wilson case by reducing the number of additional lattice operators which appear [31, 32]. The results of this work extend an earlier study with two flavors of dynamical quarks and heavier light-quark masses in Ref. [33]. The primary purpose of this paper is to demonstrate the viability of our method for 4