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26 April 2024 |
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Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case | T. Blum
; P. Chen
; N. Christ
; C. Cristian
; C. Dawson
; G. Fleming
; R. Mawhinney
; S. Ohta
; G. Siegert
; A. Soni
; P. Vranas
; M. Wingate
; L. Wu
; Y. Zhestkov
; RBC Collaboration
; | Date: |
14 Oct 2001 | Journal: | Phys.Rev. D68 (2003) 114506 | Subject: | hep-lat hep-ph | Abstract: | We report the results of a calculation of the K --> pi pi matrix elements relevant for the $DIhalf$ rule and $epe$ in quenched lattice QCD using domain wall fermions at a fixed lattice spacing $a^{-1} sim 2$ GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order, we calculate the lattice K --> pi and K --> |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K --> pi pi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the ratio of isospin amplitudes |A_0|/|A_2| we find a value of $25.3 pm 1.8$ (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10-20% below the experimental values. For $epe$, using known central values for standard model parameters, we calculate $(-4.0 pm 2.3) imes 10^{-4}$ (statistical error only) compared to the current experimental average of $(17.2 pm 1.8) imes 10^{-4}$. Because we find a large cancellation between the I = 0 and I = 2 contributions to $epe$, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, B_K and find $B_{K,ar{MS}}(2 {
m GeV}) = 0.532(11)$. Although currently unable to give a reliable systematic error, we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities. | Source: | arXiv, hep-lat/0110075 | Services: | Forum | Review | PDF | Favorites |
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