Joaquim Prades

The Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment: Where Do We Stand?

We review the status of the hadronic light-by-light contribution to the muon anomalous magnetic moment and critically compare recent calculations. We also study in detail which momentum regions the π0 exchange main contribution originates. We also argue that

Theoretical progress on the V_us determination from tau decays

a_mu^{rm lighthbox{rm-}byhbox{rm-}light}=(11pm4)times 10^{-10}

|V(us)| and m(s) from hadronic tau decays

encompasses the present understanding of this contribution and comment on some directions to improve on that.

Determination of m_s and |V_us| from hadronic tau decays

A very precise determination of V_us can be obtained from the semi-inclusive hadronic decay width of the tau lepton into final states with strangeness. The ratio of the Cabibbo-suppressed and Cabibbo-allowed tau decay widths directly measures (V_us/V_ud)^2, up to very small SU(3)-breaking corrections which can be theoretically estimated with the needed accuracy. Together with previous LEP and CLEO data, the recent measurements by Babar and Belle of some Cabibbo-suppressed tau decays imply V_us= 0.2165 +- 0.0026_exp +- 0.0005_th, which is already competitive with the standard extraction from K_l3 decays. The uncertainty is largely dominated by experimental errors and should be easily reduced with the high statistics of the B factories, providing the most accurate determination of this parameter. A 1% experimental precision on the Cabibbo-suppressed tau decay width would translate into a 0.6% uncertainty on V_us.

|Vus| from Strange Hadronic Tau Data 1

Recent experimental results on hadronic tau decays into strange particles by the OPAL Collaboration are employed to determine V(us) and m(s) from moments of the invariant mass distribution. Our results are V(us)=0.2208+/-0.0034 and m(s)(2 GeV)=81+/-22 MeV. The error on V(us) is dominated by experiment and should be improvable in the future. Nevertheless, already now our result is competitive with the standard extraction of V(us) from K(e3) decays, and it is compatible with unitarity.

|Vus| and ms from hadronic tau decays

The mass of the strange quark is determined from SU(3)-breaking effects in the τ hadronic width. Compared to previous analyses, the contributions from scalar and pseudoscalar spectral functions, which suffer from large perturbative corrections, are replaced by phenomenological parametrisations. This leads to a sizeable reduction of the uncertainties in the strange mass from τ decays. Nevertheless, the resulting ms value is still rather sensitive to the moment of the invariant mass distribution which is used for the determination, as well as the size of the quark-mixing matrix element |Vus|. Imposing the unitarity fit for the CKM matrix, we obtain ms(2 GeV) = 117 ± 17 MeV, whereas for the present Particle Data Group average for |Vus|, we find ms(2 GeV) = 103 ± 17 MeV. On the other hand, using an average of ms from other sources as an input, we are able to calculate the quark-mixing matrix element |Vus|, and we demonstrate that if the present measurement of the hadronic decay of the τ into strange particles is improved by a factor of two, the determination of |Vus| is more precise than the current world average.

Measuring the a0–a2 pion scattering lengths through K→3π decays

We report on recent work to determine the CKM matrix element |Vus| using strange hadronicdecay data. We use the recent OPAL update of the strange spectral function, while on the theory side we update the dimension-two perturbative contribution including the recently calculated � 3 terms. Our result |Vus| = 0.2220±0.0033 is already competitive with the standard extraction from Ke3 decays and other new proposals to determine |Vus|. The actual uncertainty on |Vus| fromdata is dominated largely by experiment and will eventually be much reduced by B-factories and future �-charm factory data, providing one of the most accurate determinations of this Standard Model parameter.

ChPT Progress on Non-Leptonic and Radiative Kaon Decays

Recent experimental results on hadronic tau decays into strange particles by the OPAL Collaboration are employed to determine V(us) and m(s) from moments of the invariant mass distribution. Our results are V(us)=0.2208+/-0.0034 and m(s)(2 GeV)=81+/-22 MeV. The error on V(us) is dominated by experiment and should be improvable in the future. Nevertheless, already now our result is competitive with the standard extraction of V(us) from K(e3) decays, and it is compatible with unitarity.

Meson-Baryon Effective Chiral Lagrangian at O(q 3 ) Revisited

We discuss the recent Cabibbos proposal to measure the ππ scattering lengths combination a 0 – a 2 from the cusp effect in the π 0 π 0 energy spectrum at threshold for K + → π 0 π 0 π + and K L → π 0 π 0 π 0 . We estimate the theoretical uncertainty of the a 0 – a 2 determination at NLO in our approach and obtain that it is not smaller than 5 % for K + → π 0 π 0 π + . One gets similar theoretical uncertainties if the neutral K L → π 0 π 0 π 0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lengths.