Kaon leptonic and semileptonic decays with $N_f=2+1+1$ HISQ fermions

Abstract

Precision tests of the Standard Model (SM) currently show a deficit in first-row Cabibbo-Kobayashi-Maskawa (CKM) unitarity. In this talk, we discuss progress towards a correlated analysis of the lattice-QCD inputs needed to test this relation with kaon data using highly improved staggered quarks (HISQ) on the MILC $N_{f}=2+1+1$ configurations. We present the status of a new analysis of light-meson decay constant data where chiral-continuum fits are guided by staggered chiral perturbation theory (SChPT). The goal of SChPT is twofold: it allows us to use data not only at physical pion mass but also at unphysical masses. Moreover, it provides values of ChPT low energy constants (LECs) as well as their correlations. We also present a reanalysis of our previous kaon semileptonic form factor calculation, aiming to estimate correlations between the form factor and light-meson decay constants. We discuss the new methodology, new data included, and present some preliminary results.

Figures (5)

• Figure 1: Sketch of the three-point correlation function for the scalar current $\braket{\pi|S|K}$. We use partially twisted boundary conditions to give external momentum to the pion. The $\theta$ parameter is tuned such that $q^{2}=0$.
• Figure 2: Stability of fit results for the kaon mass $M_{K}$, pion mass $M_{\pi}$ and the energy of the moving pion $E_{\pi}$ as well as the form factor $f_{+}(q^{2}=0)$ under the change of $t_{\rm min}$ for the physical quark mass $a\approx0.06$ fm ensemble. Results for different number of exponentials are shown in different colors. Blue bands correspond to our central fit. Since the data are preliminary, the vertical scale has been omitted.
• Figure 3: Top row: Comparison between our previous results in Ref Bazavov_2019 (circles), our reanalysis of the same data (squares) and the analysis of the two new physical quark mass ensembles (triangles). Bottom row: Form factor as a function of the light quark mass normalized to the physical strange quark mass. Only data points that enter the chiral-continuum fit are shown. Data points have approximately one of the three $m_l/m_s$ values shown by the vertical dashed lines, but have been displaced to the right for clarity. The blue band represents the continuum extrapolation with only statistical plus LECs errors. We show two different results for the physical point, the blue star represents the continuum extrapolation taking the LECs as fixed parameters while the blue diamond represents the result when LECs are used as fit parameters as explained in Sec \ref{['sec:corrLEC']}. Since the analysis is preliminary, the vertical scale has been omitted. See the text for further details.
• Figure 4: Left: Correlation matrix from the central fit. Right: correlation matrix reconstructed from the resampling analysis posteriors. For clarity, only parameters that are present in both the semileptonic form factor and the decay constants analyses are shown.
• Figure 5: Preliminary correlation between the semileptonic form factor $f_{+}(q^{2}=0)$ and the LO and NLO ChPT LECs as well as the hairpin parameters $\delta_{A,V}$.