  Models of new physics induce K_0-K_0bar mixing through operators having Dirac
structures other than the "left-left" form of the Standard Model. To carry out
the chiral-continuum extrapolation of results from numerical simulations, one
needs to know the quark mass and lattice spacing dependence of the
corresponding B-parameters in the partially quenched theory at least at
next-to-leading order. For simulations using staggered fermions (such as that
we are doing with HYP-smeared valence fermions on the MILC asqtad lattices) one
must determine this dependence using staggered chiral perturbation theory
(SChPT). We have calculated the required dependence in both SU(3) and SU(2)
SChPT, working at next-to-leading order, and we give here an overview of the
methodology and results. The SU(3) SChPT result turns out to be much simpler
than that for the Standard Model B_K operator, due to the absence of chiral
suppression for the new operators. The SU(2) SChPT result turns out to be
closely related to that for B_K: the chiral logarithms are identical, up to an
operator-dependent sign. Our results are also useful for fermions with chiral
symmetry as they provide, in the continuum limit, the partially quenched
generalization of existing continuum results.
