Next to Leading Order Chiral Perturbation theory of $K\pi \to \pi$ and $K\to \pi \pi$ amplitudes

Abstract

It is shown that the low energy coefficients of the next-to-leading order (NLO) chiral perturbation theory needed to determine $\Delta I=1/2$, $K\to \pi \pi$ decay amplitudes can be fixed by calculating $K\pi \to \pi$ amplitudes on lattice. Unlike using NLO $K\to \pi \pi$ amplitudes proposed by Laiho and Soni, simulating $K\pi \to \pi$ transitions on lattice does not require evaluations of s-channel disconnected diagrams which have been an obstacle in practice.

arXiv comment25 pages, 2 figures

References in corpus (21)

• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Weak transition matrix elements from finite-volume correlation functions
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum
• $K\to \pi \pi$ Decays in a Finite Volume
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• Fitting Correlated Data
• Calculation of Non-Leptonic Kaon Decay Amplitudes from $K\to \pi$ Matrix Elements in Quenched Domain-Wall QCD
• Obtaining K to pi pi from Off-Shell K to pi Amplitudes
• Analysis of O(p^2) Corrections to <pi pi|Q_{7,8}|K>
• SU(2) chiral perturbation theory for Kl3 decay amplitudes
• K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order in the Chiral Expansion
• On the Determination of Nonleptonic Kaon Decays from $K\to \pi$ Matrix Elements
• On lattice extraction of K --> pi pi amplitudes to O(p^4) in Chiral Perturbation Theory
• Dispersion relations and soft pion theorems for K -> pi pi
• K \to ππdecay amplitudes from the lattice
• Finite Volume Effects in Weak Hadronic Decays
• A note on the power divergence in lattice calculations of $\Delta I=1/2$ $K\to \pi \pi$ amplitudes at $M_K=M_{\pi }$
• Using Lattice QCD and ChPT to obtain non-leptonic K-decay amplitudes