PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

Diogo Boito

doi:10.1142/s2010194514604426

Abstract

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of αs. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

Highlights

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed
Recently,[9, 10] we investigated the convergence of the perturbative series after integration in the complex plane employing two different renormalization group improvement (RGI) prescriptions and discussed how the convergence properties of the series depend on the specific moment used
Fixed Order Perturbation Theory (FOPT) treats the running of αs and the cn,[1] coefficients on an equal footing and only includes at a Perturbative expansion of τ hadronic spectral function moments given order n terms up to order αs(√s0)n

Summary

PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework. Different moments of the spectral functions are used; their theoretical counterpart is evaluated through finite energy sum-rules, as contour integrals in the complex-energy plane. Recently,[9, 10] we investigated the convergence of the perturbative series after integration in the complex plane employing two different renormalization group improvement (RGI) prescriptions and discussed how the convergence properties of the series depend on the specific moment used. — FOPT is to be preferred for the inclusive τ hadronic width Later we extended this analysis[9, 10] in order to ascertain how the behavior of the perturbative series depends on the moment wi(x) as well as on the value of s0

Perturbative expansion of τ hadronic spectral function moments

Conclusions