ChPT Progress on Non-Leptonic and Radiative Kaon Decays

I discuss recent developments on non-leptonic and radiative kaon decays mainly related to direct CP-violation within the combined ChPT and 1/N_c expansion approaches. In particular, I review the status of K -> pi pi, epsilon_K', direct CP-violating K+ -> 3 pi Dalitz plot slope g and decay rate asymmetries, and the Standard Model prediction for Br(K_L -> pi0 e+ e-).Comment: 14 pages, 1 figure. Invited talk at KAON 07 International Conference, May 21-25 2007, Frascati, Italy. v2: Discussion in Section 3 somewhat enlarged and added references. Matches published verio

Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities

The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in $1/N_c$. We organize the calculation in an $1/N_c$-expansion and separate long- and short-distance physics contributions by introducing an Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full Chiral Perturbation Theory calculation to order $e^2$ $p^2$ for the masses and $p^6$ for the polarizabilities. For the electromagnetic corrections to the masses, we confirm a large violation of Dashen's theorem getting a more precise value for this violation. We make comparison with earlier related work. Some phenomenological consequences are discussed too.Comment: LaTeX, 5 figures, uses epsf, 39 pages, partially rewritten, more information about $\mu$ dependence include

Scheme Dependence of Weak Matrix Elements in the 1/Nc1/N_c Expansion

We show how the scheme- and scale-dependence of the short-distance operator product expansion with four-quark operators can be correctly accounted for in the framework of the $1/N_c$-expansion once the hadronization of two-quark currents has been fixed. We show formulas explicitly in the case of the $B_K$-parameter. We then use them with our earlier estimates of the long-distance effects. We compare Chiral Perturbation Theory at Leading- and Next-to-Leading-Order with the ENJL model results in the chiral limit. Good matching between the long- and short-distance regimes is obtained and our final value for the physical scheme independent $\hat B_K$ is $0.77\pm0.05\pm0.05$.Comment: 20 pages, use JHEP.cls and axodraw.sty; small error detected, numerical results changed with about quoted erro

Strange Quark Mass Determination from Cabibbo-Suppressed Tau Decays

We present a general analysis of SU(3) breaking effects in the semi-inclusive tau hadronic width. The recent ALEPH measurements of the inclusive Cabibbo--suppressed decay width of the tau and several moments of its invariant mass distribution are used to determine the value of the strange quark mass. We obtain, in the MS scheme, m_s(M_\tau^2) = (119\pm 24) MeV to O(\alpha_s^3), which corresponds to m_s (1 GeV^2) = (164 \pm 33) MeV, m_s(4 GeV^2) = (114\pm 23) MeV .Comment: 28 LaTeX pages, no figure

Status of the Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment

We review the present status of the hadronic light-by-light contribution to muon g-2 and critically compare recent calculations.Comment: 10 pages, 3 figures. Invited talk presented by JP at "Final Euridice Meeting", August 24-28 2006, Kazimierz, Polan