Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model

Abstract

We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to \pi \pi$ decay amplitude $A_0$ and ${\epsilon }^{\prime }$, the measure of direct CP-violation in $K\to \pi \pi$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi \pi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find $\mathrm{Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and $\mathrm{Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result $\mathrm{Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain $\mathrm{Re}({\epsilon }^{\prime }/\epsilon )=21.7(2.6)(6.2)(5.0)\times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2)=19.9(2.3)(4.4)$. The first agrees well with the experimental result of $\mathrm{Re}({\epsilon }^{\prime }/\epsilon )=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2)=22.45(6)$, demonstrates the Standard Model origin of this "$\Delta I=1/2$ rule" enhancement.

arXiv commentUpdated to published version. 95 pages, 12 figures

References in corpus (49)

• Weak Decays Beyond Leading Logarithms
• The four-loop beta-function in Quantum Chromodynamics
• ππscattering
• Domain wall QCD with physical quark masses
• Weak transition matrix elements from finite-volume correlation functions
• Kaon Decays in the Standard Model
• Practical all-to-all propagators for lattice QCD
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Twisted Boundary Conditions in Lattice Simulations
• A precision measurement of direct CP violation in the decay of neutral kaons into two pions
• Lattice QCD at the physical point: Simulation and analysis details
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Lattice QCD at the physical point: light quark masses
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Domain Wall QCD with Near-Physical Pions
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• Estimating epsilon'/epsilon. A Review
• I=2 $\pi \pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved Dynamical Quarks
• Improved anatomy of epsilon'/epsilon in the Standard Model
• Isospin violation in epsilon'
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Weak $K$--Amplitudes in the Chiral and $1/N_c$--Expansions
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Emerging understanding of the ΔI = 1/2 Rule from Lattice QCD
• Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• Step Scaling with off-shell renormalisation
• $K$ to $\pi \pi$ Decay amplitudes from Lattice QCD
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Exact Pseudofermion Action for Monte Carlo Simulation of Domain-Wall Fermion
• Opening the Rome-Southampton window for operator mixing matrices
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$
• Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $\Delta F=2$ four-quark operators
• Non-perturbative improvement of lattice QCD at large momenta
• $K\to \pi \pi$ and $K-\pi$ Matrix Elements of the Chromomagnetic Operators from Dual QCD
• $O(4)$-symmetric position-space renormalization of lattice operators
• Emerging lattice approach to the K-Unitarity Triangle
• Including electromagnetism in $K\to \pi \pi$ decay calculations
• Domain Wall Fermion QCD with the Exact One Flavor Algorithm
• Lattice simulations with G-parity Boundary Conditions
• Dissecting the $\Delta I=1/2$ rule at large $N_c$
• Towards a non-perturbative calculation of Weak Hamiltonian Wilson coefficients

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