On lattice extraction of K --> pi pi amplitudes to O(p^4) in Chiral Perturbation Theory

Abstract

We show that lattice calculation of K --> pi pi and $epe$ amplitudes for (8,1) and (27,1) operators to O(p^4) in chiral perturbation theory is feasible when one uses K --> pi pi computations at the two unphysical kinematics allowed by the Maiani-Testa theorem, along with the usual (computable) two and three point functions, namely K --> 0, K --> pi (with momentum) and K - bar{K}. Explicit expressions for the finite logarithms emerging from our O(p^4) analysis to the above amplitudes are also given.

20 pages, 1 figure. This is the final published version, where some minor corrections have been made

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Cited by in corpus (22)

• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Multichannel one-to-two transition amplitudes in a finite volume
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Lattice QCD with two dynamical flavors of domain wall quarks
• Twisted mass QCD and lattice approaches to the $\Delta I=1/2$ rule
• Correlators of left charges and weak operators in finite volume chiral perturbation theory
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
• Lattice extraction of $K\to \pi \pi$ amplitudes to NLO in partially quenched and in full chiral perturbation theory
• Finite-Volume Partially-Quenched Two-Pion Amplitudes in the I=0 Channel
• On the effects of (partial) quenching on penguin contributions to K-> pi pi
• Probing the chiral weak Hamiltonian at finite volumes
• The chiral logs of the K -> pi pi amplitude
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory
• The leading two loop counterterm in the nonleptonic weak sector of CHPT
• On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum
• Progress in kaon physics on the lattice
• Possible lattice approach to B to D pi (K) matrix elements
• A note on the power divergence in lattice calculations of $\Delta I=1/2$ $K\to \pi \pi$ amplitudes at $M_K=M_{\pi }$
• $K^{+}\to {\pi }^{+}{\pi }^0$ decays at next-to-leading order in the chiral expansion on finite volumes
• Next to Leading Order Chiral Perturbation theory of $K\pi \to \pi$ and $K\to \pi \pi$ amplitudes