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$K \to \pi\pi$ Decays in a Finite Volume

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arxiv hep-lat/0104006 v2 pith:4PE5QUDG submitted 2001-04-11 hep-lat hep-ph

C.-J.D. Lin , G. Martinelli , C.T. Sachrajda , M. Testa This is my paper · ORCID
classification hep-lathep-ph
keywords decaysfinite-volumeinelasticdiscusslellouchmethodthresholduscher
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and L\"uscher, is extended to all elastic states under the inelastic threshold. We present a detailed comparison of our approach with that of Lellouch and L\"uscher and discuss the possible limitations of the method which could arise due to the presence of inelastic thresholds. We also examine a standard alternative method which can be used to extract the real part of the decay amplitude from correlators of the form $< 0 |T[\pi\pi{\cal H}_WK ]| 0 >$. We show that in this case there are finite-volume corrections which vanish as inverse powers of the volume, which cannot be removed by a multiplicative factor.

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Cited by 5 Pith papers

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