Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $alpha_s$ from $tau$ decay. A physically motivated ansatz for duality violatio
ns in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedure which are absent from the currently post
Dispersive representations of the Kpi vector and scalar form factors are used to fit the spectrum of tau ---> K pi nu_tau obtained by the Belle collaboration incorporating constraints from results for K_l3 decays. The slope and curvature of the vecto
r form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find $lambda_+=(25.49 pm 0.31) times 10^{-3}$ and $lambda_+= (12.22 pm 0.14) times 10^{-4}$. From the pole position on the second Riemann sheet the mass and width of the $K^*(892)^{pm}$ are found to be $m_{K^*(892)^pm}=892.0pm 0.5$~MeV and $Gamma_{K^*(892)^pm}=46.5pm 1.1$~MeV. The phase-space integrals needed for K_l3 decays are calculated as well. Furthermore, the Kpi isospin-1/2 P-wave threshold parameters are derived from the phase of the vector form factor. For the scattering length and the effective range we find respectively $a_{1}^{1/2},= ( 0.166pm 0.004),m_pi^{-3}$ and $b_{1}^{1/2},=( 0.258pm 0.009),m_pi^{-5}$.
We present a model for the decay D+ --> K- pi+ pi+. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the Kpi s
calar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the S wave thus obtained agree nicely with experiment up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the S and P waves of -65 degrees, the Dalitz plot of the D+ --> K- pi+ pi+ decay, the Kpi invariant mass spectra and the total branching ratio due to S-wave interactions are well reproduced.
Scattering and production amplitudes involving scalar resonances are known, according to Watsons theorem, to share the same phase $delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination of $delta(s)$
with another phase $omega(s)$, which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual $K$-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.
We describe the $pipi$ $S$-wave in $D^+ topi^+ pi^- pi^+$ decays using a unitary model for the $pipi$ Final State Interactions (FSI). The three body decay is treated as a quasi two-body process where, at the weak vertex, the D meson decays into a res
onance and a pion. The weak part of the decay amplitude is evaluated using the effective weak Hamiltonian within the factorization approximation.
