Follow-up on non-leptonic kaon decays at large $N_c$

TL;DR

This paper reports on lattice simulations of SU(Nc) gauge theories with Nf=4, exploring large Nc scaling of weak matrix elements to understand the ΔI=1/2 rule, with preliminary results indicating quark loop effects enhance certain decay amplitude ratios.

Contribution

It provides new dynamical simulation data for Nc=3-6, analyzing the impact of quark loops on kaon decay amplitudes and connecting these results with NLO Chiral Perturbation Theory predictions.

Findings

Quark loops significantly enhance the A0/A2 amplitude ratio.

Preliminary Nc=3 results show effects consistent with large Nc scaling.

Theoretical predictions relate K→π and K→ππ amplitudes in the light charm limit.

Abstract

We report on the status of our dynamical simulations of a $SU (N_c )$ gauge theory with $N_c=3-6$ and $N_f =4$ fundamental fermions. These ensembles can be used to study the Large $N_c$ scaling of weak matrix elements in the GIM limit $m_c=m_u$, that might shed some light on the origin of the $\Delta I=1/2$ rule. We present preliminary results for the $K \to \pi$ matrix elements in the $N_c=3$ dynamical simulations, where we observe a significant effect of the quark loops that goes in the direction of enhancing the ratio of $A_0/A_2$ amplitudes. Finally, we present the relevant NLO Chiral Perturbation Theory predictions for the relation between $K \to \pi $ and $K \to \pi \pi$ amplitudes in the light charm limit.