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arXiv · 1607.03262

Non-leptonic kaon decays at large $N_c$

A. Donini·P. Hernández·C. Pena·F. Romero-López
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Abstract

We study the scaling with the number of colours, $N_c$, of the weak amplitudes mediating kaon mixing and decay. We evaluate the amplitudes of the two relevant current-current operators on the lattice for $N_c=3-7$. We conclude that the subleading $1/N_c$ corrections in $\hat{B}_K$ are small, but those in the $K \rightarrow \pi\pi$ amplitudes are large and fully anti-correlated in the $I=0, 2$ isospin channels. We briefly comment on the implications for the $\Delta I=1/2$ rule.

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A. Donini, P. Hernández, C. Pena, F. Romero-López. 2016-07-12. Non-leptonic kaon decays at large $N_c$. https://doi.org/10.1103/physrevd.94.114511

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