A note on the power divergence in lattice calculations of $ΔI = 1/2$ $K\toππ$ amplitudes at $M_{K}=M_π$

Physics – High Energy Physics – High Energy Physics - Lattice

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5 pages, 2 figures

Scientific paper

10.1103/PhysRevD.69.057503

In this note, we clarify a point concerning the power divergence in lattice calculations of $\Delta I = 1/2$ $K\to\pi\pi$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at $M_{K}=M_{\pi}$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order Chiral Perturbation Theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.

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