Dispersion relations and soft pion theorems for K -> pi pi

Abstract

We propose a new method to obtain the K -> pi pi amplitude from K -> pi which allows one to fully account for the effects of final state interactions. The method is based on a set of dispersion relations for the K -> pi pi amplitude in which the weak Hamiltonian carries momentum. The soft pion theorem, which relates this amplitude to the K -> pi amplitude, can be used to determine one of the two subtraction constants - the second constant is at present known only to leading order in chiral perturbation theory. We solve the dispersion relations numerically and express the result in terms of the unknown higher order corrections to this subtraction constant.

Latex, 10 pages, 1 figure. Typo in eqs. (13,14) corrected, some rephrasing in the introduction

References in corpus (14)

• S-wave Kpi scattering in chiral perturbation theory with resonances
• The pi pi S-wave scattering lengths
• Strong Enhancement of ${\epsilon }^{\prime }/\epsilon$ Through Final State Interactions
• ${\epsilon }^{\prime }/\epsilon$ at $O(p^4)$ in the Chiral Expansion
• New lattice approaches to the $\Delta I=1/2$ rule
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• The $\Delta I=1/2$ Rule in the Chiral Limit
• epsilon'/epsilon in the Chiral Limit
• Final State Interactions in Kaon Decays
• Obtaining K to pi pi from Off-Shell K to pi Amplitudes
• Analysis of ε'/εin the 1/N_c Expansion
• Comparison of Pion-Kaon Scattering in SU(3) Chiral Perturbation Theory and Dispersion Relations
• New Analysis of the Delta I = 1/2 Rule in Kaon Decays and the B_K Parameter
• A note on the dispersive treatment of K -> pi pi with the kaon off-shell

Cited by in corpus (21)

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• Patterns of Flavour Violation in Models with Vector-Like Quarks
• Rare Kaon Decays on the Lattice
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• Kaon CP violation and neutron EDM in the minimal left-right symmetric model
• Final State Interactions in $K\to \pi \pi$ Decays: $\Delta I=1/2$ Rule vs. ${\epsilon }^{\prime }/\epsilon$
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• On lattice extraction of K --> pi pi amplitudes to O(p^4) in Chiral Perturbation Theory
• Lattice extraction of $K\to \pi \pi$ amplitudes to NLO in partially quenched and in full chiral perturbation theory
• $K\to \pi \pi$ Decays in SU(2) Chiral Perturbation Theory
• A note on the dispersive treatment of K -> pi pi with the kaon off-shell
• Dispersive treatment of $K_S\to \gamma \gamma$ and $K_S\to \gamma {\ell }^{+}{\ell }^{-}$
• The chiral logs of the K -> pi pi amplitude
• Lattice Matrix Elements and CP Violation in B and K Physics: Status and Outlook
• Chiral perturbation theory, dispersion relations and final state interactions in K -> pi pi
• Status of Chiral-Scale Perturbation Theory
• Updated Standard Model Prediction for ${\epsilon }^{\prime }/\epsilon$
• The Revival of Kaon Flavour Physics
• Next to Leading Order Chiral Perturbation theory of $K\pi \to \pi$ and $K\to \pi \pi$ amplitudes