The ΔI=1/2\Delta I=1/2 Rule for Kaons

We report on recent advances at understanding the $\Delta I= 1/2$ rule for kaons. We get reasonable matching between short-- and long--distances for scales between between 0.6 and 1.0 GeV and reproduce the $\Delta I=1/2$ rule huge enhancement in the chiral limit. A detailed analysis of the different contributions to the relevant octet and 27-plet couplings is done. For the $B_6^{(1/2)}(\mu) \equiv / [ {\Large|}_{N_c}]$ parameter, we get in the chiral limit $B_6^{(1/2)}(\mu) = 2.2 \pm 0.5$ for scales $\mu \in [0.6, 1.0]$ GeV.Comment: 9 LaTeX pages, 2 ps figures included. Invited talk at QCD '99 High Energy Euro Conference on Quantum Chromodynamics, July 1999, Montpellier, France. Corrected eq. (16) and misprint

Progress in K→ππK\to\pi\pi Decays

Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance evolution into account correctly. In the second part I show the results we obtain for the $\Delta I=1/2$ rule in the chiral limit.Comment: 4 pages, uses espcrc1.sty. Talk given at PANIC99, Uppsala 10-16 june 199

A new global fit of the LirL^r_i at next-to-next-to-leading order in Chiral Perturbation Theory

A new fit is done to obtain numerical values for the order $p^4$ low-energy-constants $L_i^r$ in Chiral Perturbation Theory. This includes both new data and new calculated observables. We take into account masses, decay constants, $K_{\ell4}$, $\pi\pi$ and $\pi K$ scattering lengths and slopes and the slope of the pion scalar formfactor. We compare in detail where the changes w.r.t. to the 10 year old "fit 10" come from. We discuss several scenarios for estimating the order $p^6$ constants $C_i^r$ and search for possible values of them that provide a good convergence for the ChPT series. We present two such sets. One big change is that the fits do not have the expected behaviour in the limit of large $N_c$ as well as before.Comment: 41 pages, p^4 values of the l_i added, numerical values for f_+(0) in Kl3 added, a comparison with the LECS from Ecker et al., Phys. Lett. B692 (2010) 184 [arXiv:1004.3422 [hep-ph]] adde

A Parametrization for K+→π+π−e+νK^+\to \pi^+\pi^- e^+\nu

We discuss various models and Chiral Perturbation Theory results for the $K_{l4}$ form factors $F$ and $G$. We check in how much a simple parametrization with a few parameters can be used to extract information from experiment.Comment: 19 pages, 14 figure

Chiral Meson Physics at Two Loops

An overview of Chiral Perturbation Theory calculations in the mesonic sector at the two Loop level is given. Discussed in some detail are the partially quenched case relevant for lattice QCD, the general fitting procedures and $\pi\pi$,$\pi K$ scattering as well as the determination of $V_{us}$ and $K_{\ell3}$ decays.Comment: 7 pages, Invited plenary talk presented at the 19th European Few-Body conference, Groningen, The Netherlands, August 23-27, 200

Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon g−2g-2

We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was mistaken.Comment: 2 page

Chiral extrapolation and determination of low-energy constants from lattice data

We propose analytic approximations of chiral SU(3) amplitudes for the extrapolation of lattice data to the physical meson masses. The method allows the determination of NNLO low-energy constants in a controllable fashion. We test the approach with recent lattice data for the ratio F_K/F_pi of meson decay constants.Comment: 10 pages, 1 figure, matches version published in PLB: title enlarged, comments added, results unchange

The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched χ\chiPT

This paper presents a first study of the pseudoscalar meson masses to two loops, or NNLO, within the supersymmetric formulation of partially quenched chiral perturbation theory (PQ$\chi$PT). The expression for the pseudoscalar meson mass in the case of three valence and three sea quarks with equal masses, but different from each other, is given to ${\cal O}(p^6)$, along with a numerical analysis.Comment: 4 pages, one reference added, small changes in discussio

Semileptonic π\pi and KK Decays and the Chiral Anomaly at One-loop

We calculate the $O(p^6)$ corrections to the anomalous form factors appearing in $\pi^+$, $K^+ \to e^+ \nu \gamma,\ \mu^+\nu\gamma$ and $K_{l4}$ decays in Chiral Perturbation Theory. The relevant dimension $6$ terms of the lagrangian are evaluated assuming their saturation by the vector meson contribution.Comment: 10 pages of LaTeX (+3 figures available on request

Chiral logarithms to five loops

We investigate two specific Green functions in the framework of chiral perturbation theory. We show that, using analyticity and unitarity, their leading logarithmic singularities can be evaluated in the chiral limit to any desired order in the chiral expansion, with a modest calculational cost. The claim is illustrated with an evaluation of the leading logarithm for the scalar two-point function to five-loop order.Comment: 13 pages, 5 figure