2001/10/31 by Tom Blum, T. Blum, P. Chen +20 · 121 citations
Physics and Astronomy · #Chiral perturbation theory #Fermion #High-Energy Particle Collisions Research #Isospin #Lattice (music) #Lattice QCD #Lattice field theory #Mathematical physics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Renormalization #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.68.114506
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 68(11) (American Physical Society) · 158 pages, 51 tables, 41 figures. No numerical data or results changed in this revision, except for an improved analysis of B_K. Many improvements and modifications to the text and explanations. Table XLVII changed to include improved values for B_K. Submitted to Physical Review D
arxiv created 2002/07/19 · openalex publication_date 2003/12/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We report the results of a calculation of the \stackrel\ensuremath→K\ensuremathπ\ensuremathπ matrix elements relevant for the \ensuremathΔI=1/2 rule and \ensuremathε^\ensuremath'/\ensuremathε in quenched lattice QCD using domain wall fermions at a fixed lattice spacing a^\ensuremath-1\ensuremath∼2GeV. 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 \stackrel\ensuremath→K\ensuremathπ and \stackrel\ensuremath→K|0〉 matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield \stackrel\ensuremath→K\ensuremathπ\ensuremathπ matrix elements, which we then normalize to continuum values through a nonperturbative renormalization technique. For the ratio of isospin amplitudes |A0|/|A2| we find a value of 25.3\ifmmode±\else\textpm\fi1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10%--20% below the experimental values. For \ensuremathε^\ensuremath'/\ensuremathε, using known central values for standard model parameters, we calculate (\ensuremath-4.0\ifmmode±\else\textpm\fi2.3)\ifmmode×\else\texttimes\fi10^\ensuremath-4 (statistical error only) compared to the current experimental average of (17.2\ifmmode±\else\textpm\fi1.8)\ifmmode×\else\texttimes\fi10^\ensuremath-4. Because we find a large cancellation between the I=0 and I=2 contributions to \ensuremathε^\ensuremath'/\ensuremathε, 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 also calculate the kaon B parameter BK and find B_K,MS(2GeV)=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.