Further remarks on ππ\pi\pi scattering dispersion relations

The naive use of higher order perturbation theory leads the left--hand cut integrals in $\pi\pi$ dispersion relations~\cite{hjy,Xiao01} divergent. This problem is discussed and solved. Also we point out that the Adler zero condition imposes three constraints on the dispersion relations. The $\sigma$ pole position is determined using the improved method, $M_\sigma= 483\pm 13 {\rm MeV}$,$\Gamma_\sigma= 705 \pm 50{\rm MeV}$. The scattering length parameter is found to be in excellent agreement with the experimental result.Comment: replace with revised version to appear in Chinese Physics Letters. Numerical calculation improved. $M_\sigma\simeq 483 {\rm MeV}$,$\Gamma_\sigma\simeq 705 {\rm MeV}

Pion and Kaon Electromagnetic Form Factors

We study the electromagnetic form factor of the pion and kaons at low-energies with the use of Chiral Perturbation Theory. The analysis is performed within the three flavour framework and at next-to-next-to-leading order. We explain carefully all the relevant consistency checks on the expressions, present full analytical results for the pion form factor and describe all the assumptions in the analysis. From the phenomenological point of view we make use of our expression and the available data to obtain the charge radius of the pion obtaining $_V^\pi=(0.452+-0.013) fm^2$, as well as the low-energy constant $L_9^r(m_\rho)= (5.93+-0.43)10^{-3}$. We also obtain experimental values for 3 combinations of order $p^6$ constants.Comment: 50 page

A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00

A sample of 400000 events from the decay K+->pi+pi-e+nu(e)(K(e4)) has been collected in experiment E865 at the Brookhaven AGS. The analysis of these data yields new measurements of the K(e4) branching ratio (4.11+-0.01+-0.11)*10**(-5)), the s-wave pi-pi scattering length a00=0.228+-0.012+-0.003, and the form factors F, G, and H of the hadronic current and their dependence on the invariant pi-pi mass

πK\pi K Scattering in Three Flavour ChPT

We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from $\pi\pi$ scattering, $\pi K$ scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.Comment: 23 page