Vector and Axial-Vector Spectral Functions and QCD

TL;DR

This paper analyzes tau hadronic spectral functions from ALEPH data to extract the strong coupling constant and non-perturbative effects, providing precise measurements relevant for QCD at different energy scales.

Contribution

It presents new spectral function measurements and applies QCD sum rules to determine alpha_s and non-perturbative contributions with high precision.

Findings

Measured alpha_s(M_tau) and evolved to alpha_s(M_Z) with precision

Provided detailed spectral functions for vector and axial-vector currents

Validated QCD sum rule predictions using tau decay data

Abstract

We present new results of the tau hadronic spectral function analysis using data accumulated by the ALEPH detector at LEP during the years 1991-94. In addition to the vector spectral functions, the axial-vector spectral functions and, separately, the tau --> 3pi nu as well as the tau --> pi 2pi0 nu spectral functions are determined from their respective unfolded, i.e., physical invariant mass spectra. The spectral functions are applied to QCD chiral sum rules in order to extract information about saturation at the tau mass scale. Using the the semi-leptonic tau decay rate for vector and axial-vector currents in addition to spectral moments, we obtain precise measurements of the strong coupling constant alpha_s(M_tau) and the contributing non-perturbative power terms. The evolution to the Z mass yields alpha_s(M_Z) = 0.1219 +/- 0.0019.