Chiral extrapolation of matrix elements of BSM kaon operators

Abstract

Models of new physics induce K 0 − K 0 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 nextto-leading order. For simulations using staggered fermions (such as that we are doing with HYPsmeared 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.