Kaon mixing matrix elements from beyond-the-Standard-Model operators in staggered chiral perturbation theory

TL;DR

This paper calculates the next-to-leading order chiral perturbation theory expressions for B-parameters of beyond-the-Standard-Model K-Kbar mixing operators, aiding lattice QCD extrapolations for new physics searches.

Contribution

It provides the first detailed NLO chiral perturbation theory results for B-parameters of non-standard K-Kbar mixing operators in staggered fermion formulations.

Findings

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

SU(2) SChPT results are similar in simplicity to B_K, with some identical chiral logarithms.

Provides continuum partially quenched results not previously available.

Abstract

Models of new physics induce K-Kbar mixing operators having Dirac structures other than the "left-left" form of the Standard Model. We calculate the functional form of the corresponding B-parameters at next-to-leading order in both SU(3) and SU(2) staggered chiral perturbation theory (SChPT). Numerical results for these matrix elements are being generated using improved staggered fermions; our results can be used to extrapolate these matrix elements to the physical light and strange quark masses. The SU(3) SChPT results turn out to be much simpler than that for the Standard Model B_K operator, due to the absence of chiral suppression in the new operators. The SU(2) SChPT result is of similar simplicity to that for B_K. In fact, in the latter case, the chiral logarithms for two of the new B-parameters are identical to those for B_K, while those for the other two new B-parameters are of opposite sign. In addition to providing results for the 2+1 flavor theory in SU(3) SChPT and the 1+1+1 flavor theory in SU(2) SChPT, we present the corresponding continuum partially quenched results, as these are not available in the literature.