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Register a new usertau -> (3 pions) nu_tau decays in the Resonance Effective Theory
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D. Gomez Dumm
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tau -> (3 pions) nu_tau decays are analysed within the framework of the resonance effective theory of QCD. We work out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, in particular the local a_1(1260)-rho(770)-Goldstone interactions. The new coupling constants are constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values for the mass and on-shell width of the a_1(1260) resonance. In this way we are able to provide the structure functions that have been measured by OPAL and CLEO-II and we find an excellent agreement.
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We analyse tau -> (3 pions) nu_tau decays within the framework of the resonance chiral theory of QCD. We have worked out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, and the new coupling constants that arise have been constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values for the mass and on-shell width of the a_1(1260) resonance, and provide the tau -> (3 pions) nu_tau structure functions that have been measured by OPAL and CLEO-II finding an excellent agreement.
Tau decays into hadrons foresee the study of the hadronization of vector and axial-vector QCD currents, yielding relevant information on the dynamics of the resonances entering into the processes. We analyse tau -> (3 pion) nu_tau decays within the framework of the Resonance Chiral Theory, comparing this theoretical scheme with the experimental data, namely ALEPH spectral function and branching ratio. Hence we get values for the mass and on-shell width of the a_1(1260) resonance, and provide the structure functions that have been measured by OPAL and CLEO-II.
Recent experimental data for the differential decay distribution of the decay $tau^-to u_tau K_Spi^-$ by the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors $F_+^{Kpi}(s)$ and $F_0^{Kpi}(s)$. Both form factors are constructed such that they fulfil constraints posed by analyticity and unitarity. A good description of the experimental measurement is achieved by incorporating two vector resonances and working with a three-times subtracted dispersion relation in order to suppress higher-energy contributions. The resonance parameters of the charged $K^*(892)$ meson, defined as the pole of $F_+^{Kpi}(s)$ in the complex $s$-plane, can be extracted, with the result $M_{K^*}=892.0 pm 0.9 $MeV and $Gamma_{K^*}=46.2 pm 0.4 $MeV. Finally, employing the three-subtracted dispersion relation allows to determine the slope and curvature parameters $lambda_+^{}=(24.7pm 0.8)cdot 10^{-3}$ and $lambda_+^{}=(12.0pm 0.2)cdot 10^{-4}$ of the vector form factor $F_+^{Kpi}(s)$ directly from the data.
We compute branching ratios and invariant mass distributions of the tau decays into four pions. The hadronic matrix elements are obtained by starting from the structure of the hadronic current in chiral limit and then implementing low-lying resonances in the different channels. Reasonable agreement with experiment is obtained both for the $tau to u_{tau} + (4 pi ) $ decay rates and the $e^+e^- to (4 pi ) $ cross sections. Furthermore we supply an interface to use our matrix elements within the Tauola Monte-Carlo program.
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 vector 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 $b_{1}^{1/2},=( 0.258pm 0.009),m_pi^{-5}$.
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