Calculation Of Hadronic Matrix Elements Relevant For Delta I=1/2 Rule And Epsilon-prime In Lattice QCD With Staggered Fermions

Preprint

22 September 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-lat/9909141

Abstract

This thesis presents the setup and results of numerical calculation of hadronic matrix elements of Delta S=1 weak operators, with the aim of studying the Delta I=1/2 rule and direct CP violation. Such study provides a useful comparison of the Standard Model predictions with experiment. We work within the framework of (partially quenched) Lattice QCD with the staggered (Kogut-Susskind) version of fermions. We have achieved a reasonable statistical accuracy in calculating all matrix elements in question. Based on these results, we find that the Delta I=1/2 channel in K to 2 Pi decays is enhanced compared to the Delta I=3/2 channel. This is consistent with experiment, although the exact amount of enhancement is subject to considerable systematic errors. I also discuss the difficulties encountered in attempting to calculate the direct CP violation parameter epsilon-prime and our approximate solution leading to a crude estimate. In a related study we nonperturbatively compute bilinear renormalization factors Z_S and Z_P, which are needed for our estimate of epsilon-prime and also allow to calculate the light quark masses. For the strange quark mass in NDR MS-bar scheme at 2 GeV in the quenched approximation we find: m_s = 102.9 +/- 5.1 MeV.

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