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Padé Approximants and perturbative series of QCD in τ decays

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Fabio Henrique Oliani
Total Authors: 1
Document type: Master's Dissertation
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos
Defense date:
Examining board members:
Diogo Rodrigues Boito; Ricardo D'Elia Matheus; Fernando Silveira Navarra
Advisor: Diogo Rodrigues Boito

Perturbative QCD corrections to hadronic tau decays are obtained from the expansion of the Adler function. This series is believed to be asymptotic and is better understood when its Borel transform is considered. We use the mathematical method of Padé approximants to reconstruct the Borel transformed series and extract information about higher order corrections as well as renormalon poles associated with the divergence of the series. First, the method is tested in the large-β0 limit of QCD, where the perturbative series is known to all orders. In this limit, we observe that the renormalization scheme variation of the strong coupling, αs, can be useful in constructing approximants that converge faster. We apply the method in complete QCD to obtain predictions about the main characteristics of the series. In QCD, the analytical structure of the Borel transform of the Adler function makes the approximations with Padés less efficient, which is reflected in larger uncertainties. We obtain the result 570 ± 285 for the coefficient of the term α5s. The fixed sign nature of the series predicted by the PAs indicates that there is an indication that infrared singularities contribute more to the coefficients of the series in intermediate orders. In addition, although the results for the Borel sum of the function δ(0) are compatible with the two most frequently used prescriptions for setting the renormalization scale in tau decays, Padé approximants show a slight preference for fixed order prescription (or FOPT). (AU)

FAPESP's process: 16/01341-4 - Padé approximants and the QCD perturbative series for tau decays into hadrons
Grantee:Fabio Henrique Oliani
Support type: Scholarships in Brazil - Master