Application of chiral perturbation theory to K-->2 pi decays

Consistent Treatment of Axions in the Weak Chiral Lagrangian

We present a consistent implementation of weak decays involving an axion or axionlike particle in the context of an effective chiral Lagrangian. We argue that previous treatments of such processes have used an incorrect representation of the flavor-changing quark currents in the chiral theory. As an application, we derive model-independent results for the decays K^{-}→π^{-}a and π^{-}→e^{-}ν[over ¯]_{e}a at leading order in the chiral expansion and for arbitrary axion couplings and mass. In particular, we find that the K^{-}→π^{-}a branching ratio is almost 40 times larger than previously estimated.

The large N c limit of QCD on the lattice

We review recent progress in the study of the large N c limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of O ( N c - 1 ) corrections for values of N c ≳ 3 . Some concrete examples of the topics we include are tests of large- N c factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the Δ I = 1 / 2 rule in kaon decays.

Standard Model Prediction for Direct CP Violation in K→ππ Decay

We report the first lattice QCD calculation of the complex kaon decay amplitude A_{0} with physical kinematics, using a 32³×64 lattice volume and a single lattice spacing a, with 1/a=1.3784(68) GeV. We find Re(A_{0})=4.66(1.00)(1.26)×10(-7) GeV and Im(A_{0})=-1.90(1.23)(1.08)×10(-11) GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A_{0})=3.3201(18)×10(-7) GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ^{'}/ϵ)=1.38(5.15)(4.59)×10^{-4}, which is 2.1σ below the experimental value 16.6(2.3)×10(-4). The real part of A_{0} is CP conserving and serves as a test of our method while the result for Re(ϵ^{'}/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.

K-->pipi amplitudes from lattice QCD with a light charm quark

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K-->pipi amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.