Kaon BSM B-parameters using improved staggered fermions from $N_f=2+1$ unquenched QCD

TL;DR

This paper computes BSM B-parameters related to $ riangle S=2$ operators using improved staggered fermions on unquenched lattice QCD, providing results that help constrain new physics models beyond the Standard Model.

Contribution

The study presents new lattice QCD calculations of BSM B-parameters with improved control over systematic uncertainties, including additional ensembles and refined extrapolations.

Findings

Agreement with some previous results for B2 and B3 parameters.

Discrepancies with RI-MOM scheme results for B4 and B5, but agreement with RI-SMOM scheme.

Enhanced precision due to additional lattice ensembles and improved extrapolations.

Abstract

We present results for the matrix elements of the additional $\Delta S=2$ operators that appear in models of physics beyond the Standard Model (BSM), expressed in terms of four BSM $B$-parameters. Combined with experimental results for $\Delta M_K$ and $\epsilon_K$, these constrain the parameters of BSM models. We use improved staggered fermions, with valence HYP-smeared quarks and $N_f=2+1$ flavors of "asqtad" sea quarks. The configurations have been generated by the MILC collaboration. The matching between lattice and continuum four-fermion operators and bilinears is done perturbatively at one-loop order. We use three lattice spacings for the continuum extrapolation: $a\approx 0.09$, $0.06$ and $0.045\;$fm. Valence light-quark masses range down to $\approx m_s^{\rm phys}/13$ while the light sea-quark masses range down to $\approx m_s^{\rm phys}/20$. Compared to our previous published work, we have added four additional lattice ensembles, leading to better controlled extrapolations in the lattice spacing and sea-quark masses. We report final results for two renormalization scales, $\mu=2\;\text{GeV}$ and $3\;\text{GeV}$, and compare them to those obtained by other collaborations. Agreement is found for two of the four BSM $B$-parameters ($B_2$ and $B_3^\text{SUSY}$). The other two ($B_4$ and $B_5$) differ significantly from those obtained using RI-MOM renormalization as an intermediate scheme, but are in agreement with recent preliminary results obtained by the RBC-UKQCD collaboration using RI-SMOM intermediate schemes.