Kaon $B$-parameters for Generic $\Delta S=2$ Four-Quark Operators in Quenched Domain Wall QCD

TL;DR

This paper calculates B-parameters for ΔS=2 four-quark operators in quenched domain wall QCD, covering both SM and beyond, using one-loop renormalization and numerical simulations with different gauge actions.

Contribution

It provides a comprehensive calculation of all relevant B-parameters for neutral kaon mixing in quenched domain wall QCD, including non-SM operators and comparison with other quark actions.

Findings

Non-SM B-parameters are comparable to SM ones.

Results are consistent across different gauge actions.

Numerical values are obtained at a lattice spacing of approximately 2 GeV.

Abstract

We present a study of $B$-parameters for generic $\Delta S=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3\times 32\times 16$ and $24^3\times 32\times 16$ at the lattice spacing $1/a\approx 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, which are compared with the previous results obtained with the overlap and the clover quark actions.