  Using heavy meson chiral perturbation theory, we consider the light
quark-mass and spatial volume dependence of the matrix elements of \Delta B=2
and \Delta C=2 four-quark operators relevant for
B^{0}_{(s)}{-}\bar{B}^{0}_{(s)} and D^{0}{-}\bar{D}^{0} mixing, and the B_{s}
meson width difference. Our results for these matrix elements are obtained in
the N_{f}=2+1 partially quenched theory, which becomes full QCD in the limit
where sea and valence quark masses become equal. They can be used in
extrapolation of lattice calculations of these matrix elements to the physical
light quark masses and to infinite volume. An important conclusion of this
paper is that the chiral extrapolations for matrix elements of heavy-light
meson mixing beyond the Standard Model, and those relevant for the B_s width
difference are more complicated than that for the Standard Model mixing matrix
elements.
