Approximating chiral SU(3) amplitudes

We construct large-N_c motivated approximate chiral SU(3) amplitudes of next-to-next-to-leading order. The amplitudes are independent of the renormalization scale. Fitting lattice data with those amplitudes allows for the extraction of chiral coupling constants with the correct scale dependence. The differences between approximate and full amplitudes are required to be at most of the order of N^3LO contributions numerically. Applying the approximate expressions to recent lattice data for meson decay constants, we determine several chiral couplings with good precision. In particular, we obtain a value for F_0, the meson decay constant in the chiral SU(3) limit, that is more precise than all presently available determinations.Comment: 19 pages, 4 figures, improved presentation, results unchanged, version to appear in EPJ

Pad\'e Approximants and Resonance Poles

Based on the mathematically well defined Pad\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the Second Riemann Sheet of an amplitude to search for the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation.Comment: 12 pages, 17 figure

The eta transition form factor from space- and time-like experimental data

The $\eta$ transition form factor is analysed for the first time in both space- and time-like regions at low and intermediate energies in a model-independent approach through the use of rational approximants. The $\eta\rightarrow e^+e^-\gamma$ experimental data provided by the A2 Collaboration in the very low energy region of the dilelectron invariant mass distribution allows for the extraction of the most precise up-to-date slope and curvature parameters of the form factors as well as their values at zero and infinity. The impact of these new results on the mixing parameters of the $\eta$-$\eta^\prime$ system, together with the role played by renormalisation dependent effects, and on the determination of the $VP\gamma$ couplings from $V\to P\gamma$ and $P\to V\gamma$ radiative decays are also discussed.Comment: 16 pages, 17 figures; v2: additional comments, references added; mathces published version in EPJ

A combined study of hadronic D+→K−π+π+D^+\to K^-\pi^+\pi^+ and Ds+→K+K+π−D_s^+\to K^+K^+\pi^- decays by means of the analysis of semileptonic D+→K−π+ℓ+νℓD^+\to K^-\pi^+ \ell^+\nu_\ell decays

We perform a combined study of the two hadronic decays $D^+\to K^-\pi^+\pi^+$ and $D_s^+\to K^+K^+\pi^-$ using a detailed analysis of the semileptonic decays $D^+\to K^-\pi^+ \ell^+\nu_\ell$ ($\ell=e, \mu$) thanks to the high-statistics dataset provided by the BESIII Collaboration. We propose simple and suitable amplitude parametrizations of the studied reactions that shall be of interest to experimentalists for upcoming analyses. These new parametrizations are based on the na\"ive factorization hypothesis and the description of the resulting matrix elements in terms of well-known hadronic form factors, with special emphasis on the $K\pi$ scalar and vector cases. Such form factors account for two-body final state interactions which fulfill analyticity, unitarity and chiral symmetry constraints. As a result of our study, we find that the $P$-wave contribution fits nicely within the na\"ive-factorization approach, whereas the $S$-wave contribution requires complex Wilson coefficients that hint for possibly genuine three-body non-factorizable effects. Our hypothesis is further supported by the examination of $D_s^+\to K^+K^+\pi^-$ decays, where we achieve a description in overall good agreement with data.Comment: 23 pages, 8 figures; version accepted for publication in Phys.Rev.