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# Rencontres de Physique des Particules

14-16 mai 2012
Université Montpellier 2
Fuseau horaire Europe/Paris

## Reconstruction of non-analytic functions

16 mai 2012 à 15:35
25m
Salle des actes, bât. 7 (UM2)

### Orateur

Dr David GREYNAT (Fisica Teorica - Uni. de Zaragoza)

### Description

With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of any kind of non-analytic functions around 0, 1 and $infinity$ in a systematic way. We exemplify the method for the perturbative vector, axial scalar and pseudo-scalar correlator at $\mathcal{O}(\alpha_s^{3})$. We show that the coefficients, $\Omega(n)$, of the Taylor expansion of the vacuum polarization function in terms of the conformal variable $\omega$ admit, for large $n$, an expansion in powers of $1/n$ (up to logarithms of $n$) that we can calculate exactly. This large-$n$ expansion has a sign-alternating component given by the logarithms of the OPE, and a fixed-sign component given by the logarithms of the threshold expansion in the external momentum $q^2$.

### Auteur principal

Dr David GREYNAT (Fisica Teorica - Uni. de Zaragoza)