An exploratory lattice study of DI=3/2 K -> pi pi decays at next-to-leading order in the chiral expansion

Abstract

We present the first direct evaluation of DI = 3/2 K -> pi pi matrix elements with the aim of determining all the low-energy constants at NLO in the chiral expansion. Our numerical investigation demonstrates that it is indeed possible to determine the K -> pi pi matrix elements directly for the masses and momenta used in the simulation with good precision. In this range however, we find that the matrix elements do not satisfy the predictions of NLO chiral perturbation theory. For the chiral extrapolation we therefore use a hybrid procedure which combines the observed polynomial behaviour in masses and momenta of our lattice results, with NLO chiral perturbation theory at lower masses. In this way we find stable results for the quenched matrix elements of the electroweak penguin operators (<pi pi (I=2)|O_8|K^0>= (0.68 +- 0.09) GeV^3 and <pi pi (I=2)|O_7|K^0>= (0.12 +- 0.02) GeV^3 in the NDR-MSbar scheme at the scale 2 GeV), but not for the matrix elements of O_4 (for which there are too many Low-Energy Constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties.

arXiv comment44 pages, 10 figures. Accepted for publication on Nuclear Physics B

References in corpus (51)

• On the Viability of Lattice Perturbation Theory
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Weak transition matrix elements from finite-volume correlation functions
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• A precision measurement of direct CP violation in the decay of neutral kaons into two pions
• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• $K\to \pi \pi$ Decays in a Finite Volume
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• An Upgraded Analysis of $\epsilon \prime /\epsilon$ at the Next-to-Leading Order
• I=2 $\pi \pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved Dynamical Quarks
• The Standard Model Prediction for epsilon'/epsilon
• Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions
• Non-Perturbative Renormalization of Lattice Four-Fermion Operators without Power Subtractions
• Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators
• Standard Model Confronting New Results for epsilon'/epsilon
• Non-perturbative determination of quark masses in quenched lattice QCD with the Kogut-Susskind fermion action
• Calculation of Non-Leptonic Kaon Decay Amplitudes from $K\to \pi$ Matrix Elements in Quenched Domain-Wall QCD
• Renormalization Group Invariant Matrix Elements of DS = 2 and DI = 3/2 Four-Fermion Operators without Quark Masses
• Improved Determination of the Electroweak Penguin Contribution to epsilon'/epsilon in the Chiral Limit
• Finite-volume two-pion energies and scattering in the quenched approximation
• Remark on the Theoretical Uncertainty in B^0-\bar{B}^0 Mixing
• Determination of <2pi_{I=2}|Q_{7,8}|K0> in the Chiral Limit
• epsilon'/epsilon at the NLO: 10 Years Later
• I=2 Pion Scattering Phase Shift with Wilson Fermions
• Chiral Condensates, Q_7 and Q_8 Matrix Elements and Large-N_c QCD
• RI/MOM Renormalization Window and Goldstone Pole Contamination
• Pseudoscalar Vertex, Goldstone Boson and Quark Masses on the Lattice
• New QCD estimate of the kaon penguin matrix elements and epsilon'/epsilon
• Analysis of O(p^2) Corrections to <pi pi|Q_{7,8}|K>
• Lattice B-parameters for $\Delta S=2$ and $\Delta I=3/2$ Operators
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• Chiral corrections and lattice QCD results for fBs/fBd and (Delta ms/Delta md)
• Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
• K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order in the Chiral Expansion
• Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and on the lattice
• Remarks on the hadronic matrix elements relevant to the SUSY K-Kbar mixing amplitude
• K \to ππdecay amplitudes from the lattice
• Finite-Volume Two-Pion Amplitudes in the I=0 Channel
• Finite-Volume Partially-Quenched Two-Pion Amplitudes in the I=0 Channel
• $K^{+}\to {\pi }^{+}{\pi }^0$ Decay Amplitude with the Wilson Quark Action in Quenched Lattice QCD
• Delta S=2 and Delta I=3/2 Matrix Elements in Quenched QCD
• Perturbative renormalization of bilinear quark and gluon operators
• $K\to \pi \pi$ matrix elements beyond the leading-order chiral expansion
• Non-perturbative Renormalisation with Domain Wall Fermions
• Extraction of K-->pipi Matrix Elements with Wilson Fermions
• Kaon Weak Matrix Elements with Wilson Fermions

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• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Duality violations and spectral sum rules
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• K^0-\bar K^0 mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry
• Neutral B-meson mixing from unquenched lattice QCD with domain-wall light quarks and static b-quarks
• Standard model contribution to the electric dipole moment of the deuteron, ${}^3$H, and ${}^3$He nuclei
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Probing the chiral weak Hamiltonian at finite volumes
• On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum
• Progress in kaon physics on the lattice
• Confronting hadronic tau decays with non-leptonic kaon decays