Chiral extrapolation of matrix elements of BSM kaon operators

TL;DR

This paper calculates the quark mass and lattice spacing dependence of B-parameters for BSM kaon operators using staggered chiral perturbation theory at next-to-leading order, aiding chiral-continuum extrapolations.

Contribution

It provides the first NLO staggered chiral perturbation theory results for BSM kaon operators, including SU(3) and SU(2) analyses, essential for lattice QCD studies.

Findings

SU(3) SChPT results are simpler than for B_K due to lack of chiral suppression.

SU(2) SChPT results share identical chiral logarithms with B_K, differing only by sign.

Results facilitate continuum limit extrapolations for BSM kaon operators.

Abstract

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.