Resummation of threshold, low- and high-energy expansions for heavy-quark correlators

por David Greynat (Universidad de Zaragoza)

jueves 12 may. 2011 12:00 → 13:00 Europe/Madrid

Sala Seminarios IFIC (Edf. Institutos de Investigación)

With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of a heavy-quark correlator around $q^2=0$ (low-energy), $q^2 = 4 m^2$ (threshold, where $m$ is the quark mass) and $q^2\rightarrow-\infty$ (high-energy) 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 $q^2$.