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Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Weak Decays and Matrix Elements
Follow-up on non-leptonic Kaon decays at large $N_c$
F. Romero-Lopez,* A. Donini, P. Hernandez, C. Pena
*corresponding author
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Published on: 2019 May 29
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.
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