Qcd phenomenology with tau and charm decays
- Autores: Diogo Rodrigues Boito
- Directores de la Tesis: Rafel Escribano Carrascosa (dir. tes.), Matthias Benjamin Passer (codir. tes.)
- Lectura: En la Universitat Autònoma de Barcelona ( España ) en 2011
- Idioma: español
- Tribunal Calificador de la Tesis: Antonio Miguel Pineda Ruiz (presid.), Jorge Portolés Ibáñez (secret.), Veronique Bernard (voc.)
- Materias:
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- Resumen
In the present work we use data for decays of the $\tau$ lepton and of the $D$ meson to study aspects of the strong interactions.
First, the Belle data set for the decay $\tau\to K_S \pi^- \nu_\tau$ was fitted with a thrice subtracted dispersive description of the $K\pi$ vector form factor, $F_+^{K\pi}$. The model incorporates constraints from unitarity and analyticity. The phase of the form factor is obtained from the fit to the data. From this fit, we were able to determine the slope, $\lambda'_+,$ and curvature, $\lambda_+''$, of $F_+^{K\pi}$. The resonance parameters of the charged $K^*(892)$ meson, defined as the pole of $F_+^{K\pi}$ in the complex $s$-plane, were extracted. The analysis was improved by the inclusion of experimental constraints from $K_{l3}$ decays. We then found $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+''= (12.22 \pm 0.14) \times 10^{-4}$.
From the pole position of the $K^*(892)^{\pm}$ we obtained: $m_{K^*(892)^\pm}=892.0\pm 0.5$~MeV and $\Gamma_{K^*(892)^\pm}=46.5\pm 1.1$~MeV. The phase-space integrals needed for $K_{l_3}$ decays are calculated as well. Furthermore, the $K\pi$ isospin-$\nicefrac{1}{2}$ $P$-wave threshold parameters are derived from the phase of the vector form factor.
The model for $F_+^{K\pi}$ was subsequently used to describe the final state interactions in $\DKpp$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approximation. The model has only three free parameters; two of them were fixed from experimental branching ratios.
We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. The Dalitz plot, the $K\pi$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.
Finally, we analyse the {\sc opal} data for inclusive Cabibbo-allowed hadronic $\tau$ decays in order to produce a novel determination of $\alpha_s(m_\tau^2)$. In our theoretical description we incorporate the so-called Duality Violations, that account for the lack of convergence of the Operator Product Expansion ({\sc ope}) close to the real axis. Coherence between the truncation of the {\sc ope} and the weight function used in the sum rule is achieved. We found $\alpha_s^{\rm FO}(m_\tau^2) = 0.313 \pm 0.024$ and $\alpha_s^{\rm CI}(m_\tau^2) = 0.325 \pm 0.033$ for the Fixed Order and Contour Improved prescriptions, respectively.
