Neutral kaon mixing beyond the standard model with $n_f\mathbf{=}2+1$ chiral fermions

We compute the hadronic matrix elements of the four-quark operators needed for the study of $K^0-{\overline{K}}^0$ mixing beyond the Standard Model (SM). We use $n_f=2+1$ flavors of domain-wall fermion that exhibit good chiral-flavor symmetry. The renormalization is performed nonperturbatively through the RI-MOM scheme and our results are converted perturbatively to $\overline{\mathrm{MS}}$. The computation is performed on a single lattice spacing $a\sim 0.086$ with a lightest unitary pion mass of 290 MeV. The various systematic errors, including the discretization effects, are estimated and discussed. Our results confirm a previous quenched study, where large ratios of non-SM to SM matrix elements were obtained.

Figure 1

Diagram contributing to $K^0-{\overline{K}}^0$ mixing in the SM.

Figure 2

Ratios of the bare three-point functions from which we extract $R_i^{\mathrm{BSM}}$. Results are shown for our lightest simulated unitary kaon.

Figure 3

Renormalization factors of the four-quark operators. At each value of the simulated momentum $p$, we run to the scale of 3 GeV and convert to $\overline{\mathrm{MS}}$. The remaining scale dependence can be imputed to the truncation of the perturbative expansion. We show only the $Z$ factors allowed by chiral symmetry.

Figure 4

Renormalized BSM ratios $R_i^{\mathrm{BSM}}$ in function of the bare valence quark mass. We show the three unitary light quarks for both the unitary strange (upward blue triangles) and the partially quenched strange (downward blue triangles), together with their extrapolations in the light sector (blue and red circles) and their interpolation to the physical kaon mass (black squares).