The chiral logs of the K -> pi pi amplitude

Abstract

I calculate the leading logarithmic contributions up to two-loop order of the octet part of the K -> pi pi amplitude. This sector of the weak chiral Lagrangian is believed to be the main source of the enhancement of the I=0 relative to the I=2 K -> pi pi amplitude, the so-called Delta I = 1/2 rule. I discuss the procedure of chiral extrapolations of lattice data specific to K -> pi pi decays and study the implication of the present calculation on these numerically. The latter reinforces the fact that one has to expect a large enhancement of the I=0 part of the amplitude due to re-scattering effects between the three mesons.

arXiv comment20 pages, 4 figures, uses axodraw

References in corpus (14)

• Chiral perturbation theory
• Elastic $\pi \pi$ scattering to two loops
• Renormalization of chiral perturbation theory to order p^6
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• 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
• Double Chiral Logs
• 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
• Isospin breaking corrections to low-energy pi-K scattering
• The leading two loop counterterm in the nonleptonic weak sector of CHPT

Cited by in corpus (5)

• Kaon Decays in the Standard Model
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• The nucleon axial-vector coupling beyond one loop
• Leading Chiral Logarithms of $K_S\to \gamma \gamma$ and $K_S\to \gamma l^{+}{l}^{-}$ at two Loops
• Chiral Logarithms in $\Delta S=1$ Kaon Decay Amplitudes in General Effective Flavor Theories