Finite-Volume Two-Pion Amplitudes in the I=0 Channel

Details Finite-Volume Two-Pion Amplitudes in the I=0 Channel Finite-Volume Two-Pion Amplitudes in the I=0 Channel

2002-11-29

arxiv.org/abs/hep-lat/0211043v3

Phys.Lett.B553:229-241,2003

Physics

High Energy Physics

High Energy Physics - Lattice

Version to appear on Phys. Lett. B, with only very minor and stylistic changes

Scientific paper

10.1016/S0370-2693(02)03228-8

We perform a calculation in one-loop chiral perturbation theory of the two-pion matrix elements and correlation functions of an I=0 scalar operator, in finite and infinite volumes for both full and quenched QCD. We show that major difficulties arise in the quenched theory due to the lack of unitarity. Similar problems are expected for quenched lattice calculations of $K \to \pi \pi$ amplitudes with $\Delta I=1/2$. Our results raise the important question of whether it is consistent to study $K\to\pi\pi$ amplitudes beyond leading order in chiral perturbation theory in quenched or partially quenched QCD.

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